CN111602195A - 用于调制重叠变换的分析/合成窗口化函数 - Google Patents
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Abstract
提供用于使用分析窗口化函数(40，50，60，70，240)利用分析/合成窗口化函数执行修改余弦变换(MDCT)的方法及设备，分析窗口化函数(40，50，60，70，240)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数(40’，240’)的曲折部分(44，64，244)。
Description
1.背景
已开发重叠变换用于若干音频编码应用。通常对音频信号的较大数据集(例如，两个连续帧)的连续区块执行这些变换。后续区块可能重叠。因此，一个区块的最后部分与后续区块的第一部分重合。可使用窗口化函数。
已开发体现调制重叠变换的不对称修改离散余弦变换(MDCT)窗口、不对称修改离散正弦变换(MDST)、时间至频率变换。
在过去几年已开发不对称修改离散余弦变换(MDCT)窗口、不对称修改离散正弦变换(MDST)窗口及其他类型的窗口，因为它们相较于对称形状提供改良的频率响应，对于诸如音频编码应用的低延迟信号应用尤其如此。
第一代窗口形状仅聚焦于频率响应的设计，例如，G.718或MPEG-4AAC-ELD窗口。最新的发展也考虑到窗口的时间形状，其负责量化误差的时间调制，例如如在3GPP EVS编解码器中使用的ALDO窗口。
然而，此处呈现的设计方法伴有以下问题：窗口形状展示非连续微分，其导致次佳的频率响应。此文档中描述的发明呈现用以克服此问题的解决方案。
2.发明概要
根据一方面，提供一种用于对包含多个帧的信息信号进行编码的设备，该设备包含：
调制重叠变换工具，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，调制重叠变换工具被配置以使用分析窗口化函数执行调制重叠变换分析，该分析窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分，及；
比特流写入器，被配置以基于信息信号或其经处理版本的FD表示准备比特流；
其中分析窗口化函数被限定以便为不对称的；
其中分析窗口化函数被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中分析窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中；
其中线性函数为具有常数值1的常数函数。
分析窗口化函数可被限定以使得分析窗口化函数的最大值比线性函数在相同时刻的值大出不到25％。
用于对信息信号进行编码的设备可包含多个帧，该设备可包含：
调制重叠变换工具，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该调制重叠变换工具被配置以使用分析窗口化函数执行调制重叠变换分析，该分析窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分；以及
比特流写入器，被配置以基于信息信号或其经处理版本的FD表示准备比特流，
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数被限定以使得分析窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
用于对信息信号进行编码的设备可包含多个帧，该设备可包含：
调制重叠变换工具，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该调制重叠变换工具被配置以使用分析窗口化函数执行调制重叠变换分析，该分析窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分；以及
比特流写入器，被配置以基于信息信号或其经处理版本的FD表示准备比特流。设备可包含调制重叠变换工具，其被配置以：
用分析窗口化函数的值按比例调整时间输入缓冲区和/或余弦或正弦值。
设备可包含调制重叠变换工具，该调制重叠变换工具被配置以使用呈以下形式的输入缓冲区：
t(n)＝x(Z-NF+n)对于n＝0..2NF-1-Z，和
t(2N-Z+n)＝0对于n＝0..Z-1
其中x(n)为信息信号或信息信号的经处理版本在时刻n的TD样本，NF为在一个帧中处理的样本数量，且Z为调制重叠变换窗口中的前导零的数量。
设备可包含调制重叠变换工具，该调制重叠变换工具被配置以执行：
其中X(k)为在频率索引k处的调制重叠变换频率值，n为时间常数，wN(n)为分析窗口化函数，t(n)为时间输入缓冲区，且NF为在一个帧中处理的样本数量。
用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备，该设备可包含：
比特流读取器，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具，被配置以使用合成窗口化函数对信息信号或其经处理版本执行逆调制重叠变换合成，该合成窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分，
其中合成窗口化函数被限定以便为不对称的，
其中合成窗口化函数被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中合成窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中，
其中线性函数为具有常数值1的常数函数。
设备可包含：
合成窗口化函数，被限定以使得合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％。
用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备，该设备可包含：
比特流读取器，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具，被配置以使用合成窗口化函数对信息信号或其经处理版本执行逆调制重叠变换合成，该合成窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分，
其中合成窗口化函数被限定以便为不对称的，
其中合成窗口化函数被限定以使得合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
一种用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备，该设备可包含：
比特流读取器，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具，被配置以使用合成窗口化函数对信息信号或其经处理版本执行逆调制重叠变换合成，该合成窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分。
该设备，其中逆调制重叠变换工具可被配置以：
用合成窗口化函数的值按比例调整时域混叠缓冲区处的值。
该设备，其中逆调制重叠变换工具可被配置而以如下形式产生时域TD信号表示：
其中
为混叠缓冲区，
为信息信号或其经处理版本，且NF为TD帧的样本数量。
该设备，其中逆调制重叠变换工具可被配置以：
执行时间混叠缓冲区的窗口化。
该设备，其中逆调制重叠变换工具可被配置以通过执行以下而执行窗口化运算：
该设备，其中逆调制重叠变换工具可被配置以执行重叠相加运算。
该设备，其中逆调制重叠变换工具可被配置以如下地执行重叠相加运算：
其中
为输出值，
为经窗口化时间混叠缓冲区，且NF为一个帧中的样本数量。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以使得绝对最大值处于第一区间或第三区间中。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以使得在曲折部分中，相对最大值处于第一区间或第三区间中，且相对最小值处于第二区间中。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以使得在曲折部分中，曲折窗口函数的对应于第一区间及第三区间中的至少一个的值大于0.9。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以便在曲折部分中在由两个帧的30％与50％构成的区间中存在大于线性函数的值。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以使得分析窗口化函数和/或合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以使得分析窗口化函数和/或合成窗口化函数的最大值比线性函数在相同时刻的值大出不到5％。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以便存在介于-3*10-4与+3*10-4之间的第二数值微分。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以便存在介于-2*10-5与+2*10-5之间的第三数值微分。
该设备可使得：
分析窗口化函数和/或合成窗口化函数被限定以便存在介于-0.01与+0.01之间的第一数值微分。
该设备可使得：
分析窗口化函数和/或合成窗口化函数被限定以便存在介于-10-4与+10-4之间的第二数值微分。
该设备可使得：
分析窗口化函数和/或合成窗口化函数被限定以便存在介于-10-5与+10-5之间的第二数值微分。
该设备可使得：
线性函数可被限定以便为非递增函数。
该设备可使得：
线性函数可被限定以便为严格递减函数。
该设备可使得：
线性函数可被限定以便为非递减函数。
该设备可使得：
线性函数可被限定以便为严格递增函数。
该设备可使得：
线性函数可被限定以便具有为常数或最大改变+2％或-2％的值。
该设备可使得：
线性函数可被限定以便具有介于-0.05与-0.20之间的增量。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可被限定以便为不对称的。
该设备可使得：
分析窗口化函数与合成窗口化函数可被限定为彼此的时间反转版本。
该设备可包含：
储存空间，储存分析窗口化函数和/或合成窗口化函数的值。
该设备，其中修改重叠变换可为修改离散余弦变换MDCT或修改离散正弦变换MDST，逆修改重叠变换为逆修改离散余弦变换IMDCT或逆修改离散正弦变换IMDST。
该设备可使得：
分析窗口化函数和/或合成窗口化函数可为具有常数值1的常数函数。
一种系统，其可包含：
编码器，作为
解码器，作为该设备。
该系统，其中编码器可包含被配置以传输比特流的通信单元，和/或解码器包含被配置以接收比特流的通信单元。
根据一方面，提供一种方法，该方法包含使用分析窗口化函数执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该分析窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分。
根据一方面，提供一种方法，该方法包含使用分析窗口化函数执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该分析窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分，
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中分析窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中，
其中线性函数为具有常数值1的常数函数。
根据一方面，提供一种方法，该方法包含使用分析窗口化函数执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该分析窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分，
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数被限定以使得分析窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
根据一方面，提供一种方法，该方法包含使用合成窗口化函数执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，该合成窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分。
根据一方面，提供一种方法，该方法包含使用合成窗口化函数执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，该合成窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分，
其中合成窗口化函数被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中合成窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中，
其中线性函数为具有常数值1的常数函数。
根据一方面，提供一种方法，该方法包含使用合成窗口化函数执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，该合成窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分，
其中合成窗口化函数被限定以便为不对称的，
其中合成窗口化函数被限定以使得合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为的常数函数。
