TWI703560B - 用於經調變重疊變換之分析/合成視窗化函數技術 - Google Patents
用於經調變重疊變換之分析/合成視窗化函數技術 Download PDFInfo
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Abstract
提供用於使用一分析開窗函數利用一分析/合成開窗函數執行經修改餘弦變換(MDCT)之方法及設備，該分析開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分。
Description
本發明係有關於用於經調變重疊變換之分析/合成視窗化函數技術。
發明背景
已開發重疊變換用於若干音訊寫碼應用。通常對音訊信號之較大資料集(例如，兩個連續訊框)之連續區塊執行此等變換。後續區塊可能重疊。因此，一個區塊之最末部分與後續區塊之第一部分重合。可使用視窗化函數。
已開發出體現經調變重疊變換之不對稱經修改離散餘弦變換(MDCT)窗、不對稱經修改離散正弦變換(MDST)、時間-頻率變換。
在過去幾年已開發出不對稱經修改離散餘弦變換(MDCT)窗、不對稱經修改離散正弦變換(MDST)窗及其他類型之窗，其相較於對稱形狀提供改良之頻率回應，對於諸如音訊寫碼應用之低延遲信號應用尤其如此。
第一代窗形狀僅集中於頻率回應之設計，例如，G.718或MPEG-4 AAC-ELD窗。最新的發展亦考慮到窗之時間形狀，其負責量化誤差之時間調變，例如如在3GPP EVS編解碼器中使用之ALDO窗。
然而，此處呈現之設計方法伴有以下問題：窗形狀展示非連續微分，其導致次佳之頻率回應。此文件中描述之發明呈現用以克服此問題之解決方案。
發明概要
根據一態樣，提供一種用於對包含複數個訊框之一資訊信號進行編碼之設備，該設備包含：
一經調變重疊變換工具，其用於將該資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該經調變重疊變換工具經組配以使用一分析開窗函數執行一經調變重疊變換分析，該分析開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分，及
一位元串流寫入器，其經組配以基於該資訊信號或其一經處理版本之該FD表示來準備一位元串流，
其中該分析開窗函數經界定以便為不對稱的，
其中該分析開窗函數經界定以便在該曲折部分中
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，
其中該分析開窗函數經界定以使得絕對最大值處於該第一區間與該第三區間中之一者中，
其中該線性函數為具有常數值1之一常數函數。
該分析開窗函數可經界定以使得該分析開窗函數之該最大值在同一時刻比該線性函數之該值大出小於25%。
用於對一資訊信號進行編碼之該設備可包含複數個訊框，該設備可包含：
一經調變重疊變換工具，其用於將該資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該經調變重疊變換工具經組配以使用一分析開窗函數執行一經調變重疊變換分析，該分析開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分；以及
一位元串流寫入器，其經組配以基於該資訊信號或其一經處理版本之該FD表示來準備一位元串流，
其中該分析開窗函數經界定以便為不對稱的，
其中該分析開窗函數經界定以使得該分析開窗函數之該最大值在同一時刻比該線性函數之值大出小於25%，
其中該線性函數為一常數函數。
用於對一資訊信號進行編碼之該設備可包含複數個訊框，該設備可包含：
一經調變重疊變換工具，其用於將該資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該經調變重疊變換工具經組配以使用一分析開窗函數執行一經調變重疊變換分析，該分析開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分；以及
一位元串流寫入器，其經組配以基於該資訊信號或其一經處理版本之該FD表示來準備一位元串流。
該設備可包含該經調變重疊變換工具，其經組配以：
用該分析開窗函數之值按比例調整時間輸入緩衝區及/或餘弦或正弦值。
該設備可包含該經調變重疊變換工具，該經調變重疊變換工具經組配以使用呈以下形式之輸入緩衝區
，及
其中
為該資訊信號或該資訊信號之一經處理版本在時刻
之TD樣本，
為在一個訊框中處理的樣本之數目，且
為經調變重疊變換窗中的前導零之數目。
該設備可包含該經調變重疊變換工具，該經調變重疊變換工具經組配以執行：
其中
為在頻率索引
處的經調變重疊變換頻率值，為時間常數，
為分析開窗函數，
為時間輸入緩衝區，且為在一個訊框中處理的樣本之數目。
用於對在頻域FD中界定的一資訊信號或其一經處理版本進行解碼之設備，該設備可包含：
一位元串流讀取器，其經組配以讀取對該資訊信號進行編碼之一位元串流；以及
一逆經調變重疊變換工具，其經組配以使用一合成開窗函數對該資訊信號或其一經處理版本執行一逆經調變重疊變換合成，該合成開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分，
其中該合成開窗函數經界定以便為不對稱的，
其中該合成開窗函數經界定以便在該曲折部分中：
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，
其中該合成開窗函數經界定以使得絕對最大值處於該第一區間與該第三區間中之一者中，
其中該線性函數為具有常數值1之一常數函數。
該設備可包含
該合成開窗函數，其經界定以使得該合成開窗函數之該最大值在同一時刻比該線性函數之該值大出小於25%。
用於對在頻域FD中界定的一資訊信號或其一經處理版本進行解碼之設備，該設備可包含：
一位元串流讀取器，其經組配以讀取對該資訊信號進行編碼之一位元串流；以及
一逆經調變重疊變換工具，其經組配以使用一合成開窗函數對該資訊信號或其一經處理版本執行一逆經調變重疊變換合成，該合成開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分，
其中該合成開窗函數經界定以便為不對稱的，
其中該合成開窗函數經界定以使得該合成開窗函數之該最大值在同一時刻比該線性函數之值大出小於25%，
其中該線性函數為一常數函數。
一種用於對在頻域FD中界定的一資訊信號或其一經處理版本進行解碼之設備，該設備可包含：
一位元串流讀取器，其經組配以讀取對該資訊信號進行編碼之一位元串流；以及
一逆經調變重疊變換工具，其經組配以使用一合成開窗函數對該資訊信號或其一經處理版本執行一逆經調變重疊變換合成，該合成開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分。
該設備，其中該逆經調變重疊變換工具可經組配以：
用該合成開窗函數之值按比例調整一時域混疊緩衝區處之值。
該設備，其中該逆經調變重疊變換工具可經組配而以如下形式產生一時域TD信號表示
其中
為一混疊緩衝區，
為該資訊信號或其一經處理版本，且為一TD訊框的樣本之數目。
該設備，其中該逆經調變重疊變換工具可經組配以：
執行該時間混疊緩衝區之一開窗。
該設備，其中該逆經調變重疊變換工具可經組配以藉由執行以下操作而執行一開窗運算：
該設備，其中該逆經調變重疊變換工具可經組配以執行一疊加運算。
該設備，其中該逆經調變重疊變換工具可經組配以如下執行一疊加運算：
其中
為輸出值，
為一經開窗時間混疊緩衝區，且
為一個訊框中的樣本之數目。
該設備可使得：
該分析開窗函數及/或該合成開窗函數可經界定以便在該曲折部分中：
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以使得該絕對最大值處於該第一區間或該第三區間中。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以使得在該曲折部分中，一相對最大值處於該第一區間或該第三區間中，且一相對最小值處於該第二區間中。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以使得在該曲折部分中，曲折開窗函數對應於該第一區間及該第三區間中之至少一者的值大於0.9。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以便在該曲折部分中在由兩個訊框之30%與50%構成的一區間中存在大於該線性函數之一值。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以使得該分析開窗函數及/或該合成開窗函數之該最大值在同一時刻比該線性函數之該值大出小於25%。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以使得該分析開窗函數及/或該合成開窗函數之該最大值在同一時刻比該線性函數之該值大出小於5%。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以便存在介於-3*10-4
與+3*10-4
之間的一第二數值微分。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以便存在介於-2*10-5
與+2*10-5
之間的一第三數值微分。
該設備可使得
該分析開窗函數及/或合成開窗函數經界定以便存在介於-0.01與+0.01之間的一第一數值微分。
該設備可使得
該分析開窗函數及/或合成開窗函數經界定以便存在介於-10-4
與+10-4
之間的一第二數值微分。
該設備可使得
該分析開窗函數及/或合成開窗函數經界定以便存在介於-10-5
與+10-5
之間的一第二數值微分。
該設備可使得
該線性函數可經界定以便為一非遞增函數。
該設備可使得
該線性函數可經界定以便為一嚴格遞減函數。
該設備可使得
該線性函數可經界定以便為一非遞減函數。
該設備可使得
該線性函數可經界定以便為一嚴格遞增函數。
該設備可使得
該線性函數可經界定以便具有為常數或最大改變+2%或-2%之一值。
該設備可使得
該線性函數可經界定以便具有介於-0.05與-0.20之間的增量。
該設備可使得
該分析開窗函數及/或該合成開窗函數可經界定以便為不對稱的。
該設備可使得
該分析開窗函數與該合成開窗函數可界定為彼此之時間反轉版本。
該設備可包含：
一儲存空間，其儲存該分析開窗函數及/或該合成開窗函數之該等值。
該設備，其中經修改重疊變換可為一經修改離散餘弦變換MDCT或一經修改離散正弦變換MDST，且逆經修改重疊變換為一逆經修改離散餘弦變換IMDCT或逆經修改離散正弦變換IMDST。
該設備可使得
該分析開窗函數及/或該合成開窗函數可為具有常數值1之一常數函數。
一種系統，其可包含：
一編碼器，作為
一解碼器，作為該設備。
該系統，其中該編碼器可包含經組配以傳輸一位元串流之一通訊單元，及/或該解碼器包含經組配以接收一位元串流之一通訊單元。
根據一態樣，提供一種方法，其包含使用一分析開窗函數執行一經修改餘弦變換MDCT分析以將一資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該分析開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分。
根據一態樣，提供一種方法，其包含使用一分析開窗函數執行一經修改餘弦變換MDCT分析以將一資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該分析開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分，
其中該分析開窗函數經界定以便為不對稱的，
其中該分析開窗函數經界定以便在該曲折部分中：
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，
其中該分析開窗函數經界定以使得絕對最大值處於該第一區間與該第三區間中之一者中，
其中該線性函數為具有常數值1之一常數函數。
根據一態樣，提供一種方法，其包含使用一分析開窗函數執行一經修改餘弦變換MDCT分析以將一資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該分析開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分，
其中該分析開窗函數經界定以便為不對稱的，
其中該分析開窗函數經界定以使得該分析開窗函數之該最大值在同一時刻比該線性函數之值大出小於25%，
其中該線性函數為一常數函數。
根據一態樣，提供一種方法，其包含使用一合成開窗函數執行一經修改餘弦變換MDCT合成以將一資訊信號或其一經處理版本之一頻域FD表示變換為一時域TD表示，該合成開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分。
根據一態樣，提供一種方法，其包含使用一合成開窗函數執行一經修改餘弦變換MDCT合成以將一資訊信號或其一經處理版本之一頻域FD表示變換為一時域TD表示，該合成開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分，
其中該合成開窗函數經界定以便在該曲折部分中：
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，
其中該合成開窗函數經界定以使得絕對最大值處於該第一區間與該第三區間中之一者中，
其中該線性函數為具有常數值1之一常數函數。
根據一態樣，提供一種方法，其包含使用一合成開窗函數執行一經修改餘弦變換MDCT合成以將一資訊信號或其一經處理版本之一頻域FD表示變換為一時域TD表示，該合成開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分，
其中該合成開窗函數經界定以便為不對稱的，
其中該合成開窗函數經界定以使得該合成開窗函數之該最大值在同一時刻比該線性函數之值大出小於25%，
其中該線性函數為一常數函數。
一種非暫時性儲存單元，其儲存指令，該等指令在於一處理器上執行時可使得該處理器執行一方法。
提供一種用於對包含複數個訊框之一資訊信號進行編碼之設備，該設備包含：
一經修改離散餘弦變換MDCT工具，其用於將該資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該MDCT工具經組配以使用一分析開窗函數執行一MDCT分析，該分析開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分；以及
一位元串流寫入器，其經組配以基於該資訊信號或其一經處理版本之該FD表示來準備一位元串流。
在實例中，該工具經組配以用該分析開窗函數之值按比例調整時間輸入緩衝區及/或餘弦值。
在實例中，該MDCT工具經組配以按以下形式使用輸入緩衝區
,
其中為該資訊信號或該資訊信號之一經處理版本在時刻之一TD樣本，為在一個訊框中處理的樣本之數目，且為MDCT窗中的前導零之數目。
在實例中，一初始化可執行為：
在實例中，該MDCT (或MDST)工具經組配以執行：
其中為在一頻率索引處的該MDCT (或MDST)頻率值，為該時間常數，為該分析開窗函數，為一時間輸入緩衝區，且為在一個訊框中處理的樣本之數目。
在實例中，提供一種設備，其包含一位元串流讀取器，該位元串流讀取器經組配以讀取對該資訊信號進行編碼之一位元串流；以及
一逆經修改餘弦變換IMDCT (或IMDST)工具，其經組配以使用一合成開窗函數對該資訊信號或其一經處理版本執行一IMDCT (或IMDST)合成，該合成開窗函數具有與至少四個點對應地與一線性函數交叉之一曲折部分。
