信息处理 - 最小化 sinc 谱瓣 - 吾爱随笔录

由于某些原因，我想最小化矩形信号的 FFT 变换的次级波瓣（显示在下图的左上角）

所以我使用了窗口函数来做到这一点（左下角）。但是，如果我想直接在信号的复变换上进行（右下），则次级瓣的衰减值与时间情况不同。

有下面的测试代码，我想知道它有什么问题：

传递给编辑

     Fs = 1000; L = 2000; t = (0:L-1)*1/Fs;  
% the signal
y = zeros(1,L);  y(500:1500) = 1;     % rectangle signal

figure; 
subplot(2,2,1);
plot(Fs*t,y); title('Temporal signal'); xlabel('time (milliseconds)')

NFFT = 6*2^nextpow2(L);
Y1 = 2*abs(fft(y,NFFT)); Y1 = Y1/max(Y1);
f = 0:Fs/NFFT:Fs/2;

% the FFT of the signal
subplot(2,2,2);
semilogy(f, Y1(1:NFFT/2+1), '.-'); axis tight; grid on;
title('Signal''s spectrum'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|');

w = window(@blackman, L);
y1 = y.*w';
Y2 = 2*abs(fft(y1,NFFT)); Y2 = Y2/max(Y2);

% the FFT of the windowed signal, in time
subplot(2,2,3);
semilogy(f, Y2(1:NFFT/2+1), '.-'); axis tight; grid on;
title('FFT windowing - temporal product'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|')

% the FFT of the windowed signal, in complex
Y3 = 2*abs(fftshift(conv(Y1, fft(w,NFFT), 'same'))); Y3 = Y3/max(Y3);
subplot(2,2,4);
semilogy(f, Y3(1:NFFT/2+1), '.-');  axis tight; grid on;
title('FFT windowing - spectral convolution'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|')

编辑：
我已经根据@Matt 的评论更改了代码，但最后一张图仍然存在问题（FFT 卷积上的噪声）

NFFT = 6*2^nextpow2(L);
Y1 = fft(y,NFFT);
YY1 = 2*abs(Y1); YY1 = YY1/max(YY1);
f = 0:Fs/NFFT:Fs/2;

% the FFT of the signal
subplot(2,2,2);
semilogy(f, YY1(1:NFFT/2+1), '.-'); axis tight; grid on;
title('Signal''s spectrum'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|');

w = window(@blackman, L);
y1 = y.*w';
YY2 = 2*abs(fft(y1,NFFT)); YY2 = YY2/max(YY2);

% the FFT of the windowed signal, in time
subplot(2,2,3);
semilogy(f, YY2(1:NFFT/2+1), '.-'); axis tight; grid on;
title('FFT windowing - temporal product'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|')

% the FFT of the windowed signal, in complex
YY3 = 2*abs(cconv(Y1, fft(w,NFFT)', NFFT)); YY3 = YY3/max(YY3);
subplot(2,2,4);
semilogy(f, YY3(1:NFFT/2+1), '.-');  axis tight; grid on;
title('FFT windowing - spectral convolution'); xlabel('Frequency (Hz)'); ylabel('|Y(f)|')'