一种非暂时性储存单元，其储存指令，指令在处理器上执行时可使得该处理器执行方法。
提供一种用于对包含多个帧的信息信号进行编码的设备，该设备包含：
修改离散余弦变换MDCT工具，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，该MDCT工具被配置以使用分析窗口化函数执行MDCT分析，该分析窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分；以及
比特流写入器，被配置以基于信息信号或其经处理版本的FD表示准备比特流。
在示例中，MDCT工具被配置以用分析窗口化函数的值按比例调整时间输入缓冲区和/或余弦值。
在示例中，MDCT工具被配置以使用呈以下形式的输入缓冲区：
t(n)＝x(Z-NF+n)对于n＝0..2NF-1-Z，
其中x(n)为信息信号或信息信号的经处理版本在时刻n的TD样本，NF为在一个帧中处理的样本数量，且Z为MDCT窗口中的前导零的数量。
在示例中，初始化可执行为：
t(2N-Z+n)＝0对于n＝0..Z-1
在示例中，MDCT(或MDST)工具被配置以执行：
其中X(k)为在频率索引k处的MDCT(或MDST)频率值，n为时间常数，wN(n)为分析窗口化函数，t(n)为时间输入缓冲区，且NF为在一个帧中处理的样本数量。
在示例中，提供一种设备，该设备包含比特流读取器，比特流读取器被配置以读取对信息信号进行编码的比特流；以及
逆修改余弦变换IMDCT(或IMDST)工具，被配置以使用合成窗口化函数对信息信号或其经处理版本执行IMDCT(或IMDST)合成，该合成窗口化函数具有以至少四个点的对应性与线性函数交叉的曲折部分。
在示例中，IMDCT(或IMDST)工具被配置以用合成窗口化函数的值按比例调整时域混叠缓冲区处的值。
在示例中，IMDCT(或IMDST)工具被配置而以如下形式产生时域TD信号表示：
其中
为混叠缓冲区，
为信息信号或其经处理版本，且NF为TD帧的样本数量。
在示例中，IMDCT(或IMDST)工具被配置以执行时间混叠缓冲区的窗口化。
在示例中，IMDCT(或IMDST)工具被配置以通过执行以下而执行窗口化运算：
在示例中，IMDCT(或IMDST)工具被配置以执行重叠相加运算，其可例如为：
其中
为输出值，
为经窗口化时间混叠缓冲区，且NF为一个帧中的样本数量。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以使得绝对最大值处于第一区间或第三区间中。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以使得在曲折部分中，相对最大值处于第一区间或第三区间中，且相对最小值处于第二区间中。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以使得在曲折部分中，曲折窗口函数的对应于第一区间及第三区间中的至少一个的值大于0.9。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以便在曲折部分中在由两个帧的30％与50％构成的区间中存在大于线性函数的值。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以使得分析窗口化函数和/或合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％(特别地，5％)。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以便存在介于-3*10-4与+3*10-4之间的第二数值微分和/或介于-2*10-5与+2*10-5之间的第三数值微分。
在示例中，线性函数被限定以便具有为常数或最大改变+2％或-2％的值。
在示例中，线性函数被限定以便具有介于-0.05与-0.20之间的增量。
在示例中，分析窗口化函数和/或合成窗口化函数被限定以便为不对称的。
在示例中，分析窗口化函数与合成窗口化函数被限定为彼此对称的。
在示例中，储存空间储存分析窗口化函数和/或合成窗口化函数的值。
在示例中，提供一种系统，该系统包含：
编码器，作为如上文和/或下文所述的设备；以及
解码器，作为如上文和/或下文所述的设备。
在示例中，编码器包含被配置以传输比特流的通信单元，和/或解码器包含被配置以接收比特流的通信单元。
在示例中，提供一种方法，该方法包含使用分析窗口化函数执行MDCT(MDST)分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，分析窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分。
在示例中，提供一种方法，该方法包含使用合成窗口化函数执行MDCT(MDST)合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，该合成窗口化函数具有以至少四个点的对应性经过线性函数的曲折部分。
已注意到，用于本发明的分析窗口化函数和/或合成窗口化函数特别适合于执行MDCT(MDST)合成及分析。
在下文中公开用于调制重叠变换的分析/合成窗口化函数以及用于使用其的方法及设备的示例。
3.附图说明
图1及图2展示根据现有技术的方案。
图3至图12展示根据示例的函数的方案。
图13及图13A展示根据示例的编码器。
图14及图14A展示根据示例的解码器。
图15及图16展示根据示例的方法。
图17及图18展示根据示例的设备。
图19展示根据示例的方案。
图20展示根据现有技术的方案。
图21至图25展示根据示例的方案。
图26至图31展示根据示例的函数的方案。
4.示例
信息信号可在时域TD中描述为一连串样本(例如，对于区块b及索引(例如时刻)n为xb(n))。TD表示可由多个帧组成，每一帧与多个样本相关联。在频域FD中，帧可表示为一连串频段(例如，X(k)，每一频段与特定频率相关联(每一频率与索引k相关联))。
可以使用调制重叠变换技术(举例来说，诸如修改离散余弦变换MDCT技术或修改离散正弦变换MDST技术)将TD表示转换为FD表示。此类技术可例如在编码器侧实施，以便将所采样值变换为频率值。
可以使用逆调制重叠变换技术(诸如逆修改离散余弦变换IMDCT技术或逆修改离散正弦IMDST技术)将FD表示转换为TD表示。可例如在解码器侧实施此类技术，以便将频率值变换为TD值(例如，用于执行再现)。
下表指示在以下部分中使用的符号。
| 符号 | 描述 |
| N或N<sub>F</sub> | 帧大小；在一个帧中处理的样本数量 |
| f<sub>s</sub> | 采样率 |
| x<sub>b</sub>(n) | 区块b及索引n的时域样本 |
| X<sub>b</sub>(k) | 区块b及频率索引k的频域频段 |
| Z或L<sub>Z</sub> | MDCT窗口中的前导零的数量 |
图13及图13A分别展示编码器设备130及130A。编码器设备130或130A中的每一个可包含多个工具，诸如能够执行信号处理技术的功能区块。这些区块中的每一个可为独立装置，或可为与编码器设备130及130A的其他工具区分担硬件结构的功能区块。
编码器设备130或130A可包含调制重叠变换工具131(诸如低延迟修改离散余弦变换MDCT工具或低延迟修改离散正弦变换MDST工具，或另一类型的调制重叠变换工具)，调制重叠变换工具可将信息信号(例如，音频信号)从时域TD表示转换为频域FD表示。调制重叠变换工具131(例如，MDCT或MDST工具)执行调制重叠变换分析(例如，MDCT分析、MDST分析)。
可提供例如在调制重叠变换工具131下游或在TD中操作的其他工具。此处提及其中的一些。
编码器设备130可包含用于在FD中执行LPC分析的线性预测性编码LPC工具132。编码器设备130A可包含用于在FD中执行LPC分析的频谱噪声整形SNS工具132A。
SNS可被视为LPC的一般化，且因此，在一些示例中，LPC区块132可被视为SNS工具132A的特定示例(且编码器设备130可被视为编码器设备130A的特定示例)。
编码器设备130及130A中的每一个可包含时间噪声整形TNS工具133，以控制FD中(例如，如由调制重叠变换工具输出)的信息信号的每一窗口内的噪声的时间形状。
编码器设备130及130A中的每一个可包含在FD中处理信号的频谱量化器134。如由TNS工具133输出的信号可例如使用死区加均匀阈值标量量化来加以量化。
编码器设备130及130A中的每一个可包含例如在频谱量化器134下游的噪声级估计器136。
编码器设备130及130A中的每一个可包含编码器135，编码器在FD中处理信号以例如执行熵编码以便例如压缩比特流。编码器135可例如执行熵编码。
编码器设备130及130A中的每一个可包含带宽检测器137a，带宽检测器可控制例如解码器处的带宽控制器。
编码器设备130及130A中的每一个可包含在时域TD中处理信号的工具。举例而言，编码器设备130或130A可包含重采样工具138a(例如，降采样器)和/或长期后滤波LTPF工具138b，LTPF工具用于控制在解码器侧在TD中起作用的LTPF。
编码器设备130及130A中的每一个可包含比特流多路复用器工具(比特流写入器)137以用从置放在上游的TD和/或FD工具获得的数据准备比特流。比特流可包含信息信号以及待在解码器侧使用的控制数据的数字表示。比特流可被压缩，或包括经压缩的部分。
图14及图14A分别展示解码器设备140及140A。它们中的每一个可对例如如由编码器130或130A(举例来说)编码的信息信号的数字表示进行解码。
解码器设备140及140A中的每一个可包含逆调制重叠变换工具147(例如，低延迟逆MDCT工具或低延迟逆DMST工具)以将信号表示从FD变换为TD。调制重叠变换工具147执行调制重叠变换合成(例如，MDCT合成和/或MDST合成等)。
可提供例如在逆调制重叠变换工具147上游或在TD中操作的其他工具。此处提及其中的一些。
解码器设备140及140A中的每一个可包含比特流多路复用工具141以从编码器设备(例如，设备130或130A)获得比特流(例如，通过传输)。举例而言，从编码器设备130或130A的输出可作为输入信号提供至解码器设备140或140A。
解码器设备140及140A中的每一个可包含解码器142，解码器可例如解压缩比特流中的数据。可执行算术解码。可执行残余解码。
解码器设备140及140A中的每一个可包含在FD中处理信号的噪声填充工具143。
解码器设备140及140A中的每一个可包含在FD中处理信号的全局增益工具144。
解码器设备140及140A中的每一个可包含在FD中处理信号的TNS解码器工具145。
解码器设备140可包含MDCT(或MDST)整形工具146(其他重叠变换工具是可能的)。MDCT(或MDST)整形工具146可通过应用从变换至FD频谱(例如，MDCT或MDST频谱等)的经解码LP滤波器系数(例如从LPC解码工具146a获得)计算的增益因子而处理信号。
解码器设备140A可包含例如从SNS工具132A获得LPC系数的SNS解码器工具146A'。
解码器设备140及140A中的每一个可包含用于在TD中执行后滤波的LTPF工具148。
解码器设备140A可包含可从例如带宽检测器137a获得带宽信息的解码器带宽控制器149。
编码器设备130(或130A)及解码器设备140(或140A)可彼此组合以形成系统。
基本上，编码器设备130或130A中在调制重叠变换工具131下游的工具及解码器设备140或140A中在逆调制重叠变换工具147上游的工具可在FD中执行信号处理，且因此为FD工具。
此处关于例如在工具131及147处的转换技术论述技术。
一般而言，MDCT、MDST等为具有重叠变换的额外特性的离散变换。对较大数据集的连续区块(例如，两个连续帧)执行这些变换中的一个。后续区块可能重叠。因此，一个区块的最后部分可与后续区块的第一部分重合。可使用窗口化函数wn(n＝0，...，2N-1)。具体地，窗口化函数可用作权重。优点为可以避免或减小区块边界处的不连续性。
图15展示用于例如在调制重叠变换工具131(其可为MDCT工具)处执行调制重叠变换分析的方法150。当前帧b的输入信号xb(n)可由N个音频样本组成，其中最新样本位于xb(N-1)处。
在步骤S151处，可更新输入缓冲区。调制重叠变换t的时间输入缓冲区可根据以下加以更新：
t(n)＝xb-1(Z+n)对于n＝0..N-1-Z
t(N-Z+n)＝xb(n)对于n＝0..N-1
t(2N-Z+n)＝0对于n＝0..Z-1
后者仅为一致性所需的初始化。
在步骤S152处，可使用以下方程式将N个时间样本的区块变换为频率系数X(k)：
其中wN为根据所使用帧大小的不对称调制重叠变换窗口(例如，MDCT窗口)。
图16展示用于例如在调制重叠变换工具147(其可为IMDCT工具)处执行调制重叠变换合成(例如，MDCT合成)的方法160。此处，频谱
(即，FD中的表示)可通过以下步骤变换至TD：
在步骤S161处，可执行帧b的时域混叠缓冲区
的产生。举例而言：
在步骤S162处，可执行时域混叠缓冲区的窗口化。举例而言：
在步骤S163处，可进行重叠相加运算以获得帧b的重构时间样本
举例而言：
值得注意地，分析处的窗口化函数wN(n)(分析窗口化函数)与合成处的窗口化函数wN(2N-1-n)(合成窗口化函数)可被限定以便为彼此的时间反转。分析窗口与合成窗口的窗口系数为彼此的时间反转版本。
已注意到，特别有效的窗口化函数(例如，合成窗口化函数)可为具有曲折部分的分析窗口化函数，该曲折部分以四个点的对应性与线性函数交叉。
图4展示分析窗口化函数40。分析窗口化函数40可被限定于0与2N之间或0与在2N的80％与85％或90％中间的值(例如，81.25％)之间。在一些示例中，分析窗口化函数40可被限定于不同(例如，较宽)范围中。