在實例中，該IMDCT (或IMDST)工具經組配以用該合成開窗函數之值按比例調整一時域混疊緩衝區處的值。
在實例中，該IMDCT (或IMDST)工具經組配以按以下形式產生一時域TD信號表示
其中為一混疊緩衝區，為該資訊信號或其一經處理版本，且為一TD訊框的樣本之數目。
在實例中，該IMDCT (或IMDST)工具經組配以執行該時間混疊緩衝區之一開窗。
在實例中，該IMDCT (或IMDST)工具經組配以藉由執行以下操作而執行一開窗運算：
在實例中，該IMDCT (或IMDST)工具經組配以執行一疊加運算，其可例如為：
其中為輸出值，為一經開窗時間混疊緩衝區，且為一個訊框中的樣本之數目。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以便在該曲折部分中：
在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；
在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；
在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以使得該絕對最大值處於該第一區間或該第三區間中。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以使得在該曲折部分中，一相對最大值處於該第一區間或該第三區間中，且一相對最小值處於該第二區間中。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以使得在該曲折部分中，曲折開窗函數對應於該第一區間及該第三區間中之至少一者的值大於0.9。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以便在該曲折部分中在由兩個訊框之30%與50%構成的一區間中存在大於該線性函數之一值。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以使得該分析開窗函數及/或該合成開窗函數之該最大值在同一時刻比該線性函數之該值大出小於25% (詳言之5%)。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以便存在介於-3*10-4
與+3*10-4
之間的一第二數值微分及/或介於-2*10-5
與+2*10-5
之間的第三數值微分。
在實例中，該線性函數經界定以便具有為常數或最大改變+2%或-2%之一值。
在實例中，該線性函數經界定以便具有介於-0.05與-0.20之間的增量。
在實例中，該分析開窗函數及/或該合成開窗函數經界定以便為不對稱的。
在實例中，該分析開窗函數與該合成開窗函數界定為彼此對稱。
在實例中，一儲存空間儲存該分析開窗函數及/或該合成開窗函數之該等值。
在實例中，提供一種系統，其包含：
一編碼器，作為如上文及/或下文所述之一設備；以及
一解碼器，作為如上文及/或下文所述之一設備。
在實例中，該編碼器包含經組配以傳輸一位元串流之一通訊單元，及/或該解碼器包含經組配以接收一位元串流之一通訊單元。
在實例中，亦提供一種方法，其包含使用一分析開窗函數執行一MDCT (MDST)分析以將一資訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該分析開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分。
在實例中，亦提供一種方法，其包含使用一合成開窗函數執行一MDCT (或MDST)合成以將一資訊信號或其一經處理版本之一頻域FD表示變換為一時域TD表示，該合成開窗函數具有與至少四個點對應地經過一線性函數之一曲折部分。
已注意到，用於本發明之分析開窗函數及/或合成開窗函數特別適合於執行MDCT (或MDST)合成及分析。
在下文中揭示用於經調變重疊變換之分析/合成開窗函數以及用於使用其之方法及設備之實例。
較佳實施例之詳細說明
4. 實例
資訊信號可在時域TD中描述為一連串樣本(例如，對於區塊b及索引(例如時刻) n為xb
(n))。TD表示可由複數個訊框組成，每一訊框與複數個樣本相關聯。在頻域FD中，訊框可表示為一連串頻段(例如，X(k)，每一頻段與一特定頻率相關聯(每一頻率與一索引k相關聯)。
有可能使用經調變重疊變換技術(諸如經修改離散餘弦變換MDCT技術或經修改離散正弦變換MDST技術，舉例來說)來將TD表示轉換為FD表示。此類技術可例如在編碼器側實施，以便將所取樣值變換為頻率值。
有可能使用逆經調變重疊變換技術(諸如逆經修改離散餘弦變換IMDCT技術或逆經修改離散正弦IMDST技術)來將FD表示轉換為TD表示。可例如在解碼器側實施此類技術，以便將頻率值變換為TD值(例如，用於執行再現)。
下表指示在以下部分中使用的符號。 
圖13及圖13A分別展示編碼器設備130及130A。編碼器設備130或130A中之每一者可包含複數個工具，諸如能夠執行信號處理技術之功能區塊。此等區塊中之每一者可為獨立裝置，或可為區分硬體結構與編碼器設備130及130A之其他工具的功能區塊。
編碼器設備130或130A可包含經調變重疊變換工具131 (諸如低延遲經修改離散餘弦變換MDCT工具或低延遲經修改離散正弦變換MDST工具，或另一類型之經調變重疊變換工具)，其可將資訊信號(例如，音訊信號)自時域TD表示轉換為頻域FD表示。經調變重疊變換工具131 (例如，MDCT或MDST工具)執行經調變重疊變換分析(例如，MDCT分析、MDST分析)。
可提供例如在經調變重疊變換工具131下游或在TD中操作之其他工具。此處提及其中的一些。
編碼器設備130可包含用於在FD中執行LPC分析之線性預測性寫碼LPC工具132。編碼器設備130A可包含用於在FD中執行LPC分析之頻譜雜訊塑形SNS工具132A。
SNS可視為LPC之一般化，且因此，在一些實例中，LPC區塊132可視為SNS工具132A之特定實例(且編碼器設備130可視為編碼器設備130A之特定實例)。
編碼器設備130及130A中之每一者可包含時間雜訊塑形TNS工具133，以控制FD中(例如，如由經調變重疊變換工具輸出)的資訊信號之每一窗內的雜訊之時間形狀。
編碼器設備130及130A中之每一者可包含處理FD中之信號之頻譜量化器134。如由TNS工具133輸出的信號可例如使用零值區加均一臨限值純量量化來加以量化。
編碼器設備130及130A中之每一者可包含例如在頻譜量化器134下游之雜訊位準估計器136。
編碼器設備130及130A中之每一者可包含寫碼器135，其處理FD中之信號以例如執行熵寫碼以便例如壓縮位元串流。寫碼器135可例如執行熵寫碼。
編碼器設備130及130A中之每一者可包含頻寬偵測器137a，其可控制例如解碼器處之頻寬控制器。
編碼器設備130及130A中之每一者可包含處理時域TD中之信號之工具。舉例而言，編碼器設備130或130A可包含重取樣工具138a (例如，降頻取樣器)及/或長期後濾波LTPF工具138b，用於控制在解碼器側在TD中起作用的LTPF。
編碼器設備130及130A中之每一者可包含位元串流多工器工具(位元串流寫入器) 137以用自置放在上游之TD及/或FD工具獲得的資料準備位元串流。位元串流可包含資訊信號以及待在解碼器側使用的控制資料之數位表示。位元串流可經壓縮，或包括經壓縮之部分。
圖14及圖14A分別展示解碼器設備140及140A。其中之每一者可對例如如由編碼器130或130A (舉例來說)編碼之資訊信號之數位表示進行解碼。
解碼器設備140及140A中之每一者可包含逆經調變重疊變換工具147 (例如，低延遲逆MDCT工具或低延遲逆DMST工具)以將信號表示自FD變換為TD。經調變重疊變換工具147執行經調變重疊變換合成(例如，MDCT合成及/或MDST合成，等)。
可提供例如在逆經調變重疊變換工具147上游或在TD中操作之其他工具。此處提及其中的一些。
解碼器設備140及140A中之每一者可包含位元串流多工工具141以自編碼器設備(例如，設備130或130A)獲得位元串流(例如，藉由傳輸)。舉例而言，來自編碼器設備130或130A之輸出可作為輸入信號提供至解碼器設備140或140A。
解碼器設備140及140A中之每一者可包含解碼器142，其可例如解壓縮位元串流中之資料。可執行算術解碼。可執行殘餘解碼。
解碼器設備140及140A中之每一者可包含處理FD中之信號之雜訊填充工具143。
解碼器設備140及140A中之每一者可包含處理FD中之信號之全域增益工具144。
解碼器設備140及140A中之每一者可包含處理FD中之信號之TNS解碼器工具145。
解碼器設備140可包含MDCT (或MDST)塑形工具146 (其他重疊變換工具係可能的)。MDCT (或MDST)塑形工具146可藉由應用自變換至FD頻譜(例如，MDCT或MDST頻譜，等)之經解碼LP濾波器係數(例如，自LPC解碼工具146a獲得)計算的增益因數而處理信號。
解碼器設備140A可包含例如自SNS工具132A獲得LPC係數之SNS解碼器工具146A'。
解碼器設備140及140A中之每一者可包含用於在TD中執行後濾波之LTPF工具148。
解碼器設備140A可包含可自例如頻寬偵測器137a獲得頻寬資訊之解碼器頻寬控制器149。
編碼器設備130 (或130A)及解碼器設備140 (或140A)可彼此組合以形成一系統。
基本上，編碼器設備130或130A中在經調變重疊變換工具131下游的工具及解碼器設備140或140A中在逆經調變重疊變換工具147上游的工具可在FD中執行信號處理，且因此為FD工具。
此處關於例如在工具131及147處的轉換技術論述諸技術。
一般而言，MDCT、MDST等為額外具有重疊變換之特性的離散變換。對較大資料集之連續區塊(例如，兩個連續訊框)執行此等變換中之一者。後續區塊可能重疊。因此，一個區塊之最末部分可與後續區塊之第一部分重合。可使用開窗函數wn
(n = 0、...、2N-1)。詳言之，開窗函數可用作權重。優點為有可能避免或減小區塊邊界處之不連續性。
圖15展示用於例如在經調變重疊變換工具131 (其可為MDCT工具)處執行經調變重疊變換分析之方法150。當前訊框
之輸入信號
可由
個音訊樣本組成，其中最新樣本位於
處。
在步驟S151處，可更新輸入緩衝區。經調變重疊變換
之時間輸入緩衝區可根據以下加以更新
後者僅為一致性所需之初始化。
在步驟S152處，可使用以下方程式將具有個時間樣本之區塊變換為頻率係數
：
其中
為根據所使用的訊框大小之不對稱經調變重疊變換窗(例如，MDCT窗)。
圖16展示用於例如在經調變重疊變換工具147 (其可為IMDCT工具)處執行經調變重疊變換合成(例如，MDCT合成)之方法160。此處，頻譜
(即，FD中之表示) 可藉由以下步驟變換至TD：
在步驟S161處，可執行訊框之時域混疊緩衝區
之產生。舉例而言：
在步驟S162處，可執行時域混疊緩衝區之開窗。舉例而言：
在步驟S163處，可進行疊加運算以獲得訊框之經重建時間樣本
。舉例而言：
值得注意地，分析處之開窗函數(分析開窗函數)與合成處之開窗函數
(合成開窗函數)可經界定以便為彼此之時間反轉。分析窗與合成窗之窗係數為彼此之時間反轉版本。
已注意到，特別有效的開窗函數(例如，合成開窗函數)可為具有曲折部分的分析開窗函數，該曲折部分與四個點對應地與線性函數交叉。
圖4展示分析開窗函數40。分析開窗函數40可界定於0與2N之間或0與在2N之80%與85%或90% (例如，81.25%)中間的一值之間。在一些實例中，分析開窗函數40可界定於不同(例如，較寬)範圍中。
分析開窗函數40可至少對於一個部分參考線性函數40'而界定。在圖4中，線性函數40'為值為1的常數函數。然而， 線性函數40'可大體為例如根據
界定之線性函數，其中
為介於0與2N (或其非零部分)之間的索引，且
及為常數。
分析開窗函數40可包含曲折部分44。曲折部分44可使得分析開窗函數40在四個點#1、#2、#3、#4處與線性函數40'相遇及/或交叉。
曲折部分44可使得分析開窗函數40在大多數索引(例如，對於多於99%之索引)處不同於線性函數40'。
曲折部分44可使得，至少在緊接該等索引中與該等點(交叉點#1、#2、#3、#4)相關聯的一個索引之前的一個索引處，分析開窗函數40之值在交叉點(#1、#2、#3、#4)處大於線性函數之值(例如，1)，且至少在緊接同一索引(與交叉點相關聯)之後的索引處，分析開窗函數40之值在交叉點處小於線性函數之值。
曲折部分44可使得，至少在緊接該等索引中與交叉點#1、#2、#3、#4相關聯的一個索引之前的一個索引處，分析開窗函數40之值在交叉點(#1、#2、#3、#4)處小於線性函數之值(例如，1)，且至少在緊接同一索引(與交叉點相關聯)之後的索引處，分析開窗函數40之值在交叉點處大於線性函數之值。
曲折部分44可使得交叉點#1、#2、#3、#4中之每一者不與先前及後續交叉點緊接連續。舉例而言，在兩個交叉點#1、#2、#3與#4之間，存在分析開窗函數40之至少一個索引，使得其值不與分析開窗函數40在同一索引處的值重合。
分析開窗函數40可經界定以便對應於曲折部分44：
- 在第一交叉點#1與第二交叉點#2之間的第一區間41中大於線性函數40'；
- 在第二交叉點#2與第三交叉點#3之間的第二區間42中低於線性函數40'；
- 在第三交叉點#3與第四交叉點#4之間的第三區間43中大於線性函數40'。
第一交叉點#1可先於第二交叉點#2，該第二交叉點可先於第三交叉點#3，該第三交叉點可先於第四交叉點#4。
曲折部分44可在第一交叉點與最末(例如，第四)交叉點之間延伸。在一些實例中，交叉點可僅為四個。
分析開窗函數40亦可包含初始遞減部分45，其中可達到負最小值。負最小值可位於2N之6.25%與2N之18.75%之間。分析開窗函數40亦可包含快速遞增部分46，自負最小值朝向曲折部分44 (例如，朝向第一交叉點#1)快速遞增。分析開窗函數40亦可包含快速遞減部分47，自曲折部分44快速遞減至0。分析開窗函數40亦可包含連續空值部分48，其可在2N (兩個訊框之大小)之80%與85%或90%之間開始且繼續至2N之結束。
絕對最大值41'處於第一區間41 (或第三區間)中。
分析開窗函數40可在曲折部分44中具有處於第三區間43 (或第一區間)中的相對最大值43'，且相對最小值42'處於第二區間42中。
分析開窗函數40可在曲折部分44中使對應於第二區間42的曲折開窗函數40之值大於0.9。第二區間42可高於0.9。
分析開窗函數40可在曲折部分44中存在在由兩個訊框(2N)之30%與50%構成的區間中低於線性函數40'的值。在實例中，在兩個訊框(2N)之50%之後，開窗函數40可大於線性函數40'。因此，點#3可對應於第一訊框之最末索引或對應於第二訊框之第一索引。在兩個訊框之30%至50%區間中，曲折窗部分44可低於線性函數。
曲折開窗函數44之最大值41'可比線性函數40'在同一索引n處的值大出小於25% (且較佳小於5%或3%)。
分析開窗函數40可存在介於0.02與-0.02之間的第一數值微分。第二數值微分可介於-5*10- 4
與+5*10- 4
之間，且較佳介於-3*10- 4
與+3*10- 4
之間。第三數值微分可介於-2*10- 5
與+2*10- 5
之間。
線性函數40'可為非遞增函數。在其實例中，線性函數40'可為非遞減函數。線性函數40'可具有為常數或最大改變+2%或-2%之值。
分析開窗函數可經界定以便為不對稱的。
在一些實例中，分析開窗函數可使得曲折部分44之區間(子部分)中的一些相對於以上描述為反轉次序。
圖
26
及圖
27
展示分析開窗函數
40
(
圖
27
為圖
26
的一部分之放大視圖
)
。分析開窗函數
240
可界定於
0
與
2N
之間或
0
與在
2N
之
80
%
與
85
%
或
90
% (
例如，
81
.
