短时傅里叶变换和短时傅里叶逆变换

clc;
clear all;
close all;

% [s1, fs ] = audioread( 'Thunder5.wav' );
% [s2, fs ] = audioread( 'babble_4.wav' );
% [s3, fs ] = audioread( '123_16.wav' );

% 输入信号
[s1, fs ] = audioread( '2024.12.23.wav' );
[s2, fs ] = audioread( '2024.12.23.1.wav' );
[s3, fs ] = audioread( '2024.12.23.4.wav' );

% 将信号裁剪为1s
 s1 = s1(1:1*fs,:);
 s2 = s2(1:1*fs,:);
 s3 = s3(1:1*fs,:);

%源信号
S = [s1';s2';s3'];

%用来绘制时域图的时间轴横坐标
time = (1:length(s1))/fs; %时间轴
 A = rand(2,3);
%观测矩阵
X = A*S;

%%
% 进行STFT的参数
[m,~] = size(X);
windowlength = 1024;%窗长
nfft = 1024;
d = round(0.15*windowlength)*2;%帧移
overlap = windowlength - d;%重叠数
window = hann(windowlength);
T = size(X,2);
n_frames = fix((T-overlap)/(windowlength-overlap)); % 计算帧数

[stft_x1, f_1, t_1] = stft(X(1,:), fs, 'Window', window, 'OverlapLength', overlap, 'FFTLength', nfft);
[stft_x2, f_2, t_2] = stft(X(2,:), fs, 'Window', window, 'OverlapLength', overlap, 'FFTLength', nfft);

recovered_signals(1,:) = real(istft(stft_x1, 'Window', window, ...
                                        'OverlapLength', overlap, 'FFTLength', nfft));
recovered_signals(2,:) = real(istft(stft_x2, 'Window', window, ...
                                        'OverlapLength', overlap, 'FFTLength', nfft));

为什么使用短时傅里叶变换后直接再使用短时傅里叶逆变换后的信号要比源信号短