分析窗口化函数40可至少对于一个部分参考线性函数40'而加以限定。在图4中，线性函数40'为值为1的常数函数。然而，线性函数40'可大体为例如根据y＝an+b限定的线性函数，其中n为介于0与2N(或其非零部分)之间的索引，且a及b为常数。
分析窗口化函数40可包含曲折部分44。曲折部分44可使得分析窗口化函数40在四个点#1、#2、#3、#4处与线性函数40'相遇和/或交叉。
曲折部分44可使得分析窗口化函数40在大多数索引(例如，对于多于99％的索引)处不同于线性函数40'。
曲折部分44可使得，至少在紧接索引中与点(交叉点#1、#2、#3、#4)相关联的一个索引之前的一个索引处，分析窗口化函数40的值大于线性函数在交叉点(#1、#2、#3、#4)处的值(例如，1)，且至少在紧接同一索引(与交叉点相关联)之后的索引处，分析窗口化函数40的值小于线性函数在交叉点处的值。
曲折部分44可使得，至少在紧接索引中与交叉点#1、#2、#3、#4相关联的一个索引之前的一个索引处，分析窗口化函数40的值小于线性函数在交叉点(#1、#2、#3、#4)处的值(例如，1)，且至少在紧接同一索引(与交叉点相关联)之后的索引处，分析窗口化函数40的值大于线性函数在交叉点处的值。
曲折部分44可使得交叉点#1、#2、#3、#4中的每一个不与先前及后续交叉点紧接连续。举例而言，在两个交叉点#1、#2、#3与#4之间，存在分析窗口化函数40的至少一个索引，其值不与分析窗口化函数40在同一索引处的值重合。
分析窗口化函数40可被限定以便对应于曲折部分44：
-在第一交叉点#1与第二交叉点#2之间的第一区间41中大于线性函数40'；
-在第二交叉点#2与第三交叉点#3之间的第二区间42中低于线性函数40'；
-在第三交叉点#3与第四交叉点#4之间的第三区间43中大于线性函数40'。
第一交叉点#1可先于第二交叉点#2，该第二交叉点#2可先于第三交叉点#3，该第三交叉点#3可先于第四交叉点#4。
曲折部分44可在第一交叉点与最后(例如，第四)交叉点之间延伸。在一些示例中，交叉点可仅为四个。
分析窗口化函数40也可包含初始递减部分45，其中可达到负最小值。负最小值可位于2N的6.25％与2N的18.75％之间。分析窗口化函数40也可包含快速递增部分46，从负最小值朝向曲折部分44(例如，朝向第一交叉点#1)快速递增。分析窗口化函数40也可包含快速递减部分47，从曲折部分44快速递减至0。分析窗口化函数40也可包含连续空值部分48，其可在2N(两个帧之大小)的80％与85％或90％之间开始且继续至2N的结束。
绝对最大值41'处于第一区间41(或第三区间)中。
分析窗口化函数40可在曲折部分44中具有在第三区间43(或第一区间)中的相对最大值43'，且相对最小值42'处于第二区间42中。
分析窗口化函数40可在曲折部分44中具有大于0.9的对应于第二区间42的曲折窗口函数40的值。第二区间42可高于0.9。
分析窗口化函数40可在曲折部分44中在由两个帧(2N)的30％与50％构成的区间中存在低于线性函数40'的值。在示例中，在两个帧(2N)的50％之后，窗口化函数40可大于线性函数40'。因此，点#3可对应于第一帧的最后索引或对应于第二帧的第一索引。在两个帧的30％至50％区间中，曲折窗口部分44可低于线性函数。
曲折窗口函数44的最大值41'可比线性函数40'在同一索引n处的值大出不到25％(且较佳小于5％或3％)。
分析窗口化函数40可存在介于0.02与-0.02之间的第一数值微分。第二数值微分可介于-5*10-4与+5*10-4之间，且较佳介于-3*10-4与+3*10-4之间。第三数值微分可介于-2*10-5与+2*10-5之间。
线性函数40'可为非递增函数。在其示例中，线性函数40'可为非递减函数。线性函数40'可具有为常数或最大改变+2％或-2％的值。
分析窗口化函数可被限定以便为不对称的。
在一些示例中，分析窗口化函数可使得曲折部分44的区间(子部分)中的一些相对于以上描述为反转次序。
图26及图27展示分析窗口化函数40(图27为图26的一部分的放大视图)。分析窗口化函数240可被限定于0与2N之间或0与在2N的80％与85％或90％中间的值(例如，81.25％)之间。在一些示例中，分析窗口化函数40可被限定于不同(例如，较宽)范围中。
分析窗口化函数40可至少对于一个部分参考线性函数240'而被限定。在图27中，线性函数240'为值为1的常数函数。然而，线性函数40'可大体为例如根据y＝an+b限定的线性函数，其中n为介于0与2N(或其非零部分)之间的索引，且a及b为常数(例如，a＝0,b＝1)。
分析窗口化函数240可包含曲折部分244。曲折部分244可使得分析窗口化函数240在四个点#1、#2、#3、#4处与线性函数240'相遇和/或交叉。
曲折部分244可使得分析窗口化函数240在大多数索引(例如，对于多于99％的索引)处不同于线性函数240'。
曲折部分244可使得，至少在紧接索引中与点(交叉点)#1、#2、#3、#4相关联的一个索引之前的一个索引处，分析窗口化函数240的值大于线性函数240'在交叉点(#1、#2、#3、#4)处的值，且至少在紧接同一索引(与交叉点相关联)之后的索引处，分析窗口化函数240的值小于线性函数240'在交叉点(#1、#2、#3、#4)处的值。
曲折部分244可使得，至少在紧接索引中与交叉点#1、#2、#3、#4相关联的一个索引之前的一个索引处，分析窗口化函数40的值小于线性函数240'在交叉点(#1、#2、#3、#4)处的值，且至少在紧接同一索引(与交叉点相关联)之后的索引处，分析窗口化函数40的值大于线性函数240'在交叉点处的值。
曲折部分244可使得交叉点#1、#2、#3、#4中的每一个不与先前及后续交叉点紧接连续。举例而言，在两个交叉点#1、#2、#3与#4之间，存在分析窗口化函数240的至少一个索引，其值不与分析窗口化函数240在同一索引处的值重合。
分析窗口化函数240可被限定以便对应于曲折部分244：
-在第一交叉点#1与第二交叉点#2之间的第一区间241中大于线性函数240'；
-在第二交叉点#2与第三交叉点#3之间的第二区间242中低于线性函数240'；
-在第三交叉点#3与第四交叉点#4之间的第三区间243中大于线性函数240'。
第一交叉点#1可先于第二交叉点#2，该第二交叉点#2可先于第三交叉点#3，该第三交叉点#3可先于第四交叉点#4。
曲折部分244可在第一交叉点与最后(例如，第四)交叉点之间延伸。在一些示例中，交叉点可仅为四个。
分析窗口化函数240可具有全部正值。最小值可为0值，其可在分析窗口化函数240的第一索引处和/或分析窗口化函数240的最后索引处。分析窗口化函数240可包含快速递增部分246，朝向曲折部分244(例如，第一交叉点#1)快速递增。分析窗口化函数240也可包含快速递减部分247，从曲折部分244快速递减至0。分析窗口化函数240可包含连续空值部分248，其可在2N(两个帧的大小)的84％与90％之间开始且继续至2N的结束。
绝对最大值241'处于第一区间41(或第三区间)中。
分析窗口化函数240可在曲折部分244中具有在第三区间243(或第一区间)中的相对最大值243'，和/或相对最小值242'处于第二区间242中。
分析窗口化函数240可在曲折部分244中具有大于0.95的对应于第二区间242的曲折窗口函数240的值。第二区间242可高于0.95。第一区间241和/或第三区间243可小于1.05。
分析窗口化函数240可在曲折部分244中在由两个帧(2N)的30％与50％构成的区间中存在低于线性函数240'的值。在示例中，在两个帧(2N)的50％之后，窗口化函数240可大于线性函数240'。因此，点#3可对应于第一帧的最后索引或对应于第二帧的第一索引。在两个帧的30％至50％区间中，曲折窗口部分244可低于线性函数。
曲折窗口函数244的最大值241'可比线性函数240'在同一索引n处的值大出不到25％(且较佳小于5％或3％)。
分析窗口化函数240可存在介于-0.01与+0.01之间的第一数值微分。第二数值微分可介于-10-4与+10-4之间。第三数值微分可介于-10-5与+10-5之间。
线性函数40'可为非递增函数。在其示例中，线性函数40'可为非递减函数。线性函数40'可具有为常数或最大改变+2％或-2％的值。
分析窗口化函数可被限定以便为不对称的。
在一些示例中，分析窗口化函数240可使得曲折部分244的区间(子部分)中的一些相对于以上描述为反转次序。
图28及图29比较分析窗口化函数40与240。
图6展示分析窗口化函数60的另一示例。图7展示与曲折部分64对应的分析窗口化函数60的放大视图。
在此情况下，分析窗口化函数60可至少对于一个部分参考线性函数60'而被限定。在图7中，线性函数60'为线性递减函数(“对角线”)。
曲折部分64可使得分析窗口化函数60在四个点处与线性函数60'相遇和/或交叉。
分析窗口化函数40可被限定以便对应于曲折部分64：
-在第一交叉点#1'与第二交叉点#2'之间的第一区间61'中大于线性函数60'；
-在第二交叉点#2'与第三交叉点#3'之间的第二区间62'中低于线性函数60'；
-在第三交叉点#3'与第四交叉点#4'之间的第三区间63'中大于线性函数60'；
-在第四交叉点#4'与第五交叉点#5'之间的第四区间64'中低于线性函数60'；
-在第五交叉点#5'与第六交叉点#6'之间的第五区间65'中大于线性函数60'。
绝对最大值可处于第一区间61'中(在其他示例中，例如，在线性函数递增的情况下，可处于第五区间中)。
分析窗口化函数60可在曲折部分64中具有在第三区间63'和/或第五区间65'中的相对最大值、在第二区间62'和/或第四区间64'中的相对最小值。
分析窗口化函数60可在曲折部分64中具有大于0.9且特别地大于0.95的对应于第一区间及第三区间中的至少一个的窗口化函数的值(在其他示例中，例如，在线性函数递增的情况下，可在第三区间及第五区间中)。
分析窗口化函数60可在曲折部分64中在由两个帧(2N)的30％与50％构成的区间中存在大于线性函数60'的值。
窗口化函数60的最大值可比线性函数60在同一索引n处的值大出不到25％(且较佳小于5％)。
线性函数60'可为非递增函数，特别地为严格递减函数。
分析窗口化函数可被限定以便为不对称的。
在示例中，分析窗口化函数可具有相对于图6反转的区间。
在示例中，合成窗口化函数可解释为相对于分析窗口化函数是对称的。举例而言，对称轴可处于2N范围的中间(例如，479或480)。
合成窗口化函数90的示例提供于图9中(例如，与图4的分析窗口化函数40相关联的合成窗口化函数)。合成窗口化函数90可被限定于0与2N之间或2N的10％或15％与20％中间的值与2N之间。
合成窗口化函数90可至少对于一个部分参考线性函数(其在此情况下未展示，但为常数值1)而被限定。在图9中，线性函数可为值为1的常数函数。然而，线性函数可大体为例如根据y＝an+b限定的线性函数。
合成窗口化函数90可包含曲折部分94。曲折部分94可使得合成窗口化函数90在四个交叉点#1、#2、#3、#4(仅示出#2)处与线性函数90'(常数1，为清楚起见仅部分地展示)相遇和/或交叉。合成窗口化函数可在窗口的中间(点#2)(即样本N-1与N之间)与值1交叉。
曲折部分94可使得合成窗口化函数90在大多数索引(例如，对于多于99％的索引)处不同于线性函数90'。
曲折部分94可使得，至少在紧接索引中与交叉点#1、#2、#3、#4相关联的一个索引之前的一个索引处，合成窗口化函数90的值大于线性函数在点(#1、#2、#3、#4)处的值(例如，1)，且至少在紧接同一索引(与点相关联)之后的索引处，合成窗口化函数90的值小于线性函数在交叉点处的值。曲折部分94可使得，至少在紧接索引中与点#1、#2、#3、#4相关联的一个索引之前的一个索引处，合成窗口化函数90的值小于线性函数在点(#1、#2、#3、#4)处的值，且至少在紧接同一索引(与交叉点相关联)之后的索引处，合成窗口化函数90的值大于线性函数在交叉点(#1、#2、#3、#4)处的值。
曲折部分94可使得点#1、#2、#3、#4中的每一个不与点#1、#2、#3、#4中的另一个紧接连续。举例而言，在#1、#2、#3与#4中的两个点之间，可存在合成窗口化函数90的至少一个索引，其值不与合成窗口化函数90在同一索引处的值重合。
合成窗口化函数90可被限定以便对应于曲折部分94：
-在第一交叉点#1(未在图9中展示，但可表示为与图4中的点#4对称)与第二交叉点#2(在此情况下，其在第480个样本处，例如在2N范围的中间)之间的第一区间91中大于线性函数90'；
-在第二交叉点#2与第三交叉点#3(未在图9中展示，但可表示为与图4中的点#3对称)之间的第二区间92中低于线性函数90'；
-在第三交叉点#3与第四交叉点#4(未在图9中展示，但可表示为与图4中的点#1对称)之间的第三区间93中大于线性函数90'。
合成窗口化函数90也可包含连续空值部分98，其可位于2N的10％与15％之间。合成窗口化函数90也可包含快速递增部分97，从0朝向曲折部分94快速递增。合成窗口化函数90也可包含快速递减部分96，从曲折部分94朝向负最小值快速递减。负最小值可位于2N的81.25％与2N的93.7％之间。合成窗口化函数90也可包含最终递增部分95，其从负最小值达到0。
绝对最大值可处于第三区间93(或第一区间)中。
合成窗口化函数90可在曲折部分94中具有在第一区间91(或第三区间)中的相对最大值，且相对最小值处于第二区间中。
合成窗口化函数90可在曲折部分94中具有大于0.9的对应于第一区间(91)及第三区间(93)中的至少一个的曲折窗口函数的值。第三区间可高于0.9。
合成窗口化函数90可在曲折部分94中在由两个帧(2N)的30％与50％构成的区间中存在大于线性函数的值。
合成窗口化函数90的最大值可比线性函数在同一索引n处的值大出不到25％(且较佳小于5％)。
合成窗口化函数90可存在介于0.02与-0.02之间的数值微分。第二数值微分可介于-5*10-4与+5*10-4之间，且较佳介于-3*10-4与+3*10-4之间。第三数值微分可介于-2*10-5与+2*10-5之间。