25
%)
中間的一值之間
。在一些實例中，
分析開窗函數
40
可界定於不同
(
例如，較寬
)
範圍中。
分析開窗函數 40 可至少對於一個部分參考 線性函數 2 40
'而界定 。 在 圖 27 中， 線性函數 2 40
'為值為 1 的常數函數 。 然而， 線性函數 40
'可大體為 例如 根據 
界定之線性函數，其中 為介於 0 與 2N ( 或其非零部分 ) 之間的索引，且 
及 
為常數 ( 例如， a=0, b=1) 。
分析開窗函數 240 可包含曲折部分 244 。曲折部分 244 可使得分析開窗函數 240 在四個點 # 1 、 # 2 、 # 3 、 # 4 處與線性函數 240
'相遇 及 / 或交叉。
曲折部分 244 可使得 分析開窗函數 240 在大多數索引 ( 例如 ，對於多於 99 % 之 索引 ) 處 不同 於 線性函數 240
'。
曲折部分 244 可使得，至少在緊接該等 索引中與該等點 ( 交叉點 # 1 、 # 2 、 # 3 、 # 4 ) 相關聯的一個索引之前的一個 索引處 ， 分析開窗函數 240 之值在交叉點 (# 1 、 # 2 、 # 3 、 # 4 ) 處大於 線性函數 240
'之 值，且至少在緊接同一 索引 ( 與交叉點相關聯 ) 之後的索引處， 分析開窗函數 240 之值在交叉點 (# 1 、 # 2 、 # 3 、 # 4 ) 處小於 線性函數 240
'之 值 。
曲折部分 244 可使得，至少在緊接該等 索引中與 交叉點 # 1 、 # 2 、 # 3 、 # 4 相關聯的一個索引之前的一個 索引處 ， 分析開窗函數 40 之值在交叉點 (# 1 、 # 2 、 # 3 、 # 4 ) 處小於 線性函數 240
'之值 ，且至少在緊接同一 索引 ( 與交叉點相關聯 ) 之後的索引處， 分析開窗函數 40 之值在交叉點處大於 線性函數 240
'之 值 。
曲折部分
244
可使得交叉點
#
1
、
#
2
、
#
3
、
#
4
中之每一者不與先前及後續交叉點緊接連續。舉例而言
，
在兩個交叉點
#
1
、
#
2
、
#
3
與
#
4
之間
，
存在分析開窗函數
240
之至少一個索引
，
使得其值不與分析開窗函數
240
在同一索引處的值重合。
分析開窗函數 240 可經界定以便對應於曲折部分 244 ： - 在第一交叉點 # 1 與第二交叉點 # 2 之間的第一區間 241 中大於線性函數 240
'； - 在第二交叉點 # 2 與第三交叉點 # 3 之間的第二區間 242 中低於線性函數 240
'； - 在第三交叉點 # 3 與第四交叉點 # 4 之間的第三區間 243 中大於線性函數 240
'。
第一交叉點
#
1
可先於第二交叉點
#
2
，
該第二交叉點可先於第三交叉點
#
3
，
該第三交叉點可先於第四交叉點
#
4
。
曲折部分
244
可在第一交叉點與最末
(
例如，
第四
)
交叉點之間延伸。在一些實例中，交叉點可僅為四個。
分析開窗函數
240
的值可全部為正值。最小值可為
0
值
，
其可在分析開窗函數
240
之第一索引處及
/
或分析開窗函數
240
之最末索引處。分析開窗函數
240
可包含快速遞增部分
246
，朝向曲折部分
244
(
例如，
第一交叉點
#
1
)
快速遞增。分析開窗函數
240
亦可包含快速遞減部分
247
，
自曲折部分
244
快速遞減至
0
。分析開窗函數
240
可包含連續空值部分
248
，其可在
2N
(
兩個訊框之大小
)
之
84
%
與
90
%
之間開始且繼續至
2N
之結束。
絕對最大值 241
'處於第一區間 41 ( 或第三區間 ) 中。
分析開窗函數 240 可在曲折部分 244 中具有處於第三區間 243 ( 或第一區間 ) 中的相對最大值 243
'， 及 / 或相對最小值 242
'處於第二區間 242 中。
分析開窗函數
240
可在曲折部分
244
中使對應於第二區間
242
的
曲折開窗函數
240
之值大於
0
.
95
。第二區間
242
可高於
0
.
95
。第一區間
241
及
/
或第三區間
243
可小於
1
.
05
。
分析開窗函數 240 可在曲折部分 244 中存在在由兩個訊框 ( 2N ) 之 30 % 與 50 % 構成的區間中低於線性函數 240
'的 值。在實例中 ， 在兩個訊框 ( 2N ) 之 50 % 之後 ， 開窗函數 240 可大於線性函數 240
'。因此 ， 點 # 3 可對應於第一訊框之最末索引或對應於第二訊框之第一索引。在兩個訊框之 30 % 至 50 % 區間中 ， 曲折窗部分 244 可低於線性函數。
曲折開窗函數 244 之最大值 241
'可比線性函數 240
'在同一索引 n 處的值大出小於 25 % ( 且 較佳小於 5 % 或 3 %) 。
分析開窗函數
240
可存在介於
-
0
.
01
與
+
0
.
01
之間的第一數值微分。第二數值微分可介於
-
10
-
4
與
+
10
-
4
之間。第三數值微分可介於
-
10
-
5
與
+
10
-
5
之間。
線性函數 40
'可為非遞增函數。在其實例中 ， 線性函數 40
'可為非遞減函數。線性函數 40
'可具有為常數或最大改變 + 2 % 或 - 2 % 之 值。
分析開窗函數可經界定以便為不對稱的。
在一些實例中
，
分析開窗函數
240
可使得曲折部分
244
之區間
(
子部分
)
中的一些相對於以上描述為反轉次序。
圖28及圖29比較分析開窗函數40與240。
圖6展示分析開窗函數60之另一實例。圖7展示與曲折部分64對應的分析開窗函數60之放大視圖。
在此情況下，分析開窗函數60可至少對於一個部分參考線性函數60'而界定。在圖7中，線性函數60'為線性遞減函數(「對角線」)。
曲折部分64可使得分析開窗函數60在四個點處與線性函數60'相遇及/或交叉。
分析開窗函數40可經界定以便對應於曲折部分64：
- 在第一交叉點#1'與第二交叉點#2'之間的第一區間61'中大於線性函數60'；
- 在第二交叉點#2'與第三交叉點#3'之間的第二區間62'中低於線性函數60'；
- 在第三交叉點#3'與第四交叉點#4'之間的第三區間63'中大於線性函數60'；
- 在第四交叉點#4'與第五交叉點#5'之間的第四區間64'中低於線性函數60'；
- 在第五交叉點#5'與第六交叉點#6'之間的第五區間65'中大於線性函數60'。
絕對最大值可處於第一區間61'中(在其他實例中，例如，在線性函數遞增的情況下，可處於第五區間中)。
分析開窗函數60可在曲折部分64中具有處於第三區間63'及/或第五區間65'中之相對最大值、處於第二區間62'及/或第四區間64'中之相對最小值。
分析開窗函數60可在曲折部分64中具有大於0.9且特別地大於0.95之對應於第一區間及第三區間中之至少一者的開窗函數之值(在其他實例中，例如，在線性函數遞增的情況下，可在第三區間及第五區間中)。
分析開窗函數60可在曲折部分64中存在在由兩個訊框(2N)之30%與50%構成的區間中大於線性函數60'的值。
開窗函數60之最大值可比線性函數60在同一索引n處之值大出小於25% (且較佳小於5%)。
線性函數60'可為非遞增函數，詳言之為嚴格遞減函數。
分析開窗函數可經界定以便為不對稱的。
在實例中，分析開窗函數可具有相對於圖6反轉之區間。
在實例中，合成開窗函數可解釋為相對於分析開窗函數對稱。舉例而言，對稱軸可處於2N範圍之中間(例如，479或480)。
合成開窗函數90之實例提供於圖9中(例如，與圖4的分析開窗函數40相關聯之合成開窗函數)。合成開窗函數90可界定於0與2N之間或2N之10%或15%與20%中間的值與2N之間。
合成開窗函數90可至少對於一個部分參考線性函數(其在此情況下未展示，但為常數值1)而界定。在圖9中，線性函數可為值為1的常數函數。然而，線性函數可大體為例如根據y=an+b界定之線性函數。
合成開窗函數90可包含曲折部分94。曲折部分94可使得合成開窗函數90在四個交叉點#1、#2、#3、#4 (僅說明#2)處與線性函數90' (常數1，為清楚起見僅部分地展示)相遇及/或交叉。合成開窗函數可與窗之中間(點#2)(即樣本N-1與N之間)的值1交叉。
曲折部分94可使得合成開窗函數90在大多數索引(例如，對於多於99%之索引)處不同於線性函數90'。
曲折部分94可使得，至少在緊接該等索引中與交叉點#1、#2、#3、#4相關聯的一個索引之前的一個索引處，合成開窗函數90之值在交叉點(#1、#2、#3、#4)處大於線性函數之值(例如，1)，且至少在緊接同一索引(與交叉點相關聯)之後的索引處，合成開窗函數90之值在交叉點處小於線性函數之值。曲折部分94可使得，至少在緊接該等索引中與該等點(交叉點#1、#2、#3、#4)相關聯的一個索引之前的一個索引處，合成開窗函數90之值在該等點(#1、#2、#3、#4)處小於線性函數之值，且至少在緊接同一索引(與交叉點相關聯)之後的索引處，合成開窗函數90之值在交叉點(#1、#2、#3、#4)處大於線性函數之值。
曲折部分94可使得點#1、#2、#3、#4中之每一者不與點#1、#2、#3、#4中之另一者緊接連續。舉例而言，在#1、#2、#3與#4中的兩個點之間，可存在合成開窗函數90之至少一個索引，使得其值不與合成開窗函數90在同一索引處的值重合。
合成開窗函數90可經界定以便對應於曲折部分94：
- 在第一交叉點#1 (未在圖9中展示，但可表示為與圖4中的點#4對稱)與第二交叉點#2 (在此情況下，其在第480個樣本處，例如在2N範圍之中間)之間的第一區間91中大於線性函數90'；
- 在第二交叉點#2與第三交叉點#3 (未在圖9中展示，但可表示為與圖4中的點#3對稱)之間的第二區間92中低於線性函數90'；
- 在第三交叉點#3與第四交叉點#4 (未在圖9中展示，但可表示為與圖4中的點#1對稱)之間的第三區間93中大於線性函數90'。
合成開窗函數90亦可包含連續空值部分98，其可位於2N之10%與15%之間。合成開窗函數90亦可包含快速遞增部分97，自0朝向曲折部分94快速遞增。合成開窗函數90亦可包含快速遞減部分96，自曲折部分94朝向負最小值快速遞減。負最小值可位於2N之81.25%與2N之93.7%之間。合成開窗函數90亦可包含最終遞增部分95，其自負最小值達到0。
絕對最大值可處於第三區間93 (或第一區間)中。
合成開窗函數90可在曲折部分94中具有處於第一區間91 (或第三區間)中的相對最大值，且相對最小值處於第二區間中。
合成開窗函數90在曲折部分94中可使曲折開窗函數對應於第一區間(91)及第三區間(93)中之至少一者的值大於0.9。第三區間可高於0.9。
合成開窗函數90可在曲折部分94中存在在由兩個訊框(2N)之30%與50%構成的區間中大於線性函數的值。
合成開窗函數90之最大值可比線性函數在同一索引n處的值大出小於25% (且較佳小於5%)。
合成開窗函數90可存在介於0.02與-0.02之間的數值微分。第二數值微分可介於-5*10- 4
與+5*10- 4
之間，且較佳介於-3*10- 4
與+3*10- 4
之間。第三數值微分可介於-2*10- 5
與+2*10- 5
之間。
合成線性函數90可為非遞增函數。在其他實例中，合成線性函數90可為非遞減函數。合成線性函數90可具有為常數或最大改變+2%或-2%之值。
合成開窗函數90可經界定以便為不對稱的。
在一些實例中，合成開窗函數90可為相對於圖9中所示之形狀對稱的函數。例如，0處的值將為圖9中在960處的值；1處的值將為圖9中在959處的值，等等。
合成開窗函數
290
之實例提供於圖
30
中
(
例如，
與圖
26
至圖
29
的分析開窗函數
240
相關聯之合成開窗函數
)
。合成開窗函數
290
可界定於
0
與
2N
之間或
2N
之
10
%
或
15
%
與
20
%
中間的值與
2N
之間。
合成開窗函數 290 可至少 對於一個部分參考 線性函數 290
'( 其在此情況下未展示 ， 但為常數值 1 ) 而界定 。
在圖 30 中 ， 線性函數 290
'可為值為 1 的 常數函數。然而，線性函數可大體為例如根據 y = an + b 界定之 線性函數。
合成開窗函數 290 可包含曲折部分 294 。曲折部分 294 可使得合成開窗函數 290 在四個交叉點 # 1 、 # 2 、 # 3 、 # 4 ( 僅說明 # 2 ) 處與線性函數 290
'( 常數 1 ， 為清楚起見僅部分地展示 ) 相遇 及 / 或交叉。合成開窗函數可與窗之中間 ( 點 # 2 )( 即樣本 N - 1 與 N 之間 ) 的 值 1 交叉。
曲折部分 294 可使得 合成開窗函數 290 在大多數索引 ( 例如 ，對於多於 99 % 之 索引 ) 處 不同 於 線性函數 290
'。
曲折部分
294
可使得，至少在緊接該等
索引中與
交叉點
#
1
、
#
2
、
#
3
、
#
4
相關聯的一個索引之前的一個
索引處
，
合成開窗函數
90
之值在交叉點
(#
1
、
#
2
、
#
3
、
#
4
)
處
大於
線性函數之值
(
例如
，
1
)
，且至少在緊接同一
索引
(
與交叉點相關聯
)
之後的索引處，
合成開窗函數
90
之值在交叉點處
小於
線性函數之
值
。
曲折部分
294
可使得，至少在緊接該等
索引中與該等點
(
交叉點
#
1
、
#
2
、
#
3
、
#
4
)
相關聯的一個索引之前的一個
索引處
，
合成開窗函數
290
之值在該等點
(#
1
、
#
2
、
#
3
、
#
4
)
處
小於
線性函數之
值，且至少在緊接同一
索引
(
與交叉點相關聯
)
之後的索引處，
合成開窗函數
290
之值在交叉點
(#
1
、
#
2
、
#
3
、
#
4
)
處
大於
線性函數之
值
。
曲折部分
294
可使得交叉點
#
1
、
#
2
、
#
3
、
#
4
中之每一者不與點
#
1
、
#
2
、
#
3
、
#
4
中之另一者
緊接連續。舉例而言
，
在
#
1
、
#
2
、
#
3
與
#
4
中的
兩個交叉點之間
，可
存在合成開窗函數
290
之至少一個索引
，
使得其值不與合成開窗函數
290
在同一索引處的值重合。
合成開窗函數 290 可經界定以便對應於曲折部分 294 ： - 在第一交叉點 # 1 與 第二交叉點 # 2 ( 在此情況下 ， 其在第 480 個 樣本處 ， 例如在 2N 範圍之中間 ) 之間的第一區間 291 中大於線性函數 290
'( 例如， 大於 1 ) ； - 在第二交叉點 # 2 與第三交叉點 # 3 之間的第二區間 292 中低於線性函數 290
'； - 在第三交叉點 # 3 與第四交叉點 # 4 之間的第三區間 293 中大於線性函數 290
'。
合成開窗函數
290
可包含連續空值部分
298
，
其可位於窗
(
2N
個
樣本
)
之一個邊界處
，
且可處於樣本之
10
%
與
15
%
之間。合成開窗函數
290
亦可包含快速遞增部分
297
，
自
0
朝向曲折部分
294
快速遞增。合成開窗函數
290
可包含快速遞減部分
296
，自曲折部分
294
朝向
0
快速遞減。
絕對最大值可處於第三區間
293
(
或第一區間
)
中。
合成開窗函數
290
可在曲折部分
294
中具有處於第一區間
291
(
或第三區間
)
中的相對最大值
，且
相對最小值處於第二區間中。
合成開窗函數
290
在曲折部分
294
中可使曲折開窗函數對應於第一區間
(
291
)
及第三區間
(
293
)
中之至少一者的值大於
0
.
9
或
0
.
95
。第三區間可高於
0
.
95
。
合成開窗函數
290
可在曲折部分
294
中存在在由兩個訊框
(
2N
)
之
30
%
與
50
%
構成的區間中大於線性函數
的
值。
合成開窗函數
290
之最大值可比線性函數在同一索引
n
處之值大出小於
25
% (
且
較佳小於
5
%
或
3
%)
。
合成開窗函數
290
可存在介於
-
0
.
01
與
+
0
.
01
之間的數值微分。第二數值微分可介於
-
10
-
4
與
+
10
-
4
之間。第三數值微分可介於
-
10
-
5
與
+
10
-
5
之間。
合成線性函數
90
可為非遞增函數。在其他實例中
，
合成線性函數
90
可為非遞減函數。合成線性函數
90
可具有為常數或最大改變
+
2
%
或
-
2
%
之