合成线性函数90可为非递增函数。在其他示例中，合成线性函数90可为非递减函数。合成线性函数90可具有为常数或最大改变+2％或-2％的值。
合成窗口化函数90可被限定以便为不对称的。
在一些示例中，合成窗口化函数90可为相对于图9中所示的形状对称的函数。例如，0处的值将为图9中在960处的值；1处的值将为图9中在959处的值，等等。
合成窗口化函数290的示例提供于图30中(例如，与图26至图29的分析窗口化函数240相关联的合成窗口化函数)。合成窗口化函数290可被限定于0与2N之间或2N的10％或15％与20％中间的值与2N之间。
合成窗口化函数290可至少对于一个部分参考线性函数290'(其在此情况下未展示，但为常数值1)而被限定。
在图30中，线性函数290'可为值为1的常数函数。然而，线性函数可大体为例如根据y＝an+b限定的线性函数。
合成窗口化函数290可包含曲折部分294。曲折部分294可使得合成窗口化函数290在四个交叉点#1、#2、#3、#4(仅示出#2)处与线性函数290'(常数1，为清楚起见仅部分地展示)相遇和/或交叉。合成窗口化函数可在窗口的中间(点#2)(即样本N-1与N之间)与值1交叉。
曲折部分294可使得合成窗口化函数290在大多数索引(例如，对于多于99％的索引)处不同于线性函数290'。
曲折部分294可使得，至少在紧接索引中与点#1、#2、#3、#4相关联的一个索引之前的一个索引处，合成窗口化函数90的值大于线性函数在点(#1、#2、#3、#4)处的值(例如，1)，且至少在紧接同一索引(与交叉点相关联)之后的索引处，合成窗口化函数90的值小于线性函数在交叉点处的值。
曲折部分294可使得，至少在紧接索引中与点#1、#2、#3、#4相关联的一个索引之前的一个索引处，合成窗口化函数290的值小于线性函数在交叉点(#1、#2、#3、#4)处的值，且至少在紧接同一索引(与交叉点相关联)之后的索引处，合成窗口化函数290的值大于线性函数在交叉点(#1、#2、#3、#4)处的值。
曲折部分294可使得交叉点#1、#2、#3、#4中的每一个不与点#1、#2、#3、#4中的另一个紧接连续。举例而言，在#1、#2、#3与#4中的两个交叉点之间，可存在合成窗口化函数290的至少一个索引，其值不与合成窗口化函数290在同一索引处的值重合。
合成窗口化函数290可被限定以便对应于曲折部分294：
-在第一交叉点#1与第二交叉点#2(在此情况下，其在第480个样本处，例如在2N范围的中间)之间的第一区间291中大于线性函数290'(例如，大于1)；
-在第二交叉点#2与第三交叉点#3之间的第二区间292中低于线性函数290'；
-在第三交叉点#3与第四交叉点#4之间的第三区间293中大于线性函数290'。
合成窗口化函数290可包含连续空值部分298，其可位于窗口(2N个样本)的一个边界处，且可包含样本的10％与15％之间。合成窗口化函数290也可包含快速递增部分297，从0朝向曲折部分294快速递增。合成窗口化函数290可包含快速递减部分296，从曲折部分294朝向0快速递减。
绝对最大值可处于第三区间293(或第一区间)中。
合成窗口化函数290可在曲折部分294中具有在第一区间291(或第三区间)中的相对最大值，且相对最小值处于第二区间中。
合成窗口化函数290在曲折部分294中可具有大于0.9或0.95的对应于第一区间及第三区间(291，293)中的至少一个的曲折窗口函数的值。第三区间可高于0.95。
合成窗口化函数290可在曲折部分294中在由两个帧(2N)的30％与50％构成的区间中存在大于线性函数的值。
合成窗口化函数290的最大值可比线性函数在同一索引n处的值大出不到25％(且较佳小于5％或3％)。
合成窗口化函数290可存在介于-0.01与+0.01之间的数值微分。第二数值微分可介于-10-4与+10-4之间。第三数值微分可介于-10-5与+10-5之间。
合成线性函数90可为非递增函数。在其他示例中，合成线性函数90可为非递减函数。合成线性函数90可具有为常数或最大改变+2％或-2％的值。
合成窗口化函数90可被限定以便为不对称的。
在一些示例中，合成窗口化函数90可为相对于图9中所示的形状对称的函数。例如，0处的值将为图9中在960处的值；1处的值将为图9中在959处的值，等等。
5.论述
已注意到，此函数具有特别受关注的特征，其极其适合于MDCT(或MDST或其他)及IMDCT(或IMDST或其他)技术，特别地适合于音频编码。
作为MDCT窗口形状的平滑度的量度，使用数值微分，如
用以评定MDCT窗口的质量的另一量度为量化误差的时间形状，其由以下描述
Sq(t)＝w2(t+N)+w2(t)对于t＝0..N-1
量化误差可以作为音频编码过程的部分而引入谱域中。
此处论述ALDO窗口。ALDO为用于提供改良的时间形状的不对称窗口的设计方法。在(3GPP)及[2]中描述了如在EVS编解码器中使用的ALDO窗口的设计过程。图1展示用于ALDO窗口方案的示意性窗口形状。
ALDO窗口由四个区段组成：上升函数、严格一区段、衰减函数及零。w4中零的数量也确定w2中一的数量，其中w2＝2*w4。在[1]及[2]中描述了获得w1及w3的方式。
图2展示根据[1]及[2]对于参数Lz＝180(在图1中的MDCT窗口W4(n)中前导零的数目)设计的ALDO窗口，且总窗口长度为960个样本。
如图2的第四子图(“时间调制量化误差”)中可见，ALDO展示量化误差的良好时间形状，这意味着两个后续重叠合成窗口的能量总和接近于一。最佳结果将仅需要通过对称窗口形状达成的一。
此设计方法的缺陷主要在图2的第二子图(“数值微分”)中可见，其中概述数值微分。可看出，窗口形状并非连续可微分数学函数，且因此关于频率响应为非最佳的。由于窗口形状中的静态一，来自上升函数及进入衰减函数的平滑过度是不可能的。
本发明打破设计约束以维持严格一区段以便优化时间形状。实际上，一由围绕线性函数(例如，常数值，诸如“1”)曲折的值序列替换。此解决方案允许平滑且连续的窗口形状，同时保持时间形状接近于最佳状态。
图3展示根据本发明的设计成具有曲折区段(部分)的示例窗口。如图3的第四子图(“时间调制量化误差”)中可见，关于量化误差的时间整形的窗口特性类似于ALDO窗口。然而，比较图3的第二子图(“数值微分”)与图2的第二子图(ALDO窗口)，可理解，本发明准许产生连续可微分的窗口形状。此使得例如能够以较高停止频带衰减设计窗口形状，到目前为止对于用于ALDO窗口的设计过程是不可能的。
图4更详细地概述示例窗口形状40。在此示例中，曲折区段基于以四个点的对应性与线性函数(在此情况下，常数值“1”)交叉。更高数量的交叉点是可能的，但四个被视为最小数量。
此类窗口可为组合用于频率响应的一个误差函数和表示与量化噪声的最佳时间整形的偏差的误差函数的数学优化过程的结果。
一些实施需要特定数据格式，例如，固定点实施。对于此类实施，窗口系数的值范围可为标量，因为高于一的值需要不同缩放。在此类情况下，曲折区段可能不围绕一。仅在解除缩放之后，值才变为显而易见的范围。
图5展示如何在固定点实施内部呈现MDCT窗口系数50的示例。其为一些值通过2x缩放且其他值通过2x-1缩放(由于固定点架构)的示例表示。
考虑通用情况，窗口不必围绕1曲折，但可围绕虚拟对角线曲折而不与一交叉。图6展示三个不同窗口，即
-w1：围绕1曲折的新优化(窗口化函数70)；
-w2：G.718窗口(完全不曲折)(窗口化函数70′)；
-w3：用于特殊情况的新优化窗口：围绕对角曲折(窗口化函数60)。
所描述的MDCT窗口满足完美的重构特性。由此，考虑MDCT分解为窗口化运算、时域混叠消除(TDAC)步骤及离散余弦变换(DCT)类型IV内核，如例如[3]中所描述。
因此，窗口化及TDAC可被视为分析侧的折叠步骤及合成侧的展开步骤。在后者处，在重叠相加运算中组合两个区块的展开序列。见图8，其指区块1(81)及区块2(82)的方案。
对于分析侧的重叠区，区块1的窗口化及TDAC可被描述为：
P1(n)＝wa(N+n)-wa(2N-1-n)对于n＝0...N-1
且区块2的窗口化及TDAC可被描述为：
P2(n)＝wa(N+n)+wa(N-1-n)对于n＝0...N-1
对于合成侧，P1及P2经展开、窗口化，且执行重叠相加：
O(n)＝ws(N+n)P1(n)+ws(n)P2(n)对于n＝0...N-1
此可被写为
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)
对于n＝0...N-1
其可分离成两个分量：
PR1：完美重构分量
wa(N+n)ws(N+n)+wa(n)ws(n)＝1
对于n＝0...N-1
-PR2：混叠消除分量
wa(N-1-n)ws(n)-wa(2N-1-n)ws(N+n)＝0
对于n＝0...N-1
图9至图12展示分析及合成序列。
现关于本发明的分析及合成窗口化函数的数值微分参考图19及20。
通过还考虑第2及第3数值微分，可以清楚地区分本发明示例(例如，参考图4的示例的图19及参考图26的示例的图31)的特性与现有技术(ALDO，图20)的特性。
作为调制重叠变换窗口形状(例如，MDCT或MDST窗口形状)的平滑度的量度，可使用数值微分，如：
为了加权每一系数的重要性，即较高振幅具有较高权重，以下描述经加权
此允许在窗口形状的连续性的分析中忽略低水平窗口系数。
在图19及图20以及图31中，第1数值微分被绘示为规则且经加权的版本(短划线)。1902及3102指本发明窗口化函数的第1数值微分；1904及3104(短划线)指本发明窗口化函数的第1数值微分的经加权版本。2002指ALDO窗口化函数的第1数值微分；2004(短划线)指ALDO窗口化函数的第1数值微分的经加权版本。
对于第2及第3数值微分(ND)，使用第1数值微分的经加权版本。1910及3110指本发明窗口化函数的第2数值微分的经加权版本。2010指ALDO窗口化函数的第2数值微分的经加权版本。1920指本发明窗口化函数的第3数值微分的经加权版本。2020及3120指ALDO窗口化函数的第3数值微分的经加权版本。
如可观察到，第2ND版本展示ALDO窗口的一些明显峰值2021，而本发明窗口展示仅适中的改变。对于第3ND，也可清楚区分且可表示两个窗口的振幅水平。
此处呈现对ALDO与本发明窗口化函数的窗口设计的自由度的分析。
ALDO设计方法[2]仅提供参数C1、C2及零的数量Lz作为自由度。通过所提出的方法，关于近场或远场衰减的任何聚焦是不可能的，因为设计过程中的给定自由度非常有限。
为了扩展ALDO算法且允许较高自由度，[2]中的设计方法需被放弃且需由数值优化方法交换。在第一步骤中，维持窗口中间的严格一区段，同时使自由窗口系数(或设计参数)优化。
假定分析和合成窗口总是彼此的时间反转版本，完美重构约束可由以下来表示：
wa(N+n)ws(N+n)+wa(n)ws(n)＝1对于n＝0...N-1
→w(N+n)w(2N-n)+w(n)w(N+n)＝1对于n＝0...N-1
此可始终通过将自由系数的数量限制为1.5N来满足，例如通过
w(2N-n)＝(1-w(n)w(N+n))/w(N+n)对于n＝0...N-1
零区段位于w(2N-n)内部。对于中间的严格一的约束，窗口系数的2*Lz被视为非自由系数。对于N＝480的变换长度及2N的窗口大小及Lz＝180，此导致1.5N-2*Lz＝360个自由系数的自由度。此窗口称为中间窗口。
新发明通过围绕一或围绕任何其他线性(例如，对角)线(例如，40'、60'、90')的曲折区段(例如，44、64、94)交换严格一的部分来将自由度增大至最大值。因此，仅一半中间区段需要从自由系数中排除。因此，可用系数的数量增大至1.5*480-180＝540个自由系数。此允许朝向任何凹入焦点最大限度地优化频率响应。
图21及图22展示设计方法的比较。特别地，图21展示比较ALDO窗口形状(211)与中间窗口形状(212)与新发明窗口形状(213)。图22展示ALDO窗口形状(211)、中间窗口形状(212)、新发明窗口形状(213)的缩放(放大视图)。
中间窗口及新发明窗口朝向同一焦点优化。
图23展示利用ALDO(231)、中间(232)、新发明(233)的曲线图频率响应。中间(231)及新发明窗口(233)可聚焦于不同区域，从而在此情况下达成较佳远场衰减。需要此例如以避免由频带受限信号造成或每当信号通过滤波器组重采样时的任何混叠失真。此焦点对于ALDO窗口是不可能的，因为仅存在两个可用于控制形状的参数。比较中间与新发明窗口，显而易见，新发明达成响应中的小得多的波动(由于时域中非常连续的形状)。
图24展示比较中间(242)与新发明(243)的频率响应的缩放(放大视图)。如可观察到，新发明窗口(243)始终展示所有旁波带的显著较高衰减。此确认曲折部分(44、64、94)在窗口设计中优于严格一的部分。
参考窗口的时间调制，应注意，ALDO窗口的主要动机为组合不对称形状与最大振幅1，以便避免量化误差的大时间波动。量化误差在频域中相加，且其时间形状由合成窗口形状控制。
实际上，此处，曲折序列也甚至进一步改良此窗口特性。图25展示由ALDO窗口(253)及所提出的发明(251)造成的量化误差的时间调制的直接比较。如可看出，最大时间失真对于新发明较低，且因此提供较不明显的失真。
在以上示例中，曲折部分可例如与DCT内核(至少部分)对应。在示例中，至少一个第一交叉点(例如，#1)处于第一帧中，而至少另一交叉点(例如，#3)处于后续帧中。在示例中，一个交叉点(例如，#2)处于第一帧与后续帧之间的边界处。
在示例中，“曲折”指以下事实：存在与线性函数的至少四个相交点(曲折部分在至少两个点或在一些情况下在至少四个点中与线性函数交叉)。举例而言，曲折部分可具有递增部分，之后为递减部分，之后为递增部分，以此类推，或递减部分，之后为递增部分，之后为递减部分，以此类推。
6.其他示例