值。
合成開窗函數
90
可經界定以便為不對稱的。
在一些實例中 ， 合成開窗函數 90 可為相對於圖 9 中所示之形狀對稱的函數。例如， 0 處的 值將為圖 9 中在 960 處的 值； 1 處的 值將為圖 9 中在 959 處的 值，等等。
5. 論述
已注意到，此函數具有特別受關注之特徵，其極其適合於MDCT (或或其他)及IMDCT (或IMDST或其他)技術，詳言之適合於音訊寫碼。
作為MDCT窗形狀之平滑度之量度，吾人使用數值微分，如
用以評定MDCT窗之品質的另一量度為量化誤差之時間形狀，其由以下描述
量化誤差可能作為音訊寫碼過程之部分而引入譜域中。
此處論述ALDO窗。ALDO為用於不對稱窗之設計方法，其提供改良之時間形狀。如在EVS編解碼器中使用的ALDO窗之設計過程描述於(3GPP)及[2]中。圖1展示用於ALDO窗方案之示意性窗形狀。
ALDO窗由四個區段組成：上升函數、嚴格一區段、衰減函數及零。w4
中零之數目亦判定w2
中一之數目，其中w2
=2*w4
。獲得w1
及w3
之方式描述於[1]及[2]中。
圖2展示根據[1]及[2]對於參數Lz=180 (在圖1中的MDCT窗W4
(n)中前導零之數目)設計的ALDO窗，且總窗長度為960個樣本。
如圖2之第四子圖(「時間調變量化誤差」)中可見，ALDO展示量化誤差之良好時間形狀，其意謂兩個後續重疊合成窗之能量總和接近於一。最佳結果將僅需要藉由對稱窗形狀達成之結果。
此設計方法之缺陷主要在圖2之第二子圖(「數值微分」)中可見，其中概述數值微分。可看出，窗形狀並非連續可微分數學函數，且因此對於頻率回應為非最佳的。由於窗形狀中之靜態一，來自上升函數及進入衰減函數之平滑轉變係不可能的。
本發明打破設計約束以維持嚴格一區段以便最佳化時間形狀。實際上，該等一由圍繞線性函數(例如，常數值，諸如「1」)曲折之一序列值替換。此解決方案允許平滑且連續之窗形狀，同時保持時間形狀接近於最佳狀態。
圖3展示根據本發明之設計成具有曲折區段(部分)之實例窗。如圖3的第四子圖(「時間調變量化誤差」)中可見，關於量化誤差之時間塑形之窗特性類似於ALDO窗。然而，比較圖3的第二子圖(「數值微分」)與圖2之第二子圖(ALDO窗)，可理解，本發明准許產生連續可微分的窗形狀。此使得例如能夠以較高停止頻帶衰減設計窗形狀，此到目前為止對於用於ALDO窗之設計過程係不可能的。
圖4更詳細地概述實例窗形狀40。在此實例中，曲折區段係基於與四個點對應地與線性函數(在此情況下，常數值「1」)交叉。更高數目之交叉點係可能的，但四個視為最小數目。
此類窗可為組合用於頻率回應之一個誤差函數與表示自量化雜訊之最佳時間塑形之偏差的誤差函數之數學最佳化過程之結果。
一些實施需要特定資料格式，例如，固定點實施。對於此類實施，窗係數之值範圍可為標度，因為高於一之值需要不同縮放。在此類情況下，曲折區段可能不圍繞一。僅在解除縮放之後，該等值才變為顯而易見的範圍。
圖5展示如何在固定點實施內部呈現MDCT窗係數50之實例。其為一些值藉由2x
縮放且其他值藉由2x - 1
縮放(由於固定點架構)之實例表示。
考慮通用情況，窗不必圍繞1曲折，但可圍繞虛擬對角線曲折而不與一交叉。圖6展示三個不同窗，即
- w1
：圍繞1曲折之新最佳化(開窗函數70)；
- w2
：G.718窗(完全不曲折)(開窗函數70')；
- w3
：用於特殊情況之新最佳化窗：圍繞對角曲折(開窗函數60)。
所描述的MDCT窗滿足完美的重建特性。由此，吾人考慮MDCT分解為開窗運算、時域混疊消除(TDAC)步驟及離散餘弦變換(DCT)類型IV內核，如例如[3]中所描述。
因此，開窗及TDAC可視為分析側上的摺疊步驟及合成側上之展開步驟。在後者處，在疊加運算中組合兩個區塊之展開序列。見圖8，其係指區塊1 (81)及區塊2 (82)之方案。
對於分析側上之重疊區，區塊1之開窗及TDAC可描述為
P1
(n)=wa
(N+n)-wa
(2N-1-n) 對於n=0…N-1
且區塊2之開窗及TDAC可描述為
P2
(n)=wa
(N+n)+wa
(N-1-n) 對於n=0…N-1
對於合成側，P1及P2經展開、開窗，且執行疊加：
O(n)= ws
(N+n)P1
(n)+ws
(n)P2
(n) 對於n=0…N-1
此可寫為
O(n)= wa
(N+n)ws
(N+n)-wa
(2N-1-n)ws
(N+n)+wa
(n)ws
(n)+wa
(N-1-n)ws
(n)
對於n=0…N-1
其可分離成兩個分量：
PR1：完美重建分量
wa
(N+n)ws
(N+n)+wa
(n)ws
(n)=1
對於n=0…N-1
- PR2：混疊消除分量
- wa
(N-1-n)ws
(n)-wa
(2N-1-n)ws
(N+n)=0
- 對於n=0…N-1
圖9至圖12展示分析及合成序列。
現關於本發明之分析及合成開窗函數之數值微分參考圖19及20。
藉由亦考慮第2及第3數值微分，有可能清楚地區分本發明實例(例如，參考圖4的實例之圖19及參考圖26之實例的圖31)之特性與先前技術(ALDO，圖20)之特性。
作為經調變重疊變換窗形狀(例如，MDCT或MDST窗形狀)之平滑度的量度，吾人可使用數值微分，如：
為了衡量每一係數之重要性，即較高振幅具有較高權重，以下描述經加權
此允許在分析窗形狀之連續性時忽略低等級窗係數。
在圖19及圖20以及圖31中，第1數值微分標繪為規則且經加權之版本(短劃線)。1902及3102指代本發明開窗函數之第1數值微分；1904及3104 (短劃線)指代本發明開窗函數之第1數值微分之經加權版本。2002指代ALDO開窗函數之第1數值微分；2004 (短劃線)指代ALDO開窗函數之第1數值微分之經加權版本。
對於第2及第3數值微分(ND)，使用第1數值微分之經加權版本。1910及3110指代本發明開窗函數之第2數值微分之經加權版本。2010指代ALDO開窗函數之第2數值微分之經加權版本。1920指代本發明開窗函數之第3數值微分之經加權版本。2020及3120指代ALDO開窗函數之第3數值微分之經加權版本。
如可觀察到，第2 ND版本展示ALDO窗之一些明顯峰值2021，而本發明窗展示僅適中之改變。對於第3 ND，亦可清楚區分且可表達兩個窗之振幅等級。
此處呈現對ALDO與本發明開窗函數之窗設計的自由度之分析。
ALDO設計方法[2]僅提供參數C1、C2及零之數目Lz作為自由度。關於近場或遠場衰減之任何聚焦對於所提出的方法係不可能的，因為設計過程中的給定自由度非常有限。
為了擴展ALDO算法且允許較高自由度，[2]中的設計方法必須被放棄且必須由數值最佳化方法交換。在第一步驟中，維持窗中間之嚴格一區段，同時使自由窗係數(或設計參數)最佳化。
假定分析與合成窗始終為彼此之時間反轉版本，則完美重建約束可由下式表達
wa
(N+n)ws
(N+n)+wa
(n)ws
(n)=1 對於n=0…N-1
è w(N+n)w(2N-n)+w(n)w(N+n)=1 對於n=0…N-1
此可始終藉由將自由係數之數目限制為1.5N來滿足，例如藉由
w(2N-n) = (1- w(n)w(N+n)) / w(N+n) 對於n=0…N-1
零區段位於w(2N-n)內部。對於中間中嚴格一之約束，窗係數之2*Lz視為非自由係數。對於N=480之變換長度及2N之視窗大小及Lz=180，此導致1.5N-2*Lz = 360個自由係數之自由度。此窗稱為中間窗。
新發明藉由用圍繞一或圍繞任何其他線性(例如，對角)線(例如，40'、60'、90')之曲折區段(例如，44、64、94)交換嚴格一部分來將自由度增大至最大值。因此，僅一半中間區段需要自自由係數排除。因此，可用係數之數目增大至1.5*480-180=540個自由係數。此允許朝向任何凹入焦點最大限度地最佳化頻率回應。
圖21及圖22展示設計方法之比較。詳言之，圖21展示比較ALDO窗形狀(211)與中間窗形狀(212)與新發明窗形狀(213)。圖22展示ALDO窗形狀(211)、中間窗形狀(212)、新發明窗形狀(213)之縮放(放大視圖)。
中間窗及新發明窗朝向同一焦點最佳化。
圖23展示ALDO曲線圖頻率回應(231)、中間曲線圖頻率回應(232)、新發明曲線圖頻率回應(233)。中間(231)及新發明窗(233)可聚焦於不同區域，從而在此情況下達成較佳遠場衰減。需要此例如以避免由頻帶受限信號造成或每當信號經由濾波器組重取樣時之之任何混疊失真。此焦點對於ALDO窗係不可能的，因為僅存在兩個可用於控制形狀之參數。比較中間與新發明窗，顯而易見，新發明達成回應中的小得多的波動(由於時域中非常連續之形狀)。
圖24展示比較中間頻率回應(242)與新發明頻率回應(243)之縮放(放大視圖)。如可觀察到，新發明窗(243)始終展示所有旁波帶之顯著較高衰減。此確認曲折部分(44、64、94)在窗設計中優於嚴格一部分。
參考窗之時間調變，應注意，ALDO窗之主要動機為組合不對稱形狀與最大振幅1，以便避免量化誤差之大時間波動。量化誤差在頻域中相加，且其時間形狀由合成窗形狀控制。
實際上，此處，曲折序列亦進一步改良此窗特性。圖25展示由ALDO窗(253)及所提出的發明(251)造成的量化誤差之時間調變之直接比較。如可看出，最大時間失真對於新發明較低，且因此提供較不明顯之失真。
在以上實例中，曲折部分可例如與DCT內核對應(至少部分)。在實例中，至少一個第一交叉點(例如，#1)處於第一訊框中，而至少另一交叉點(例如，#3)處於後續訊框中。在實例中，一個交叉點(例如，#2)處於第一訊框與後續訊框之間的邊界處。
在實例中，「曲折」係指以下事實：存在與線性函數之至少四個相交點(曲折部分在至少兩個點或在一些情況下在至少四個點中與線性函數交叉)。舉例而言，曲折部分可具有遞增部分，之後為遞減部分，之後為遞增部分，以此類推，或遞減部分，之後為遞增部分，之後為遞減部分，以此類推。
6. 其他實例
圖17展示可實施編碼器設備130 (或130A)及/或MDCT工具131及/或執行方法150之至少一些步驟的設備110。設備110可包含處理器111及非暫時性記憶體單元112，其中區塊114儲存指令，該等指令在由處理器111執行時可使得處理器111執行MDCT合成。非暫時性記憶體單元112亦可儲存(區塊113)分析開窗函數，例如如上文所論述。設備110可包含輸入單元116，其可獲得輸入資訊信號(例如，音訊信號)。暫時性儲存空間118可經保留用於儲存待更新之資料(例如，輸入緩衝區)。
圖18展示可實施解碼器設備140 (或140A)及/或IMDCT 147及/或執行方法160之設備120。設備120可包含處理器121及非暫時性記憶體單元122，其中區塊124儲存指令，該等指令在由處理器121執行時可使得處理器121尤其執行MDCT合成過程。設備120可包含輸入單元126，其可獲得在FD中之資訊信號(例如，音訊信號)之經解碼表示。處理器121可因此執行處理以獲得資訊信號之TD表示。可使用輸出單元127將此經解碼表示提供至外部單元。輸出單元127可包含例如通訊單元以與外部裝置(例如，使用無線通訊，諸如藍芽)及/或外部儲存空間通訊。處理器121可將音訊信號之經解碼表示儲存在本端儲存空間128中。
在實例中，設備110與120可為相同裝置。在實例中，設備110與120例如無線地(例如，使用協定藍芽)交換資訊信號及/或控制資料。
取決於特定實施要求，實例可以硬體實施。可使用數字儲存媒體執行該實施，例如軟碟、數位多功能光碟(DVD)、藍光光碟、緊密光碟(CD)、唯讀記憶體(ROM)、可規劃唯讀記憶體(PROM)、可擦除及可規劃唯讀記憶體(EPROM)、電可擦除可規劃唯讀記憶體(EEPROM)或快閃記憶體，其上儲存有電子可讀控制信號，其與可規劃電腦系統協作(或能夠協作)使得執行相應方法。因此，數位儲存媒體可為電腦可讀的。
通常，實例可實施為具有程式指令之電腦程式產品，當電腦程式產品執行於電腦上時，程式指令操作性地用於執行該等方法中之一者。程式指令可例如儲存於機器可讀媒體上。
其他實例包含用於執行本文所描述之方法中之一者、儲存於機器可讀載體上之電腦程式。換言之，方法之實例因此為電腦程式，其具有用於在電腦程式於電腦上執行時執行本文中所描述之方法中之一者的程式指令。
方法之另一實例因此為資料載體媒體(或數位儲存媒體，或電腦可讀媒體)，其上包含、記錄用於執行本文所描述之方法中之一者的電腦程式。資料載體媒體、數位儲存媒體或記錄媒體為有形及/或非瞬變的，而非無形及暫時性的信號。
另一實例包含處理單元，例如電腦或可規劃邏輯裝置，其執行本文所描述之方法中之一者。
另一實例包含電腦，其上安裝有用於執行本文中所描述之方法中之一者的電腦程式。
另一實例包含將用於執行本文所描述之方法中之一者的電腦程式傳送(例如以電子方式或以光學方式)至接收器之設備或系統。舉例而言，接收器可為電腦、行動裝置、記憶體裝置或其類似者。設備或系統可(例如)包含用於傳送電腦程式至接收器之檔案伺服器。
在一些實例中，可規劃邏輯裝置(例如，場可規劃閘陣列)可用以執行本文中所描述之方法的功能性中之一些或全部。在一些實例中，場可規劃閘陣列可與微處理器協作，以便執行本文中所描述之方法中的一者。通常，該等方法可由任何適當的硬體設備執行。
上述實例說明上文所論述的原理。應理解，本文中所描述的配置及細節之修改及變化將為顯而易見的。因此，希望受到接下來的申請專利範圍之範圍限制，而不受藉由本文中之實例之描述及解釋所呈現的特定細節限制。
7. 開窗函數之一些實例
此處提供數值實例。由於尚未發現用於獲得函數之呈閉合形式之數學公式，因此在此提供實例。下文中可以反向或前向次序提供值，即在一些實例中，第一值與時刻n=0相關聯，最末值與最末時刻n=2N-1相關聯(正向方向)，而在一些實例中，第一值與時刻n=2N-1相關聯，而最末值與第一時刻n=0相關聯(反轉方向)。在一些情況下，分析開窗函數與合成開窗函數係獲自相同清單，但分析開窗函數係在反轉或前向)方向上讀取，而合成開窗函數係在前向(或反轉)方向上讀取。
為了體現以下實例中之至少一者，有可能提取至少10個值之子系列(例如，連續值)，此時該10個值不同於0 (例如，所有樣本或至少其大多數可形成至少10個值)。
1%之容限可為可能的，在一些情況下，0.5%、0.05%，在一些情況下2%、5%，在其他情況下0%。
7.1 與圖4及圖9相關聯之實例
在實例中，諸如-7.078546706512391e-04f之表示法意謂-7.078546706512391*10-4
「f」係指浮點表示法(在一些情況下，其可省略)。
對於訊框大小N=80，開窗函數
之數值實例在此藉由160個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
-7.078546706512391e-04f, -2.098197727900724e-03f, -4.525198076002370e-03f,
-8.233976327300612e-03f, -1.337713096257934e-02f, -1.999721557401502e-02f,
-2.800909464274782e-02f, -3.721502082245055e-02f, -4.731768261606175e-02f,
-5.794654834034055e-02f, -6.867606753531441e-02f, -7.904647440788692e-02f,
-8.859705468085925e-02f, -9.688303623049199e-02f, -1.034961241263523e-01f,
-1.080766457616878e-01f, -1.103242262600913e-01f, -1.099809851424550e-01f,
-1.068172142230882e-01f, -1.006190418791648e-01f, -9.116452506492527e-02f,
-7.820617483254730e-02f, -6.146688124166948e-02f, -4.063362855701623e-02f,
-1.536329520788766e-02f, +1.470155068746303e-02f, +4.989736509080558e-02f,
+9.050369257152079e-02f, +1.366911019414417e-01f, +1.884686389218322e-01f,