图17展示可实施编码器设备130(或130A)和/或MDCT工具131和/或执行方法150的至少一些步骤的设备110。设备110可包含处理器111及非暂时性存储器单元112，其中区块114储存指令，指令在由处理器111执行时可使得处理器111执行MDCT合成。非暂时性存储器单元112也可储存(区块113)分析窗口化函数，例如如上文所论述。设备110可包含输入单元116，输入单元可获得输入信息信号(例如，音频信号)。暂时性储存空间118可被保留用于保存待更新的数据(例如，输入缓冲区)。
图18展示可实施解码器设备140(或140A)和/或IMDCT 147和/或执行方法160的设备120。设备120可包含处理器121及非暂时性存储器单元122，其中区块124储存指令，指令在由处理器121执行时可使得处理器121尤其执行MDCT合成过程。设备120可包含输入单元126，输入单元可获得在FD中的信息信号(例如，音频信号)的经解码表示。处理器121可因此执行过程以获得信息信号的TD表示。可使用输出单元127将此经解码表示提供至外部单元。输出单元127可包含例如通信单元以与外部装置(例如，使用无线通信，诸如蓝牙)和/或外部储存空间通信。处理器121可将音频信号的经解码表示保存在本地储存空间128中。
在示例中，设备110与120可为相同装置。在示例中，设备110与120例如无线地(例如，使用协议蓝牙)交换信息信号和/或控制数据。
取决于特定实施要求，示例可以以硬件实施。可使用数字储存介质执行该实施，例如软盘、数字多功能光盘(DVD)、蓝光光盘、紧密光盘(CD)、只读存储器(ROM)、可编程只读存储器(PROM)、可擦除及可编程只读存储器(EPROM)、电可擦除可编程只读存储器(EEPROM)或闪存，其上储存有电子可读控制信号，电子可读控制信号与可编程计算机系统协作(或能够协作)使得执行相应方法。因此，数字储存介质可为计算机可读的。
通常，示例可实施为具有程序指令的计算机程序产品，当计算机程序产品执行于计算机上时，程序指令操作性地用于执行方法中的一个。程序指令可例如储存于机器可读介质上。
其他示例包含用于执行本文所描述的方法中的一个、储存于机器可读载体上的计算机程序。换言之，方法的示例因此为计算机程序，其具有用于在计算机程序于计算机上执行时执行本文中所描述的方法中的一个的程序指令。
方法的另一示例因此为数据载体介质(或数字储存介质，或计算机可读介质)，包含其上记录的用于执行本文所描述的方法中的一个的计算机程序。数据载体介质、数字储存介质或记录介质为有形和/或非瞬变的，而非无形及暂时性的信号。
另一示例包含处理单元，例如计算机或可编程逻辑设备，其执行本文所描述的方法中的一个。
另一示例包含计算机，其上安装有用于执行本文中所描述的方法中的一个的计算机程序。
另一示例包含将用于执行本文所描述的方法中的一个的计算机程序传送(例如以电子方式或以光学方式)至接收器的设备或系统。举例而言，接收器可为计算机、移动装置、存储器装置或其类似者。设备或系统可(例如)包含用于传送计算机程序至接收器的文件服务器。
在一些示例中，可编程逻辑装置(例如，场可编程门阵列)可用以执行本文中所描述的方法的功能性中的一些或全部。在一些示例中，场可编程门阵列可与微处理器协作，以便执行本文中所描述的方法中的一个。通常，方法可由任何适当的硬件设备执行。
上述示例说明上文所论述的原理。应理解，本文中所描述的配置及细节的修改及变化将为显而易见的。因此，希望受到接下来的权利要求的范围限制，而不受通过本文中的示例的描述及解释所呈现的特定细节限制。
7.窗口化函数的一些示例
此处提供数值示例。由于尚未发现用于获得函数的呈闭合形式的数学公式，因此在此提供示例。下文中可以以反向或正向次序提供值，即在一些示例中，第一值与时刻n＝0相关联，最后值与最后时刻n＝2N-1相关联(正向方向)，而在一些示例中，第一值与时刻n＝2N-1相关联，而最后值与第一时刻n＝0相关联(反向方向)。在一些情况下，分析窗口化函数与合成窗口化函数从相同列表获得，但分析窗口化函数在反向(或前向)方向上读取，而合成窗口化函数在前向(或反向)方向上读取。
为了体现以下示例中的至少一个，当10个值不同于0时(例如，所有样本或至少其大多数可形成至少10个值)，可以提取至少10个值的子系列(例如，连续值)，。±1％的容限可为可能的，在一些情况下，±0.5％、±0.05％，在一些情况下±2％、±5％，在其他情况下0％。
7.1与图4及图9相关联的示例
在示例中，诸如-7.078546706512391e-04f的记数法意味着-7.078546706512391*10-4。”f”指浮点记数法(在一些情况下，其可省略)。
对于帧大小N＝80，窗口化函数w80的数值示例在此通过160个条目提供(对于n＝0…2N-1)。如上所解释，最后值可连续为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,
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+9.928619727154252e-01f,+9.941156069136238e-01f,+9.956033775539884e-01f,
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+1.007189345025525e+00f,+1.008200146369426e+00f,+1.008949493525753e+00f,
+1.009458241425143e+00f,+1.009768980817384e+00f,+1.009940336228694e+00f,
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+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
对于帧大小N＝160，窗口化函数w160的数值示例在此通过320个条目提供(对于n＝0…2N-1)。如上所解释，最后值可连续为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,
-3.967067992672979e-02f,-4.472698045914417e-02f,-4.994225863256500e-02f,
-5.526334794593565e-02f,-6.063717235243996e-02f,-6.600961519440657e-02f,
-7.131966266443390e-02f,-7.651178225890490e-02f,-8.152964005319532e-02f,
-8.631137544905677e-02f,-9.080411291245728e-02f,-9.495377758870335e-02f,
-9.870736514214426e-02f,-1.020202684361974e-01f,-1.048438825017798e-01f,
-1.071382314127799e-01f,-1.088690135027248e-01f,-1.099969655786929e-01f,
-1.104898474883336e-01f,-1.103225838568563e-01f,-1.094621746650760e-01f,
-1.078834293141886e-01f,-1.055612509762041e-01f,-1.024650162703341e-01f,
-9.857014566194629e-02f,-9.384684920715425e-02f,-8.826309993000785e-02f,
-8.178792716809512e-02f,-7.438785600211463e-02f,-6.602189797715241e-02f,
-5.665655641133161e-02f,-4.624456893420224e-02f,-3.474585776145929e-02f,
-2.211581608120528e-02f,-8.310425696208936e-03f,+6.717697635290676e-03f,
+2.300642061077823e-02f,+4.060106462625085e-02f,+5.953239090915557e-02f,
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+4.261772971493010e-01f,+3.845172335531009e-01f,+3.435228672445613e-01f,
+3.036004651973099e-01f,+2.651434678028531e-01f,+2.285283969438072e-01f,
+1.941021906320984e-01f,+1.621735416384830e-01f,+1.330015240938615e-01f,
+1.067840430193724e-01f,+8.365057236623041e-02f,+6.365188111381356e-02f,
+4.676538412257621e-02f,+3.288072750732215e-02f,+2.183057564646270e-02f,
+1.336381425803019e-02f,+6.758124889697787e-03f,+0.000000000000000e+00f,
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+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,
+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
在此提供对于帧大小N＝240的窗口化函数w240的数值示例(480个样本)：
-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,
-1.762979910961727e-02f,-1.999721557401502e-02f,-2.252080561390149e-02f,
-2.519406300389030e-02f,-2.800909464274782e-02f,-3.095765092956728e-02f,
-3.402996266948349e-02f,-3.721502082245055e-02f,-4.050053247568393e-02f,
-4.387219218706189e-02f,-4.731768261606175e-02f,-5.082325342672667e-02f,
-5.437166635159518e-02f,-5.794654834034055e-02f,-6.153426201732499e-02f,
-6.511708163113709e-02f,-6.867606753531441e-02f,-7.219447805250771e-02f,
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在此提供对于帧大小N＝320的窗口化函数w320的数值示例(640个样本)：
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在此提供对于帧大小N＝480的窗口化函数w480的数值示例(960个样本)：
-2.353032150516754e-04f,-4.619898752628163e-04f,-6.262931535610879e-04f,
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在此提供对于帧大小N＝960的窗口化函数w960的数值示例(1920个样本)：
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+9.464262017505555e-03,+8.433087782643726e-03,+7.364501936162659e-03,
+6.073847663871269e-03,+4.449668997344740e-03,+2.485333612762431e-03,
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7.2与图26至图30相关联的示例
对于帧大小N＝40，窗口化函数w40的数值示例在此通过80个条目提供(对于n＝0…2N-1)。如上所解释，最后值可为0。
+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,
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+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,
+0.000000000000000e+00,+0.000000000000000e+00.
对于帧大小N＝80，窗口化函数w80的数值示例在此通过160个条目提供(对于n＝0…2N-1)。如上所解释，最后值可为0。
+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,
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+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,
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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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+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,
+0.000000000000000e+00.