+2.456456803467095e-01f, +3.077789078889820e-01f, +3.741642373060188e-01f,
+4.438114799213576e-01f, +5.154735456539700e-01f, +5.876661722564289e-01f,
+6.587619767809000e-01f, +7.270576699841359e-01f, +7.908752989295335e-01f,
+8.486643364959733e-01f, +8.991320235484349e-01f, +9.413348145272842e-01f,
+9.747634827941575e-01f, +9.994114730415857e-01f, +1.015760373791603e+00f,
+1.024736164069697e+00f, +1.027634294456205e+00f, +1.025991493983836e+00f,
+1.021427210603284e+00f, +1.015439859549357e+00f, +1.009366925499550e+00f,
+1.003508162416449e+00f, +9.988898206257559e-01f, +9.953133902427869e-01f,
+9.925943919208190e-01f, +9.905771957917731e-01f, +9.891371616557014e-01f,
+9.881790747212391e-01f, +9.876249269174586e-01f, +9.874056275509585e-01f,
+9.874524849192456e-01f, +9.876951134084213e-01f, +9.880640617030884e-01f,
+9.884926873551375e-01f, +9.889230031022089e-01f, +9.893074965384659e-01f,
+9.896146331889107e-01f, +9.898319269347060e-01f, +9.899693102025342e-01f,
+9.900603352632121e-01f, +9.901575015155720e-01f, +9.903255289051605e-01f,
+9.906303787150326e-01f, +9.911298894709990e-01f, +9.918665491182922e-01f,
+9.928619727154252e-01f, +9.941156069136238e-01f, +9.956033775539884e-01f,
+9.972793109558521e-01f, +9.990784840729244e-01f, +1.000922365901945e+00f,
+1.002728111386909e+00f, +1.004416038098237e+00f, +1.005919224127911e+00f,
+1.007189345025525e+00f, +1.008200146369426e+00f, +1.008949493525753e+00f,
+1.009458241425143e+00f, +1.009768980817384e+00f, +1.009940336228694e+00f,
+1.010039453539107e+00f, +1.010132323996401e+00f, +1.010272524848519e+00f,
+1.010494354532353e+00f, +1.010808068774316e+00f, +1.011201071127927e+00f,
+1.011641272406023e+00f, +1.012080125934687e+00f, +1.012458183122033e+00f,
+1.012706955800289e+00f, +1.012755013843985e+00f, +1.012530134411619e+00f,
+1.011962331100864e+00f, +1.010982135506986e+00f, +1.009512438049510e+00f,
+1.007460860286395e+00f, +1.004708677491086e+00f, +1.001111413242302e+00f,
+9.965041017623596e-01f, +9.907199995730845e-01f, +9.823765865983288e-01f,
+9.708821747608998e-01f, +9.546732976073705e-01f, +9.321553861564006e-01f,
+9.018003682081348e-01f, +8.623984077953557e-01f, +8.132817365236141e-01f,
+7.544551974836834e-01f, +6.866580716267418e-01f, +6.113488038789190e-01f,
+5.306181649316597e-01f, +4.471309850999502e-01f, +3.639114681156236e-01f,
+2.841647033392408e-01f, +2.110209448747969e-01f, +1.472287968327703e-01f,
+9.482665349502291e-02f, +5.482436608328477e-02f, +2.701461405056264e-02f,
+9.996743588367519e-03f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f, +0.000000000000000e+00f, +0.000000000000000e+00f,
+0.000000000000000e+00f
對於訊框大小N=160，開窗函數
之數值實例在此藉由320個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
-4.619898752628163e-04f, -9.747166718929050e-04f, -1.664473096973725e-03f,
-2.597106916737789e-03f, -3.806285163352241e-03f, -5.324608721716763e-03f,
-7.175885277771099e-03f, -9.382480860899108e-03f, -1.195270300743193e-02f,
-1.489528159506296e-02f, -1.820666399965468e-02f, -2.187570925786862e-02f,
-2.588471937157619e-02f, -3.020862738245264e-02f, -3.481597793538342e-02f,
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-5.526334794593565e-02f, -6.063717235243996e-02f, -6.600961519440657e-02f,
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在此提供對於訊框大小N=240之開窗函數
之數值實例(480個樣本)：
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在此提供對於訊框大小N=320之開窗函數
之數值實例(640個樣本)：
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在此提供對於訊框大小N=480之開窗函數
之數值實例(960個樣本)：
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在此提供對於訊框大小N=960之開窗函數
之數值實例(1920個樣本)：
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+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
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7.2與圖26至圖30相關聯之實例
對於訊框大小N=40，開窗函數
之數值實例在此藉由80個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
+9.959086585790517e-04, +3.819056787237678e-03, +9.540832613229890e-03,
+1.921659800166160e-02, +3.382719081038548e-02, +5.424831667522354e-02,
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+2.049363422022628e-01, +2.601166575816199e-01, +3.212814164616093e-01,
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+6.003522489375573e-01, +6.706896380227332e-01, +7.378044458510402e-01,
+8.000925313431716e-01, +8.561409184410547e-01, +9.048272294524792e-01,
+9.453685031730190e-01, +9.773507430600533e-01, +1.000800872826561e+00,
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+9.892206942816891e-01, +9.879658322200813e-01, +9.881273531631907e-01,
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+5.282077505750667e-01, +4.486552956056635e-01, +3.691875990296312e-01,
+2.924566408966777e-01, +2.210718537110463e-01, +1.573148583944309e-01,
+1.030525757797768e-01, +5.982732244758054e-02, +2.871831923385133e-02,
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+0.000000000000000e+00, +0.000000000000000e+00.
對於訊框大小N=80，開窗函數之數值實例在此藉由160個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
+6.143388180964179e-04, +1.489582832987000e-03, +2.884104959764029e-03,
+4.934298832466617e-03, +7.779130464154915e-03, +1.154910606525086e-02,
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+4.286789889246253e-01, +3.889032719013045e-01, +3.496431418636314e-01,
+3.112360816586544e-01, +2.740128472224535e-01, +2.382847225401666e-01,
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+1.156385879569741e-01, +9.115821766571995e-02, +6.952749039054593e-02,
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+1.338005016725895e-02, +6.640506529168652e-03, +0.000000000000000e+00,
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+0.000000000000000e+00.
對於訊框大小N=120，開窗函數
之數值實例在此藉由240個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
+5.087227626168386e-04, +9.959086585790517e-04, +1.682208006328800e-03,
+2.609697259047744e-03, +3.819056787237678e-03, +5.349319592933909e-03,
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+5.543129276657669e-01, +5.282077505750727e-01, +5.018369724442092e-01,
+4.752902962082383e-01, +4.486552956056652e-01, +4.220281118338883e-01,
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+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
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+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00.
對於訊框大小N=160，開窗函數
之數值實例在此藉由320個條目提供(對於n = 0…2N-1)。如上所解釋，最末的值可連續為0。
+4.595886345493055e-04, +7.919323614002698e-04, +1.227927169310031e-03,
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+0.000000000000000e+00, +0.000000000000000e+00, +0.000000000000000e+00,
+0.000000000000000e+00, +0.000000000000000e+00.
在此提供對於訊框大小N=240之開窗函數之數值實例(480個樣本)：
+4.090106504820579e-04, +6.143388180964179e-04, +8.571759876954877e-04,
+1.147015057857495e-03, +1.489582832987000e-03, +1.889770382231583e-03,
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在此提供對於訊框大小N=320之開窗函數之數值實例(640個樣本)。如上所解釋，最末的值可為0。
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在此提供對於訊框大小N=480之開窗函數之數值實例(960個樣本)。如上所解釋，最末的值可為0。
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在此提供對於訊框大小N=960之開窗函數之數值實例(1920個樣本)。如上所解釋，最末的值可為0。