对于帧大小N＝120，窗口化函数w120的数值示例在此通过240个条目提供(对于n＝0…2N-1)。如上所解释，最后值可为0。
+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,
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+5.764872452085427e-01,+6.003522489375573e-01,+6.240509872809882e-01,
+6.475182586093196e-01,+6.706896380227332e-01,+6.935029068990036e-01,
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+7.799586608897265e-01,+8.000925313431716e-01,+8.195318652294690e-01,
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+9.934523971504882e-01,+9.920995520917141e-01,+9.909475998606236e-01,
+9.899902426925508e-01,+9.892206942816891e-01,+9.886318043013834e-01,
+9.882160904669929e-01,+9.879658322200813e-01,+9.878730767519871e-01,
+9.879296932443894e-01,+9.881273531631907e-01,+9.884575535474619e-01,
+9.889115869213529e-01,+9.894805541465801e-01,+9.901553455166457e-01,
+9.909266562913843e-01,+9.917849916000535e-01,+9.927206838643636e-01,
+9.937239208721489e-01,+9.947847580943504e-01,+9.958931493776203e-01,
+9.970389567617592e-01,+9.982119669301160e-01,+9.994020338838508e-01,
+1.000598323893564e+00,+1.001791235858836e+00,+1.002969837054169e+00,
+1.004123786397111e+00,+1.005242583245485e+00,+1.006315717067918e+00,
+1.007332693127034e+00,+1.008283053756130e+00,+1.009156423082384e+00,
+1.009942535308151e+00,+1.010631281038659e+00,+1.011212744622770e+00,
+1.011677230257499e+00,+1.012015300253356e+00,+1.012217779097186e+00,
+1.012275790821109e+00,+1.012180753005270e+00,+1.011924425888915e+00,
+1.011498917644724e+00,+1.010896765282633e+00,+1.010110965619444e+00,
+1.009135094671655e+00,+1.007963362035220e+00,+1.006590756505588e+00,
+1.005013115379014e+00,+1.003227255072391e+00,+1.001231060075500e+00,
+9.990235555436858e-01,+9.966050551498514e-01,+9.939894706113089e-01,
+9.904539200261149e-01,+9.868284225039941e-01,+9.827716736909488e-01,
+9.782206672373213e-01,+9.731250287581631e-01,+9.674323528812744e-01,
+9.610947043524248e-01,+9.540636479502398e-01,+9.462952991190324e-01,
+9.377489107516087e-01,+9.283864275822276e-01,+9.181762606422500e-01,
+9.070861558801854e-01,+8.950916858157935e-01,+8.821696237804294e-01,
+8.683025287048570e-01,+8.534769362643825e-01,+8.376852006833730e-01,
+8.209275259764013e-01,+8.032090930429980e-01,+7.845450482523652e-01,
+7.649554851899686e-01,+7.444735201251689e-01,+7.231348066419057e-01,
+7.009860555207412e-01,+6.780787033699450e-01,+6.544686506489734e-01,
+6.302212149502727e-01,+6.053970453856138e-01,+5.800715766089168e-01,
+5.543129276657669e-01,+5.282077505750727e-01,+5.018369724442092e-01,
+4.752902962082383e-01,+4.486552956056652e-01,+4.220281118338883e-01,
+3.955057965950340e-01,+3.691875990296320e-01,+3.431732847389720e-01,
+3.175633015043183e-01,+2.924566408966782e-01,+2.679463783886042e-01,
+2.441231331518492e-01,+2.210718537110466e-01,+1.988719153219592e-01,
+1.775967625327044e-01,+1.573148583944310e-01,+1.380903364946733e-01,
+1.199837497591550e-01,+1.030525757797769e-01,+8.735085011789188e-02,
+7.292811584897502e-02,+5.982732244758056e-02,+4.808178837444506e-02,
+3.771135297837851e-02,+2.871831923385135e-02,+2.108352028641225e-02,
+1.476289412849005e-02,+9.683884928956495e-03,+5.642168789286858e-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,+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.
对于帧大小N＝160，窗口化函数w160的数值示例在此通过320个条目提供(对于n＝0…2N-1)。如上所解释，最后值可为0。
+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,
+6.792906550106088e-01,+6.963256426589250e-01,+7.131194393772130e-01,
+7.296469905863920e-01,+7.458864594794676e-01,+7.618094719403713e-01,
+7.773958448163656e-01,+7.926208751337592e-01,+8.074666387233143e-01,
+8.219101564897180e-01,+8.359343163788637e-01,+8.495180470826319e-01,
+8.626485837105826e-01,+8.753083234662220e-01,+8.874884715160425e-01,
+8.991737724042251e-01,+9.103527429187326e-01,+9.210144133066616e-01,
+9.311556192776946e-01,+9.407644740241826e-01,+9.498382236872068e-01,
+9.583732599601223e-01,+9.663690412284377e-01,+9.738235617865406e-01,
+9.807442506043361e-01,+9.871297972052695e-01,+9.929872268444632e-01,
+9.983241398929388e-01,+1.003150760219063e+00,+1.007473713377193e+00,
+1.011309151636166e+00,+1.014666681083198e+00,+1.017563337333301e+00,
+1.020014681326785e+00,+1.022039872150903e+00,+1.023654257342442e+00,
+1.024881624147540e+00,+1.025739288978437e+00,+1.026250709375593e+00,
+1.026436666375082e+00,+1.026320857404224e+00,+1.025922917798664e+00,
+1.025269979527211e+00,+1.024382188798244e+00,+1.023284940887058e+00,
+1.022000829220643e+00,+1.020555973231408e+00,+1.018971390778550e+00,
+1.017275179369116e+00,+1.015489129111694e+00,+1.013639356938881e+00,
+1.011747750709711e+00,+1.009840844244693e+00,+1.007939764480188e+00,
+1.006407400915498e+00,+1.004374825095777e+00,+1.002469814737132e+00,
+1.000689073754539e+00,+9.990346001249977e-01,+9.975024904153303e-01,
+9.960941547576162e-01,+9.948051243621099e-01,+9.936362728142866e-01,
+9.925826537087717e-01,+9.916447007525191e-01,+9.908170758245324e-01,
+9.900998445795673e-01,+9.894873685512386e-01,+9.889794323427195e-01,
+9.885701787626714e-01,+9.882591911282058e-01,+9.880404423341358e-01,
+9.879133688360181e-01,+9.878718098237022e-01,+9.879150762106034e-01,
+9.880368938846610e-01,+9.882364564839506e-01,+9.885073687439192e-01,
+9.888487088987707e-01,+9.892539488627546e-01,+9.897220412447528e-01,
+9.902463287269285e-01,+9.908256340476208e-01,+9.914531811725067e-01,
+9.921276814881759e-01,+9.928422499725458e-01,+9.935955098307742e-01,
+9.943804814776256e-01,+9.951957244449919e-01,+9.960341878404958e-01,
+9.968943831870675e-01,+9.977692009836100e-01,+9.986571134591464e-01,
+9.995509738170480e-01,+1.000449227898040e+00,+1.001344692310058e+00,
+1.002235786606954e+00,+1.003115291715261e+00,+1.003981602446902e+00,
+1.004827468041713e+00,+1.005651275972376e+00,+1.006445772052972e+00,
+1.007209352772459e+00,+1.007934783656087e+00,+1.008620496650569e+00,
+1.009259314290145e+00,+1.009849742422788e+00,+1.010384692193296e+00,
+1.010862783160582e+00,+1.011277044709547e+00,+1.011626247430694e+00,
+1.011903571699736e+00,+1.012107954864219e+00,+1.012232755709885e+00,
+1.012277089047072e+00,+1.012234505114778e+00,+1.012104319978655e+00,
+1.011880293122688e+00,+1.011561972516341e+00,+1.011143373963981e+00,
+1.010624321020038e+00,+1.009999148545101e+00,+1.009268031808824e+00,
+1.008425698479647e+00,+1.007472774447058e+00,+1.006404483571931e+00,
+1.005222003295591e+00,+1.003921160689206e+00,+1.002503762756151e+00,
+1.000966332772540e+00,+9.993114007411373e-01,+9.975362702189898e-01,
+9.956442306333592e-01,+9.936333924912825e-01,+9.908677480361242e-01,
+9.882326326262749e-01,+9.853620567056602e-01,+9.822305093671991e-01,
+9.788185853162172e-01,+9.751026333215268e-01,+9.710631852370086e-01,
+9.666759668947944e-01,+9.619242192293307e-01,+9.567841986369235e-01,
+9.512394303101863e-01,+9.452700238623795e-01,+9.388615698236068e-01,
+9.319946435581106e-01,+9.246592033932568e-01,+9.168383396399868e-01,
+9.085218034087421e-01,+8.996967011299613e-01,+8.903562054918268e-01,
+8.804877931535187e-01,+8.700884209228057e-01,+8.591492134848259e-01,
+8.476686394755906e-01,+8.356428970797861e-01,+8.230753889817990e-01,
+8.099649296155544e-01,+7.963204506324437e-01,+7.821460539775005e-01,
+7.674541821769616e-01,+7.522563457568547e-01,+7.365702052057368e-01,
+7.204090552899627e-01,+7.037975107157410e-01,+6.867542812151157e-01,
+6.693041888771051e-01,+6.514710959179395e-01,+6.332854832820911e-01,
+6.147685389896460e-01,+5.959553778639692e-01,+5.768737955463938e-01,
+5.575534287167304e-01,+5.380320138068979e-01,+5.183454027643563e-01,
+4.985259415650634e-01,+4.786156067459849e-01,+4.586473038370941e-01,
+4.386643656872842e-01,+4.187046888325280e-01,+3.988123056192917e-01,
+3.790262923635886e-01,+3.593914828698096e-01,+3.399474132903109e-01,
+3.207392420889753e-01,+3.018061113177048e-01,+2.831905952786929e-01,
+2.649288369241889e-01,+2.470608550624402e-01,+2.296201119084317e-01,
+2.126433716126151e-01,+1.961601816145380e-01,+1.802035203864437e-01,
+1.647996883470626e-01,+1.499787548077656e-01,+1.357643522991611e-01,
+1.221842534547464e-01,+1.092601994264172e-01,+9.701788451015501e-02,
+8.547680283183663e-02,+7.465976378295235e-02,+6.458254322751883e-02,
+5.526281189874138e-02,+4.670976978373095e-02,+3.893244425578719e-02,
+3.192976013776996e-02,+2.569810636390756e-02,+2.022259265088492e-02,
+1.548317776486452e-02,+1.144924909653903e-02,+8.076482660383199e-03,
+5.300044080947794e-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,
+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.
在此提供对于帧大小N＝240的窗口化函数w240的数值示例(480个样本)：
+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,
+2.363479205237173e-01,+2.457259744642953e-01,+2.552771551741124e-01,
+2.649981094228982e-01,+2.748839432649996e-01,+2.849296444030153e-01,
+2.951306505827265e-01,+3.054824712370942e-01,+3.159799638238941e-01,
+3.266169794538543e-01,+3.373873799614014e-01,+3.482855915638277e-01,
+3.593057693987583e-01,+3.704415932452488e-01,+3.816862385160692e-01,
+3.930329782788047e-01,+4.044749630814483e-01,+4.160051103939122e-01,
+4.276159595085598e-01,+4.393004362003260e-01,+4.510516333434032e-01,
+4.628616046119925e-01,+4.747225454237193e-01,+4.866266705542529e-01,
+4.985664508456704e-01,+5.105341492548225e-01,+5.225212793188740e-01,
+5.345190505841265e-01,+5.465201916422433e-01,+5.585172769552711e-01,
+5.705021536899105e-01,+5.824658100332457e-01,+5.943991720381216e-01,
+6.062948176207270e-01,+6.181452662624718e-01,+6.299422016714543e-01,
+6.416768736044914e-01,+6.533411462740817e-01,+6.649277540000037e-01,
+6.764292700223311e-01,+6.878367295965062e-01,+6.991421467689277e-01,
+7.103379606632721e-01,+7.214176027060971e-01,+7.323746102405828e-01,
+7.432008025932804e-01,+7.538887973483771e-01,+7.644315495717613e-01,
+7.748223151443820e-01,+7.850546571907628e-01,+7.951223518167163e-01,
+8.050193862201107e-01,+8.147397447696774e-01,+8.242774413707643e-01,
+8.336267114335371e-01,+8.427819363777799e-01,+8.517386186427548e-01,
+8.604920874939698e-01,+8.690376742017057e-01,+8.773720451249032e-01,
+8.854927938913381e-01,+8.933935477349644e-01,+9.010727088526728e-01,
+9.085249398881980e-01,+9.157483563218768e-01,+9.227413839712016e-01,
+9.295017469413066e-01,+9.360270196617569e-01,+9.423143052164881e-01,
+9.483629792665091e-01,+9.541731142261065e-01,+9.597438382130120e-01,
+9.650738394220176e-01,+9.701635474343885e-01,+9.750143364412617e-01,
+9.796277191617885e-01,+9.840036439809510e-01,+9.881426772731259e-01,
+9.920470446911211e-01,+9.957199420334376e-01,+9.991640812275709e-01,
+1.002381307710643e+00,+1.005374268639838e+00,+1.008146718214831e+00,
+1.010703123647275e+00,+1.013046655758663e+00,+1.015181271161417e+00,
+1.017111643578857e+00,+1.018843380560658e+00,+1.020381713994816e+00,
+1.021731101971518e+00,+1.022896948293643e+00,+1.023885455671576e+00,
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在此提供对于帧大小N＝320的窗口化函数w320的数值示例(640个样本)。如上所解释，最后值可为0。
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在此提供对于帧大小N＝480的窗口化函数w480的数值示例(960个样本)。如上所解释，最后值可为0。
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在此提供对于帧大小N＝960的窗口化函数的数值示例(1920个样本)。如上所解释，最后值可为0。
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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,
+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,+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,+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,
+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,+0.000000000000000e+00,
+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,
8.参考文献
[1]3GPP,"Codec for Enhanced Voice Services(EVS)；Detailed algorithmicdescription,"[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.