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8 參考文獻
[1] 3GPP, "Codec for Enhanced Voice Services (EVS); Detailed algorithmic description," [Online]. Available: http://www.3gpp.org/ftp/Specs/archive/26_series/26.445/26445-d00.zip.
[2] P. P. Julien Faure, "Delay-optimized overlap transform, coding/decoding weighting windows". US Patent US8847795, 28 06 2011.
[3] Geiger, Audio Coding based on integer transform, Ilmenau: https://www.db-thueringen.de/receive/dbt_mods_00010054, 2004.
40、240‧‧‧分析開窗函數
40'、60'、90'、240'、290'‧‧‧線性函數
41、61'、91、241、291‧‧‧第一區間
41'‧‧‧絕對最大值
42、62'、92、242、292‧‧‧第二區間
42'、242'‧‧‧相對最小值
43、63'、93、243、293‧‧‧第三區間
43'、243'‧‧‧相對最大值
44、64、94、244、294‧‧‧曲折部分
45‧‧‧初始遞減部分
46、97、246、297‧‧‧快速遞增部分
47、96、247、296‧‧‧快速遞減部分
48、98、248、298‧‧‧連續空值部分
50‧‧‧MDCT窗係數
60、70、70'、‧‧‧開窗函數
64'‧‧‧第四區間
65'‧‧‧第五區間
81‧‧‧區塊1
82‧‧‧區塊2
90‧‧‧合成線性函數
95‧‧‧最終遞增部分
110、130、130A‧‧‧編碼器
111、121‧‧‧處理器
112、122‧‧‧非暫時性記憶體單元
113、114、124‧‧‧區塊
116‧‧‧輸入單元
117、126‧‧‧通訊單元
118‧‧‧暫時性儲存空間
120‧‧‧設備
127‧‧‧輸出單元
128‧‧‧本端儲存空間
131‧‧‧MDCT工具
132‧‧‧LPC區塊
132A‧‧‧SNS工具
133‧‧‧時間雜訊塑形TNS工具
134‧‧‧頻譜量化器
135‧‧‧寫碼器
136‧‧‧雜訊位準估計器
137‧‧‧位元串流寫入器
137a‧‧‧頻寬偵測器
138a‧‧‧重取樣工具
138b‧‧‧長期後濾波LTPF工具
140、140A、142‧‧‧解碼器
141‧‧‧位元串流多工工具
143‧‧‧雜訊填充工具
144‧‧‧全域增益工具
145‧‧‧TNS解碼器工具
146‧‧‧MDCT (或MDST)塑形工具
146a‧‧‧LPC解碼工具
146A'‧‧‧SNS解碼器工具
147‧‧‧逆經調變重疊變換工具
148‧‧‧LTPF工具
149‧‧‧解碼器頻寬控制器
150、160‧‧‧方法
211‧‧‧ALDO窗形狀
212‧‧‧中間窗形狀
213‧‧‧新發明窗形狀
231‧‧‧ALDO曲線圖頻率回應
232‧‧‧中間曲線圖頻率回應
233‧‧‧新發明曲線圖頻率回應
251‧‧‧所提出的發明
290‧‧‧合成開窗函數
1902、3102‧‧‧本發明開窗函數之第1數值微分
1904、3104‧‧‧本發明開窗函數之第1數值微分之經加權版本
1910、3110‧‧‧本發明開窗函數之第2數值微分之經加權版本
1920‧‧‧本發明開窗函數之第3數值微分之經加權版本
2002‧‧‧ALDO開窗函數之第1數值微分
2004‧‧‧ALDO開窗函數之第1數值微分之經加權版本
2010‧‧‧ALDO開窗函數之第2數值微分之經加權版本
2020‧‧‧ALDO開窗函數之第3數值微分之經加權版本
2021‧‧‧峰值
3120‧‧‧ALDO開窗函數之第3數值微分之經加權版本
圖1及圖2展示根據先前技術之方案。
圖3至圖12展示根據實例之函數之方案。
圖13及圖13A展示根據實例之編碼器。
圖14及圖14A展示根據實例之解碼器。
圖15及圖16展示根據實例之方法。
圖17及圖18展示根據實例之設備。
圖19展示根據實例之方案。
圖20展示根據先前技術之方案。
圖21至圖25展示根據實例之方案。
圖26至圖31展示根據實例之函數之方案。
40‧‧‧分析開窗函數
40'‧‧‧線性函數
41‧‧‧第一區間
41'‧‧‧絕對最大值
42‧‧‧第二區間
42'‧‧‧相對最小值
43‧‧‧第三區間
43'‧‧‧相對最大值
44‧‧‧曲折部分
45‧‧‧初始遞減部分
46‧‧‧快速遞增部分
47‧‧‧快速遞減部分
48‧‧‧連續空值部分
Claims (44)
- 一種用於對包含複數個訊框之音訊信號進行編碼之設備，該設備包含：一經調變重疊變換工具，用於將該音訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該經調變重疊變換工具組配來使用一分析開窗函數執行一經調變重疊變換分析，該分析開窗函數具有與至少四個點對應地與一線性函數交叉之一判定部分；以及一位元串流寫入器，其組配來基於該音訊信號或其一經處理版本之該FD表示來準備一位元串流，其中該分析開窗函數係界定成呈不對稱，其中該分析開窗函數係界定成在該判定部分中：在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，其中該分析開窗函數係界定成使得絕對最大值處於該第一區間與該第三區間中之一者中，其中該線性函數為具有常數值1之一常數函數。
- 如請求項1之設備，其中該分析開窗函數係界定成使得該分析開窗函數之最大值在同一時刻比該線性函數之該值大出小於25%。
- 如請求項1之設備，其中該經調變重疊變換工具組配來：用該分析開窗函數之值按比例調整時間輸入緩衝區及/或餘弦或正弦值。
- 如請求項3之設備，其中該經調變重疊變換工具組配來使用呈以下形式之輸入緩衝區：t(n)=x(Z-N F +n)對於n=0..2N F -1-Z，及t(2N-Z+n)=0對於n=0..Z-1其中x(n)為該音訊信號或該音訊信號之一經處理版本在時刻n之一TD樣本，N F 為在一個訊框中處理的樣本之數目，且Z為經調變重疊變換窗中的前導零之數目。
- 如請求項1之設備，其中該經調變重疊變換工具組配來執行：對於k=0..N F -1其中X(k)為在一頻率索引k處的經調變重疊變換頻率值，n為時間常數，w N (n)為分析開窗函數，t(n)為一時間輸入緩衝區，且N F 為在一個訊框中處理的樣本之數目。
- 一種用於對在頻域FD中界定的音訊信號或其經處理版本進行解碼之設備，該設備包含：一位元串流讀取器，其組配來讀取將該音訊信號予以編碼之一位元串流；以及一逆經調變重疊變換工具，其組配來使用一合成開窗函數對該資訊信號或其一經處理版本執行一逆經調變重疊 變換合成，該合成開窗函數具有與至少四個點對應地與一線性函數交叉之一判定部分，其中該合成開窗函數係界定成呈不對稱，其中該合成開窗函數係界定成在該判定部分中：在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，其中該合成開窗函數係界定成使得絕對最大值處於該第一區間與該第三區間中之一者中，其中該線性函數為具有常數值1之一常數函數。
- 如請求項6之設備，其中該合成開窗函數係界定成使得該合成開窗函數之最大值在同一時刻比該線性函數之該值大出小於25%。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來：用該合成開窗函數之值按比例調整一時域混疊緩衝區處之值。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來以如下形式產生一時域TD信號表示：對於n=0..2N F -1 其中
(n)為一混疊緩衝區，
(k)為該音訊信號或其一經處理版本，且N F 為一TD訊框的樣本之數目。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來：執行該時間混疊緩衝區之一開窗。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來藉由執行以下操作而執行一開窗運算：對於n=0..2N F -1。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來執行一疊加運算。
- 如請求項6之設備，其中該逆經調變重疊變換工具組配來如下執行一疊加運算：對於n=0..N F -Z-1
對於n=N F -Z..N F -1
對於n=0..N F -Z-1其中
(n)為輸出值，
(.)為一經開窗時間混疊緩衝區，且N F 為一個訊框中的樣本之數目。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成使得在該判定部分中，一相對最大值處於該第一區間或該第三區間中，且一相對最小值處於該第二區間中。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成在該判定部分中在由兩個訊框之30%與50%構成的一區間中 存在大於該線性函數之一值。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成使得該分析開窗函數及/或該合成開窗函數之最大值在同一時刻比該線性函數之該值大出小於25%。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成使得該分析開窗函數及/或該合成開窗函數之最大值在同一時刻比該線性函數之該值大出小於5%。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成存在介於-3 * 10-4與+3 * 10-4之間的一第二數值微分。
- 如請求項1或6之設備，其中：該分析開窗函數及/或該合成開窗函數係界定成存在介於-2 * 10-5與+2 * 10-5之間的一第三數值微分。
- 如請求項1或6之設備，其中：該分析開窗函數與該合成開窗函數係界定為彼此之時間反轉版本。
- 如請求項1或6之設備，其進一步包含：一儲存空間，用以儲存該分析開窗函數及/或該合成開窗函數之該等值。
- 如請求項1或6之設備，其中經修改重疊變換為一經修改離散餘弦變換MDCT或一經修改離散正弦變換MDST，且逆經修改重疊變換為一逆經修改離散餘弦 變換IMDCT或逆經修改離散正弦變換IMDST。
- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：-7.078546706512391e-04f,-2.098197727900724e-03f,-4.525198076002370e-03f,-8.233976327300612e-03f,-1.337713096257934e-02f,-1.999721557401502e-02f,-2.800909464274782e-02f,-3.721502082245055e-02f,-4.731768261606175e-02f,-5.794654834034055e-02f,-6.867606753531441e-02f,-7.904647440788692e-02f,-8.859705468085925e-02f,-9.688303623049199e-02f,-1.034961241263523e-01f,-1.080766457616878e-01f,-1.103242262600913e-01f,-1.099809851424550e-01f,-1.068172142230882e-01f,-1.006190418791648e-01f,-9.116452506492527e-02f,-7.820617483254730e-02f,-6.146688124166948e-02f,-4.063362855701623e-02f,-1.536329520788766e-02f,+1.470155068746303e-02f,+4.989736509080558e-02f,+9.050369257152079e-02f,+1.366911019414417e-01f,+1.884686389218322e-01f,+2.456456803467095e-01f,+3.077789078889820e-01f,+3.741642373060188e-01f,+4.438114799213576e-01f,+5.154735456539700e-01f,+5.876661722564289e-01f,+6.587619767809000e-01f,+7.270576699841359e-01f,+7.908752989295335e-01f,+8.486643364959733e-01f,+8.991320235484349e-01f,+9.413348145272842e-01f,+9.747634827941575e-01f,+9.994114730415857e-01f,+1.015760373791603e+00f,+1.024736164069697e+00f,+1.027634294456205e+00f,+1.025991493983836e+00f,+1.021427210603284e+00f,+1.015439859549357e+00f,+1.009366925499550e+00f,+1.003508162416449e+00f,+9.988898206257559e-01f,+9.953133902427869e-01f,+9.925943919208190e-01f,+9.905771957917731e-01f,+9.891371616557014e-01f,+9.881790747212391e-01f,+9.876249269174586e-01f,+9.874056275509585e-01f,+9.874524849192456e-01f,+9.876951134084213e-01f,+9.880640617030884e-01f,+9.884926873551375e-01f,+9.889230031022089e-01f,+9.893074965384659e-01f,+9.896146331889107e-01f,+9.898319269347060e-01f,+9.899693102025342e-01f,+9.900603352632121e-01f,+9.901575015155720e-01f,+9.903255289051605e-01f,+9.906303787150326e-01f,+9.911298894709990e-01f,+9.918665491182922e-01f,+9.928619727154252e-01f,+9.941156069136238e-01f,+9.956033775539884e-01f,+9.972793109558521e-01f,+9.990784840729244e-01f,+1.000922365901945e+00f,+1.002728111386909e+00f,+1.004416038098237e+00f,+1.005919224127911e+00f,+1.007189345025525e+00f,+1.008200146369426e+00f,+1.008949493525753e+00f,+1.009458241425143e+00f,+1.009768980817384e+00f,+1.009940336228694e+00f, +1.010039453539107e+00f,+1.010132323996401e+00f,+1.010272524848519e+00f,+1.010494354532353e+00f,+1.010808068774316e+00f,+1.011201071127927e+00f,+1.011641272406023e+00f,+1.012080125934687e+00f,+1.012458183122033e+00f,+1.012706955800289e+00f,+1.012755013843985e+00f,+1.012530134411619e+00f,+1.011962331100864e+00f,+1.010982135506986e+00f,+1.009512438049510e+00f,+1.007460860286395e+00f,+1.004708677491086e+00f,+1.001111413242302e+00f,+9.965041017623596e-01f,+9.907199995730845e-01f,+9.823765865983288e-01f,+9.708821747608998e-01f,+9.546732976073705e-01f,+9.321553861564006e-01f,+9.018003682081348e-01f,+8.623984077953557e-01f,+8.132817365236141e-01f,+7.544551974836834e-01f,+6.866580716267418e-01f,+6.113488038789190e-01f,+5.306181649316597e-01f,+4.471309850999502e-01f,+3.639114681156236e-01f,+2.841647033392408e-01f,+2.110209448747969e-01f,+1.472287968327703e-01f,+9.482665349502291e-02f,+5.482436608328477e-02f,+2.701461405056264e-02f,+9.996743588367519e-03f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f,+0.000000000000000e+00f。
- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：-4.619898752628163e-04f,-9.747166718929050e-04f,-1.664473096973725e-03f,-2.597106916737789e-03f,-3.806285163352241e-03f,-5.324608721716763e-03f,-7.175885277771099e-03f,-9.382480860899108e-03f,-1.195270300743193e-02f,-1.489528159506296e-02f,-1.820666399965468e-02f,-2.187570925786862e-02f,-2.588471937157619e-02f,-3.020862738245264e-02f,-3.481597793538342e-02f,-3.967067992672979e-02f,-4.472698045914417e-02f,-4.994225863256500e-02f,-5.526334794593565e-02f,-6.063717235243996e-02f.-6.600961519440657e-02f, 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- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：-3.613496418928369e-04f,-7.078546706512391e-04f,-1.074443637110903e-03f,-1.533478537964509e-03f,-2.098197727900724e-03f,-2.778420871815740e-03f,-3.584129920673041e-03f,-4.525198076002370e-03f,-5.609327243712055e-03f,-6.843234536105624e-03f,-8.233976327300612e-03f,-9.785314755557023e-03f,-1.149880303071551e-02f,-1.337713096257934e-02f,-1.542181679511618e-02f, 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- 如請求項1或6之設備，其中該分析開窗函 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- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+9.959086585790517e-04,+3.819056787237678e-03,+9.540832613229890e-03,+1.921659800166160e-02,+3.382719081038548e-02,+5.424831667522354e-02,+8.120777668775610e-02,+1.152171887125930e-01,+1.564942331034909e-01,+2.049363422022628e-01,+2.601166575816199e-01,+3.212814164616093e-01,+3.873472997948746e-01,+4.569497078592333e-01,+5.285192958868393e-01,+6.003522489375573e-01,+6.706896380227332e-01,+7.378044458510402e-01,+8.000925313431716e-01,+8.561409184410547e-01,+9.048272294524792e-01,+9.453685031730190e-01,+9.773507430600533e-01,+1.000800872826561e+00,+1.016171590112097e+00,+1.024315247630982e+00,+1.026415431432931e+00,+1.023858366571912e+00,+1.018135705524407e+00,+1.010794822557756e+00,+1.003406509762925e+00,+9.967831265986109e-01,+9.920995520917141e-01,+9.892206942816891e-01,+9.879658322200813e-01,+9.881273531631907e-01,+9.894805541465801e-01,+9.917849916000535e-01,+9.947847580943504e-01,+9.982119669301160e-01,+1.001791235858836e+00,+1.005242583245485e+00,+1.008283053756130e+00,+1.010631281038659e+00,+1.012015300253356e+00,+1.012180753005270e+00,+1.010896765282633e+00,+1.007963362035220e+00, +1.003227255072391e+00,+9.966050551498514e-01,+9.868284225039941e-01,+9.731250287581631e-01,+9.540636479502398e-01,+9.283864275822276e-01,+8.950916858157935e-01,+8.534769362643825e-01,+8.032090930429980e-01,+7.444735201251689e-01,+6.780787033699449e-01,+6.053970453856138e-01,+5.282077505750667e-01,+4.486552956056635e-01,+3.691875990296312e-01,+2.924566408966777e-01,+2.210718537110463e-01,+1.573148583944309e-01,+1.030525757797768e-01,+5.982732244758054e-02,+2.871831923385133e-02,+9.683884928956490e-03,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00。
- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+6.143388180964179e-04,+1.489582832987000e-03,+2.884104959764029e-03,+4.934298832466617e-03,+7.779130464154915e-03,+1.154910606525086e-02,+1.637155619860352e-02,+2.237116158648752e-02,+2.966159685753317e-02,+3.835663329277230e-02,+4.855610986150206e-02,+6.035055738891727e-02,+7.382288203064732e-02,+8.903563687211119e-02,+1.060356225286319e-01,+1.248534855777947e-01,+1.454931890869180e-01,+1.679435556337752e-01,+1.921728622634411e-01,+2.181238261985594e-01,+2.457259744642953e-01,+2.748839432649996e-01,+3.054824712370942e-01,+3.373873799614014e-01,+3.704415932452488e-01,+4.044749630814483e-01,+4.393004362003260e-01,+4.747225454237193e-01,+5.105341492548225e-01,+5.465201916422433e-01,+5.824658100332457e-01,+6.181452662624718e-01,+6.533411462740817e-01,+6.878367295965062e-01,+7.214176027060971e-01,+7.538887973483771e-01,+7.850546571907628e-01,+8.147397447696774e-01,+8.427819363777799e-01,+8.690376742017057e-01,+8.933935477349644e-01,+9.157483563218768e-01,+9.360270196617569e-01,+9.541731142261065e-01,+9.701635474343885e-01,+9.840036439809510e-01,+9.957199420334376e-01,+1.005374268639838e+00,+1.013046655758663e+00,+1.018843380560658e+00,+1.022896948293643e+00,+1.025355286710874e+00,+1.026382881625701e+00,+1.026155530733488e+00,+1.024853974580724e+00,+1.022664602721801e+00,+1.019779396547454e+00,+1.016391686789653e+00,+1.012697033320358e+00,+1.008885191761748e+00, +1.005378742804807e+00,+1.001563778373068e+00,+9.982531564931281e-01,+9.954346644968789e-01,+9.930950268060122e-01,+9.912170911359961e-01,+9.897805192546195e-01,+9.887624937408933e-01,+9.881383235740961e-01,+9.878819413827574e-01,+9.879662130250981e-01,+9.883630508181326e-01,+9.890434070785485e-01,+9.899772316163624e-01,+9.911334564321237e-01,+9.924800441092685e-01,+9.939841207305906e-01,+9.956121471675398e-01,+9.973300590248015e-01,+9.991033633647473e-01,+1.000897441314013e+00,+1.002677088643863e+00,+1.004407190937699e+00,+1.006052289109999e+00,+1.007576934100958e+00,+1.008945862447015e+00,+1.010124241309341e+00,+1.011077969726137e+00,+1.011773962181442e+00,+1.012180362866919e+00,+1.012266707295288e+00,+1.012004064757857e+00,+1.011365223023975e+00,+1.010324996851905e+00,+1.008860731864438e+00,+1.006952983357691e+00,+1.004586273379809e+00,+1.001749900308864e+00,+9.984386632116344e-01,+9.946500332901397e-01,+9.895756853352172e-01,+9.838303127859196e-01,+9.769999155793757e-01,+9.689141159310996e-01,+9.594038121639412e-01,+9.483086322505029e-01,+9.354860218216989e-01,+9.208101305030523e-01,+9.041732260327581e-01,+8.854882249661838e-01,+8.646864947605046e-01,+8.417237467711145e-01,+8.165875713256009e-01,+7.892986353718001e-01,+7.599171886893816e-01,+7.285474515411827e-01,+6.953282935906302e-01,+6.604334017809461e-01,+6.240661431421666e-01,+5.864461424698465e-01,+5.478160663871147e-01,+5.084499758302218e-01,+4.686361426418982e-01,+4.286789889246253e-01,+3.889032719013045e-01,+3.496431418636314e-01,+3.112360816586544e-01,+2.740128472224535e-01,+2.382847225401666e-01,+2.043379825955252e-01,+1.724305860483632e-01,+1.427939789949265e-01,+1.156385879569741e-01,+9.115821766571995e-02,+6.952749039054593e-02,+5.088975408628225e-02,+3.533430192568954e-02,+2.286680405144430e-02,+1.338005016725895e-02,+6.640506529168652e-03,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00。
- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下 值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+5.087227626168386e-04,+9.959086585790517e-04,+1.682208006328800e-03,+2.609697259047744e-03,+3.819056787237678e-03,+5.349319592933909e-03,+7.243906383895192e-03,+9.540832613229890e-03,+1.227637642543709e-02,+1.548950238899404e-02,+1.921659800166160e-02,+2.349369619441617e-02,+2.835199581667961e-02,+3.382719081038548e-02,+3.994939538719628e-02,+4.674775238543380e-02,+5.424831667522354e-02,+6.247770776443612e-02,+7.145835917501348e-02,+8.120777668775610e-02,+9.174400412319896e-02,+1.030764959637497e-01,+1.152171887125930e-01,+1.281665713944242e-01,+1.419264381068653e-01,+1.564942331034909e-01,+1.718593189799504e-01,+1.880134254543744e-01,+2.049363422022628e-01,+2.226123055761096e-01,+2.410151242797736e-01,+2.601166575816199e-01,+2.798871008989962e-01,+3.002880135563586e-01,+3.212814164616093e-01,+3.428208463088390e-01,+3.648596557863134e-01,+3.873472997948746e-01,+4.102294951869188e-01,+4.334494534591082e-01,+4.569497078592333e-01,+4.806696403251166e-01,+5.045473815014847e-01,+5.285192958868393e-01,+5.525196099932443e-01,+5.764872452085427e-01,+6.003522489375573e-01,+6.240509872809882e-01,+6.475182586093196e-01,+6.706896380227332e-01,+6.935029068990036e-01,+7.158927516396895e-01,+7.378044458510402e-01,+7.591787241845952e-01,+7.799586608897265e-01,+8.000925313431716e-01,+8.195318652294690e-01,+8.382288957404715e-01,+8.561409184410547e-01,+8.732316951214179e-01,+8.894702022170831e-01,+9.048272294524792e-01,+9.192736375782965e-01,+9.327940405054362e-01,+9.453685031730190e-01,+9.569883933538136e-01,+9.676486424195593e-01,+9.773507430600533e-01,+9.861027831072527e-01,+9.939122412655677e-01,+1.000800872826561e+00,+1.006787811971719e+00,+1.011901269172423e+00,+1.016171590112097e+00,+1.019636414864842e+00,+1.022336613864005e+00,+1.024315247630982e+00,+1.025621299895396e+00,+1.026303439275662e+00,+1.026415431432931e+00,+1.026007933174836e+00,+1.025137435167917e+00,+1.023858366571912e+00,+1.022226936424625e+00,+1.020300550334848e+00,+1.018135705524407e+00,+1.015792146756340e+00,+1.013325966774524e+00,+1.010794822557756e+00,+1.008265131568879e+00,+1.006046874304407e+00,+1.003406509762925e+00,+1.000977398831985e+00,+9.987704535700208e-01,+9.967831265986109e-01,+9.950118905889862e-01,+9.934523971504882e-01,+9.920995520917141e-01,+9.909475998606236e-01,+9.899902426925508e-01,+9.892206942816891e-01,+9.886318043013834e-01, 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- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+4.595886345493055e-04,+7.919323614002698e-04,+1.227927169310031e-03,+1.783653266717233e-03,+2.479549413444207e-03,+3.329799454594261e-03,+4.353535478916468e-03,+5.564965156664018e-03,+6.986108359341676e-03,+8.629882322202329e-03,+1.051343406844975e-02,+1.265082642578719e-02,+1.506090447446532e-02,+1.775591229287213e-02,+2.075475983187825e-02,+2.406813715401559e-02,+2.771207863541604e-02,+3.169933248543932e-02,+3.604609640533871e-02,+4.076128638095439e-02,+4.586038120884381e-02,+5.135136676471998e-02,+5.724780220726930e-02,+6.355854744461048e-02,+7.029450733434550e-02,+7.745987198268531e-02,+8.506635369887924e-02,+9.311641620512773e-02,+1.016162955027316e-01,+1.105690806271684e-01,+1.199789286645804e-01,+1.298417294090302e-01,+1.401623800497866e-01,+1.509371564593891e-01,+1.621632295622287e-01,+1.738354123649302e-01,+1.859520359191026e-01,+1.985008828937603e-01,+2.114778554475382e-01,+2.248732557074316e-01,+2.386763947872762e-01,+2.528729453658238e-01,+2.674547009618951e-01,+2.824031465430401e-01,+2.977050145264297e-01,+3.133419120661713e-01,+3.292976696294886e-01,+3.455490160824131e-01,+3.620795045342974e-01,+3.788648665671841e-01,+3.958851576591690e-01,+4.131143794748322e-01,+4.305308301005456e-01,+4.481076715576617e-01,+4.658227790464821e-01,+4.836466393241829e-01,+5.015564851667653e-01,+5.195228071176610e-01,+5.375197039843709e-01,+5.555183841040963e-01,+5.734957812557457e-01,+5.914186654649489e-01,+6.092622887527459e-01,+6.269981160888640e-01,+6.446002007776794e-01,+6.620384583071039e-01, 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- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+4.090106504820579e-04,+6.143388180964179e-04,+8.571759876954877e-04,+1.147015057857495e-03,+1.489582832987000e-03,+1.889770382231583e-03,+2.353000800169909e-03,+2.884104959764029e-03,+3.488213786635855e-03,+4.170040431489613e-03,+4.934298832466617e-03,+5.787076505403503e-03,+6.733811743137561e-03,+7.779130464154915e-03,+8.927044958757816e-03,+1.018202888968871e-02,+1.154910606525086e-02,+1.303349217699797e-02,+1.463951288465963e-02,+1.637155619860352e-02,+1.823455383898077e-02,+2.023309488998589e-02,+2.237116158648752e-02,+2.465237348403478e-02,+2.708101935270475e-02,+2.966159685753317e-02,+3.239884850877327e-02,+3.529601774976465e-02,+3.835663329277230e-02,+4.158447932459513e-02,+4.498322421745353e-02,+4.855610986150206e-02,+5.230596475016741e-02,+5.623624576084146e-02,+6.035055738891727e-02,+6.465186317477950e-02,+6.914195749790462e-02,+7.382288203064732e-02,+7.869709331995660e-02,+8.376761638427657e-02,+8.903563687211118e-02,+9.450199243028472e-02,+1.001680193006426e-01,+1.060356225286319e-01,+1.121060220821844e-01,+1.183788547045326e-01,+1.248534855777947e-01,+1.315302847610869e-01,+1.384103079528939e-01,+1.454931890869180e-01,+1.527772946853750e-01,+1.602608842337125e-01,+1.679435556337752e-01,+1.758245615079801e-01,+1.839020119821303e-01,+1.921728622634411e-01,+2.006344295681524e-01,+2.092853879977170e-01,+2.181238261985594e-01,+2.271462264407930e-01, 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- 如請求項1或6之設備，其中該分析開窗函數及/或該合成開窗函數包含呈前向或反向次序的由以下值形成的至少一系列或若不同於0則具有以下值中的10個的至少一子系列，具有±1%之容限：+3.538498803770035e-04,+4.595886345493055e-04,+5.595519647227489e-04,+6.718404887323839e-04,+7.919323614002698e-04,+9.254835101516548e-04,+1.069418485858920e-03,+1.227927169310031e-03,+1.398277791978983e-03,+1.584491535026729e-03,+1.783653266717233e-03,+1.999873692180148e-03, 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- 如請求項1或6之設備，其中該分析開窗函數及/或合成開窗函數係界定成存在介於-0.01與+0.01之間的一第一數值微分。
- 如請求項1或6之設備，其中該分析開窗函數及/或合成開窗函數係界定成存在介於-10-4與+10-4之間的一第二數值微分。
- 如請求項1或6之設備，其中該分析開窗函數及/或合成開窗函數係界定成存在介於-10-5與+10-5之間的一第二數值微分。
- 一種系統，其包含：一編碼器，其作為如請求項1之設備；以及一解碼器，其作為如請求項6之設備。
- 如請求項40之系統，其中該編碼器包含組配來發送一位元串流之一通訊單元，及/或該解碼器包含組配來接收該位元串流之一通訊單元。
- 一種用於對包含多個訊框之音訊信號進行編碼之方法，包含：使用一分析開窗函數執行一經修改餘弦變換MDCT分析以將一音訊信號或其一經處理版本之一時域TD表示變換為一頻域FD表示，該分析開窗函數具有與至少四個點對應地經過一線性函數之一判定部分；以及基於該音訊信號或其經處理版本之該FD表示來寫入一位元串流，其中該分析開窗函數係界定成呈不對稱， 其中該分析開窗函數係界定成在該判定部分中：在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；在該第三交叉點與一第四交叉點之間的一第三區間中大於該線性函數，其中該分析開窗函數係界定成使得絕對最大值處於該第一區間與該第三區間中之一者中，其中該線性函數為具有常數值1之一常數函數。
- 一種用於對在頻域FD中界定的音訊信號或其經處理版本進行解碼之方法，包含：讀取將該音訊信號或其經處理版本予以編碼之一位元串流；以及使用一合成開窗函數執行一經修改餘弦變換MDCT合成以將該音訊信號或其經處理版本之該FD表示變換為一時域TD表示，該合成開窗函數具有與至少四個點對應地經過一線性函數之一判定部分，其中該合成開窗函數係界定成在該判定部分中：在一第一交叉點與一第二交叉點之間的一第一區間中大於該線性函數；在該第二交叉點與一第三交叉點之間的一第二區間中低於該線性函數；在該第三交叉點與一第四交叉點之間的一第三 區間中大於該線性函數，其中該合成開窗函數係界定成使得絕對最大值處於該第一區間與該第三區間中之一者中，其中該線性函數為具有常數值1之一常數函數。
- 一種儲存有指令之非暫時性儲存單元，該等指令在於一處理器上執行時使得該處理器執行如請求項42或43之方法。
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