Claims (65)
1.一种用于对包含多个帧的信息信号进行编码的设备(130，130A，110)，设备包含：
调制重叠变换工具(131)，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，调制重叠变换工具(131)被配置以使用分析窗口化函数(40，50，70，240)执行调制重叠变换分析，分析窗口化函数(40，50，70，240)具有以至少四个点(#1，#2，#2，#4)的对应性与线性函数(40’，240’)交叉的曲折部分(44，64，244)；以及
比特流写入器(137)，被配置以基于信息信号或其经处理版本的FD表示准备比特流；
其中分析窗口化函数被限定以便为不对称的；
其中分析窗口化函数(40，240)被限定以便在曲折部分(44，94，244)中：
在第一交叉点(#1)与第二交叉点(#2)之间的第一区间(41，241)中大于线性函数(40’，240’)；
在第二交叉点(#2)与第三交叉点(#3)之间的第二区间(42，242)中低于线性函数(40’，240’)；
在第三交叉点(#3)与第四交叉点(#4)之间的第三区间(43，243)中大于线性函数(40’，240’)，
其中分析窗口化函数被限定以使得绝对最大值(41’，241’)处于第一区间与第三区间中的一个中，
其中线性函数(40，240)为具有常数值1的常数函数。
2.如权利要求1所述的设备，
其中分析窗口化函数(40，240)被限定以使得分析窗口化函数(40，240)的最大值比线性函数(40，240)在相同时刻的值大出不到25％。
3.一种用于对包含多个帧的信息信号进行编码的设备(130，130A，110)，设备包含：
调制重叠变换工具(131)，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，调制重叠变换工具(131)被配置以使用分析窗口化函数(40，50，70，240)执行调制重叠变换分析，分析窗口化函数(40，50，70，240)具有以至少四个点(#1，#2，#2，#4)的对应性与线性函数(40’，60’，240’)交叉的曲折部分(44，64)；以及
比特流写入器(137)，被配置以基于信息信号或其经处理版本的FD表示准备比特流，
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数(40，240)被限定以使得分析窗口化函数(40，240)的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
4.一种用于对包含多个帧的信息信号进行编码的设备(130，130A，110)，设备包含：
调制重叠变换工具(131)，用于将信息信号或其经处理版本的时域TD表示变换为频域FD表示，调制重叠变换工具(131)被配置以使用分析窗口化函数(40，50，70，240)执行调制重叠变换分析，分析窗口化函数(40，50，70，240)具有以至少四个点的对应性与线性函数(40’，240’)交叉的曲折部分(44，64)；以及
比特流写入器(137)，被配置以基于信息信号或其经处理版本的FD表示准备比特流。
5.如前述权利要求中任一项所述的设备，其中调制重叠变换工具被配置以：
用分析窗口化函数(40，50，70，240)的值按比例调整时间输入缓冲区和/或余弦或正弦值。
6.如权利要求5所述的设备，其中调制重叠变换工具被配置以使用呈以下形式的输入缓冲区：
t(n)＝x(Z-NF+n)对于n＝0..2NF-1-Z，和
t(2N-Z+n)＝0对于n＝0..Z-1
其中x(n)为信息信号或信息信号的经处理版本在时刻n的TD样本，NF为在一个帧中处理的样本数量，以及Z为调制重叠变换窗口中的前导零的数量。
7.如前述权利要求中任一项所述的设备，其中调制重叠变换工具(131)被配置以执行：
其中X(k)为在频率索引k处的调制重叠变换频率值，n为时间常数，wN(n)为分析窗口化函数，t(n)为时间输入缓冲区，以及NF为在一个帧中处理的样本数量。
8.一种用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备(140，140A，120)，设备包含：
比特流读取器(141)，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具(147)，被配置以使用合成窗口化函数(90)对信息信号或其经处理版本执行逆调制重叠变换合成，合成窗口化函数(90)具有以至少四个点(#1，#2，#3，#4)的对应性与线性函数交叉的曲折部分(94)，
其中合成窗口化函数(90，290)被限定以便为不对称的，
其中合成窗口化函数(90，290)被限定以便在曲折部分(44，94，244)中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中合成窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中，其中线性函数为具有常数值1的常数函数。
9.如权利要求8所述的设备，
其中合成窗口化函数(90，290)被限定以使得合成窗口化函数(90，290)的最大值比线性函数(90，290)在相同时刻的值大出不到25％。
10.一种用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备(140，140A，120)，设备包含：
比特流读取器(141)，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具(147)，被配置以使用合成窗口化函数(90，290)对信息信号或其经处理版本执行逆调制重叠变换合成，合成窗口化函数(90，290)具有以至少四个点(#1，#2，#3，#4)的对应性与线性函数交叉的曲折部分(94，294)，
其中合成窗口化函数被限定以便为不对称的，
其中合成窗口化函数被限定以使得合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
11.一种用于对在频域FD中限定的信息信号或其经处理版本进行解码的设备(140，140A，120)，设备包含：
比特流读取器(141)，被配置以读取对信息信号进行编码的比特流；以及
逆调制重叠变换工具(147)，被配置以使用合成窗口化函数(90，290)对信息信号或其经处理版本执行逆调制重叠变换合成，合成窗口化函数(90，290)具有以至少四个点(#1，#2，#3，#4)的对应性与线性函数交叉的曲折部分(94，294)。
12.如权利要求8至11中任一项所述的设备，其中逆调制重叠变换工具(147)被配置以：
用合成窗口化函数(90)的值按比例调整时域混叠缓冲区处的值。
13.如权利要求8至12中任一项所述的设备，其中逆调制重叠变换工具(147)被配置为以如下形式产生时域TD信号表示：
其中
为混叠缓冲区，
为信息信号或其经处理版本，且NF为TD帧的样本数量。
14.如权利要求8至13中任一项所述的设备，其中逆调制重叠变换工具(147)被配置以：
执行时间混叠缓冲区的窗口化(S162)。
15.如权利要求8至14中任一项所述的设备，其中逆调制重叠变换工具(147)被配置以通过执行以下而执行窗口化运算：
16.如权利要求8至15中任一项所述的设备，其中逆调制重叠变换工具(147)被配置以执行重叠相加运算(S163)。
17.如权利要求8至16中任一项所述的设备，其中逆调制重叠变换工具(147)被配置以执行重叠相加运算如下：
其中
为输出值，
为经窗口化时间混叠缓冲区，且NF为一个帧中的样本数量。
18.如前述权利要求中任一项所述的设备(13，140，140A，110，120)，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以便在曲折部分(44，64，94)中：
在第一交叉点(#1)与第二交叉点(#2)之间的第一区间(41，241，91)中大于线性函数(40’，240’)；
在第二交叉点(#2)与第三交叉点(#3)之间的第二区间(42，242，92)中低于线性函数(40’，240’)；
在第三交叉点(#3)与第四交叉点(#4)之间的第三区间(43，243，93)中大于线性函数(40’，240’)。
19.如权利要求18所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以使得绝对最大值(41’，241)处于第一区间或第三区间(41，43，241，243)中。
20.如权利要求19所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以使得在曲折部分(44，244)中，相对最大值(43’，243’)处于第一区间或第三区间(41，43，241，243)中，且相对最小值(42’，242’)处于第二区间(42，242)中。
21.如权利要求18至20中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以使得在曲折部分(44，244，94)中，曲折窗口函数的对应于第一区间及第三区间(41，43，241，243，91，93)中的至少一个的值大于0.9。
22.如前述权利要求中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以便在曲折部分(44，244，94)中在由两个帧的30％与50％构成的区间中存在大于线性函数的值。
23.如权利要求18至22中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以使得分析窗口化函数(40，240)和/或合成窗口化函数(90)的最大值比线性函数在相同时刻的值大出不到25％。
24.如权利要求18至23中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以使得分析窗口化函数(40，240)和/或合成窗口化函数(90)的最大值(41’，241’)比线性函数在相同时刻的值大出不到5％。
25.如权利要求18至24中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以便存在介于-3*10-4与+3*10-4之间的第二数值微分。
26.如权利要求18至25中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以便存在介于-2*10-5与+2*10-5之间的第三数值微分。
27.如前述权利要求中任一项所述的设备，其中：
线性函数(40’，240’)被限定以便为非递增函数。
28.如权利要求4或11所述的设备，其中：
线性函数(40’，60’)被限定以便为严格递减函数。
29.如权利要求1至27中任一项所述的设备，其中：
线性函数(40’，60’)被限定以便为非递减函数。
30.如权利要求4或11所述的设备，其中：
线性函数被限定以便为严格递增函数。
31.如前述权利要求中任一项所述的设备，其中：
线性函数(40’，240’)被限定以便具有为常数或最大改变+2％或-2％的值。
32.如前述权利要求中任一项所述的设备，其中：
线性函数(40’，240)被限定以便具有介于-0.05与-0.20之间的增量。
33.如前述权利要求中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定以便为不对称的。
34.如前述权利要求中任一项所述的设备，其中：
分析窗口化函数(40，240)和/或合成窗口化函数(90)被限定为彼此的时间反转版本。
35.如前述权利要求中任一项所述的设备，进一步包含：
储存空间(113)，储存分析窗口化函数(40，60)和/或合成窗口化函数(90)的值。
36.如前述权利要求中任一项所述的设备，其中修改重叠变换为修改离散余弦变换MDCT或修改离散正弦变换MDST，且逆修改重叠变换为逆修改离散余弦变换IMDCT或逆修改离散正弦变换IMDST。
37.如前述权利要求中任一项所述的设备，进一步包含：
分析窗口化函数(40，240)和/或合成窗口化函数(90)为具有常数值1的常数函数。
38.如前述权利要求中任一项所述的设备，其中分析窗口化函数(40)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
-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。
39.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(40，60)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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40.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(40)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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41.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(40)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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42.如权利要求1至37中任一项所述的设备，其分析窗口化函数(40)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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43.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(40)和/或合成窗口化函数(90)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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44.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
+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。
45.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
+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。
46.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
+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,+9.882160904669929e-01,+9.879658322200813e-01,+9.878730767519871e-01,+9.879296932443894e-01,+9.881273531631907e-01,+9.884575535474619e-01,+9.889115869213529e-01,+9.894805541465801e-01,+9.901553455166457e-01,+9.909266562913843e-01,+9.917849916000535e-01,+9.927206838643636e-01,+9.937239208721489e-01,+9.947847580943504e-01,+9.958931493776203e-01,+9.970389567617592e-01,+9.982119669301160e-01,+9.994020338838508e-01,+1.000598323893564e+00,+1.001791235858836e+00,+1.002969837054169e+00,+1.004123786397111e+00,+1.005242583245485e+00,+1.006315717067918e+00,+1.007332693127034e+00,+1.008283053756130e+00,+1.009156423082384e+00,+1.009942535308151e+00,+1.010631281038659e+00,+1.011212744622770e+00,+1.011677230257499e+00,+1.012015300253356e+00,+1.012217779097186e+00,+1.012275790821109e+00,+1.012180753005270e+00,+1.011924425888915e+00,+1.011498917644724e+00,+1.010896765282633e+00,+1.010110965619444e+00,+1.009135094671655e+00,+1.007963362035220e+00,+1.006590756505588e+00,+1.005013115379014e+00,+1.003227255072391e+00,+1.001231060075500e+00,+9.990235555436858e-01,+9.966050551498514e-01,+9.939894706113089e-01,+9.904539200261149e-01,+9.868284225039941e-01,+9.827716736909488e-01,+9.782206672373213e-01,+9.731250287581631e-01,+9.674323528812744e-01,+9.610947043524248e-01,+9.540636479502398e-01,+9.462952991190324e-01,+9.377489107516087e-01,+9.283864275822276e-01,+9.181762606422500e-01,+9.070861558801854e-01,+8.950916858157935e-01,+8.821696237804294e-01,+8.683025287048570e-01,+8.534769362643825e-01,+8.376852006833730e-01,+8.209275259764013e-01,+8.032090930429980e-01,+7.845450482523652e-01,+7.649554851899686e-01,+7.444735201251689e-01,+7.231348066419057e-01,+7.009860555207412e-01,+6.780787033699450e-01,+6.544686506489734e-01,+6.302212149502727e-01,+6.053970453856138e-01,+5.800715766089168e-01,+5.543129276657669e-01,+5.282077505750727e-01,+5.018369724442092e-01,+4.752902962082383e-01,+4.486552956056652e-01,+4.220281118338883e-01,+3.955057965950340e-01,+3.691875990296320e-01,+3.431732847389720e-01,+3.175633015043183e-01,+2.924566408966782e-01,+2.679463783886042e-01,+2.441231331518492e-01,+2.210718537110466e-01,+1.988719153219592e-01,+1.775967625327044e-01,+1.573148583944310e-01,+1.380903364946733e-01,+1.199837497591550e-01,+1.030525757797769e-01,+8.735085011789188e-02,+7.292811584897502e-02,+5.982732244758056e-02,+4.808178837444506e-02,+3.771135297837851e-02,+2.871831923385135e-02,+2.108352028641225e-02,+1.476289412849005e-02,+9.683884928956495e-03,+5.642168789286858e-03,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000000000000e+00,+0.000000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47.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
+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,+6.792906550106088e-01,+6.963256426589250e-01,+7.131194393772130e-01,+7.296469905863920e-01,+7.458864594794676e-01,+7.618094719403713e-01,+7.773958448163656e-01,+7.926208751337592e-01,+8.074666387233143e-01,+8.219101564897180e-01,+8.359343163788637e-01,+8.495180470826319e-01,+8.626485837105826e-01,+8.753083234662220e-01,+8.874884715160425e-01,+8.991737724042251e-01,+9.103527429187326e-01,+9.210144133066616e-01,+9.311556192776946e-01,+9.407644740241826e-01,+9.498382236872068e-01,+9.583732599601223e-01,+9.663690412284377e-01,+9.738235617865406e-01,+9.807442506043361e-01,+9.871297972052695e-01,+9.929872268444632e-01,+9.983241398929388e-01,+1.003150760219063e+00,+1.007473713377193e+00,+1.011309151636166e+00,+1.014666681083198e+00,+1.017563337333301e+00,+1.020014681326785e+00,+1.022039872150903e+00,+1.023654257342442e+00,+1.024881624147540e+00,+1.025739288978437e+00,+1.026250709375593e+00,+1.026436666375082e+00,+1.026320857404224e+00,+1.025922917798664e+00,+1.025269979527211e+00,+1.024382188798244e+00,+1.023284940887058e+00,+1.022000829220643e+00,+1.020555973231408e+00,+1.018971390778550e+00,+1.017275179369116e+00,+1.015489129111694e+00,+1.013639356938881e+00,+1.011747750709711e+00,+1.009840844244693e+00,+1.007939764480188e+00,+1.006407400915498e+00,+1.004374825095777e+00,+1.002469814737132e+00,+1.000689073754539e+00,+9.990346001249977e-01,+9.975024904153303e-01,+9.960941547576162e-01,+9.948051243621099e-01,+9.936362728142866e-01,+9.925826537087717e-01,+9.916447007525191e-01,+9.908170758245324e-01,+9.900998445795673e-01,+9.894873685512386e-01,+9.889794323427195e-01,+9.885701787626714e-01,+9.882591911282058e-01,+9.880404423341358e-01,+9.879133688360181e-01,+9.878718098237022e-01,+9.879150762106034e-01,+9.880368938846610e-01,+9.882364564839506e-01,+9.885073687439192e-01,+9.888487088987707e-01,+9.892539488627546e-01,+9.897220412447528e-01,+9.902463287269285e-01,+9.908256340476208e-01,+9.914531811725067e-01,+9.921276814881759e-01,+9.928422499725458e-01,+9.935955098307742e-01,+9.943804814776256e-01,+9.951957244449919e-01,+9.960341878404958e-01,+9.968943831870675e-01,+9.977692009836100e-01,+9.986571134591464e-01,+9.995509738170480e-01,+1.000449227898040e+00,+1.001344692310058e+00,+1.002235786606954e+00,+1.003115291715261e+00,+1.003981602446902e+00,+1.004827468041713e+00,+1.005651275972376e+00,+1.006445772052972e+00,+1.007209352772459e+00,+1.007934783656087e+00,+1.008620496650569e+00,+1.009259314290145e+00,+1.009849742422788e+00,+1.010384692193296e+00,+1.010862783160582e+00,+1.011277044709547e+00,+1.011626247430694e+00,+1.011903571699736e+00,+1.012107954864219e+00,+1.012232755709885e+00,+1.012277089047072e+00,+1.012234505114778e+00,+1.012104319978655e+00,+1.011880293122688e+00,+1.011561972516341e+00,+1.011143373963981e+00,+1.010624321020038e+00,+1.009999148545101e+00,+1.009268031808824e+00,+1.008425698479647e+00,+1.007472774447058e+00,+1.006404483571931e+00,+1.005222003295591e+00,+1.003921160689206e+00,+1.002503762756151e+00,+1.000966332772540e+00,+9.993114007411373e-01,+9.975362702189898e-01,+9.956442306333592e-01,+9.936333924912825e-01,+9.908677480361242e-01,+9.882326326262749e-01,+9.853620567056602e-01,+9.822305093671991e-01,+9.788185853162172e-01,+9.751026333215268e-01,+9.710631852370086e-01,+9.666759668947944e-01,+9.619242192293307e-01,+9.567841986369235e-01,+9.512394303101863e-01,+9.452700238623795e-01,+9.388615698236068e-01,+9.319946435581106e-01,+9.246592033932568e-01,+9.168383396399868e-01,+9.085218034087421e-01,+8.996967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48.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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49.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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50.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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51.如权利要求1至37中任一项所述的设备，其中分析窗口化函数(240)和/或合成窗口化函数(290)包含呈前向或反向次序的通过以下值形成的至少系列或在不同于0的情况下具有以下值中的10个的至少子系列，具有±1％的容限：
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52.如前述权利要求中任一项所述的设备，其中分析窗口化函数和/或合成窗口化函数被限定以便存在介于-0.01与+0.01之间的第一数值微分。
53.如前述权利要求中任一项所述的设备，其中分析窗口化函数和/或合成窗口化函数被限定以便存在介于-10-4与+10-4之间的第二数值微分。
54.如前述权利要求中任一项所述的设备，第三其中分析窗口化函数和/或合成窗口化函数被限定以便存在介于-10-5与+10-5之间的第二数值微分。
55.如前述权利要求中任一项所述的设备，其中信息信号为音频信号。
56.一种系统，包含：
编码器130，130A，110)，作为如权利要求1至7中任一项或权利要求18至54结合权利要求1至7中任一项所述的设备；以及
解码器(140，140A，120)，作为如权利要求8至17中任一项或权利要求18至54结合权利要求8至17中任一项所述的设备。
57.如权利要求56所述的系统，其中编码器包含被配置以传输比特流的通信单元(117)，和/或解码器包含被配置以接收比特流的通信单元(126)。
58.一种方法，包含使用分析窗口化函数(40，50，240，70)执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，分析窗口化函数(40，50，240，70)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数(40’，240’)的曲折部分(44，244)。
59.一种方法，包含使用分析窗口化函数(40，50，240，70)执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，分析窗口化函数(40，50，240，70)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数(40’，240’)的曲折部分(44，244)：
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数(40，240)被限定以便在曲折部分(44，94，244)中：
在第一交叉点(#1)与第二交叉点(#2)之间的第一区间(41，241)中大于线性函数(40’，240’)；
在第二交叉点(#2)与第三交叉点(#3)之间的第二区间(42，242)中低于线性函数(40’，240’)；
在第三交叉点(#3)与第四交叉点(#4)之间的第三区间(43，243)中大于线性函数(40’，240’)，
其中分析窗口化函数被限定以使得绝对最大值(41’，241’)处于第一区间与第三区间中的一个中，
其中线性函数(40，240)为具有常数值1的常数函数。
60.一种方法，包含使用分析窗口化函数(40，50，240，70)执行修改余弦变换MDCT分析以将信息信号或其经处理版本的时域TD表示变换为频域FD表示，分析窗口化函数(40，50，240，70)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数(40’，240’)的曲折部分(44，244)，
其中分析窗口化函数被限定以便为不对称的，
其中分析窗口化函数(40，60)被限定以使得分析窗口化函数(40，60)的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
61.一种方法，包含使用合成窗口化函数(90)执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，合成窗口化函数(90)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数的曲折部分(94)。
62.一种方法，包含使用合成窗口化函数(90)执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，合成窗口化函数(90)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数的曲折部分(94)，
其中合成窗口化函数(90，290)被限定以便在曲折部分中：
在第一交叉点与第二交叉点之间的第一区间中大于线性函数；
在第二交叉点与第三交叉点之间的第二区间中低于线性函数；
在第三交叉点与第四交叉点之间的第三区间中大于线性函数，
其中合成窗口化函数被限定以使得绝对最大值处于第一区间与第三区间中的一个中，其中线性函数为具有常数值1的常数函数。
63.一种方法，包含使用合成窗口化函数(90)执行修改余弦变换MDCT合成以将信息信号或其经处理版本的频域FD表示变换为时域TD表示，合成窗口化函数(90)具有以至少四个点(#1，#2，#2，#4)的对应性经过线性函数的曲折部分(94)，
其中合成窗口化函数被限定以便为不对称的，
其中合成窗口化函数被限定以使得合成窗口化函数的最大值比线性函数在相同时刻的值大出不到25％，
其中线性函数为常数函数。
64.如权利要求58至63中任一项所述的方法，其中信息信号为音频信号。
65.一种非暂时性储存单元，储存指令，指令当在处理器上执行时使得处理器执行如权利要求58至63中任一项所述的方法。
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| EP3707711A1 (en) | 2020-09-16 |
| CA3082279A1 (en) | 2019-05-16 |
| KR20200088375A (ko) | 2020-07-22 |
| RU2740148C1 (ru) | 2021-01-11 |
| US11562754B2 (en) | 2023-01-24 |
| AU2018365209B2 (en) | 2021-05-13 |
| JP2021502604A (ja) | 2021-01-28 |
| EP3707711C0 (en) | 2023-09-06 |
| US20200272685A1 (en) | 2020-08-27 |
| AR113497A1 (es) | 2020-05-13 |
| TW201923756A (zh) | 2019-06-16 |
| AU2018365209A1 (en) | 2020-05-28 |
| WO2019092061A1 (en) | 2019-05-16 |
| ZA202002523B (en) | 2021-08-25 |
| ES2963344T3 (es) | 2024-03-26 |
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