Matlab 實現信號的時域和頻域的濾波

目錄

1. 頻域濾波
2. 時域濾波

1. 頻域濾波

% https://ccrma.stanford.edu/~jos/parshl/Overlap_Add_Synthesis.html
function overlap_add_synthesis
    
    close all;

    infile = 'P501_C_chinese_f1_FB_48k.wav';
    infile = 'P501_C_chinese_m1_FB_48k.wav';
    outfile = regexprep(infile, '\.wav', '_20200527_new.wav');
    [data, fs] = audioread(infile); % 384000, 48k
    
    %%
    figure;
    plot(data);
    title('原始信號時域');
    xlabel('t/s');
    ylabel('幅度');
    
    %%
    frame_length = 1024;
    frame_shift = 512;
    frame_overlap = frame_length - frame_shift;
    
    fftsize = 2^nextpow2(frame_length);
    % hamming windows: sqrt would make the values larger, periodic
    analysis_window = sqrt(hamming(frame_length, 'periodic')); 
%     analysis_window = ones(frame_length, 1);  square windows
    synthesis_window = analysis_window;
    
    % 1024 * 749 (frame_length * num_frames)
    x = buffer(data, frame_length, frame_overlap, 'nodelay'); % 'nodelay' means start from zero, withour padding

    % Analysis windowing: (1024, 749) * (1024,1) could be multiplied by .*
    x_anawin = x.*repmat(analysis_window(:), [1, size(x, 2)]); 
    
    % To frequency-domain
    X = fft(x_anawin, fftsize); %  default: fft(x_anawin, fftsize, 1);
    figure;
    f = linspace(-24000, 24000, 1024);
    plot(abs(X));
    title('原始信號頻域');
    xlabel('f/Hz');
    ylabel('幅度');
   
    %%
    % Modify the spectrum X here
    % generate filter, i.e., (1024, 1)
    x_f=[0, 1000, 2000, 3500, 24000]; 
    y_f=[1, 0.98, 0.7, 0.55, 0.1];
    % 1 means DC offset, X(k) should equal X(1026-k), thus X(513) is the
    % center, X(512) = X(514), X(2) = X(1024), X(1) = DC offset.
    xx=1:48000/1024:48000/1024*513; 
    fil=interp1(x_f,y_f,xx,'cubic');
    % [513, 1026] 513 points, while X(513) and X(last) should be removed,
    % since X(513) is contained in fil, X(last) is not used(X(0) has no synmetric point)
    fil2=fliplr(fil);
    fil2(1) = [];
    fil2(512) = [];
    fil = [fil fil2];
    figure;
    plot(fil);
    
    X = X.* fil';    
%   X = X.* 0.2; 
    figure;
    plot(f, abs(X));
%     X(1:513,:) = X(1:513,:) * 0.2;
    
    %%
    % To time-domain
    y = ifft(X);
    
    % Synthesis windowing
    y_synwin = y.* repmat(synthesis_window(:), [1, size(y, 2)]);
    
    % Overlap-add
    y_ola = y_synwin(:, 1);
    for i = 2:size(y_synwin, 2)
        y_ola(end+(1:frame_shift)) = zeros(frame_shift, 1);
        y_ola(end+(-frame_length+1:0)) = y_ola(end+(-frame_length+1:0)) + y_synwin(:, i);
    end
    
    % Output
    audiowrite(outfile, y_ola, fs);
    
end

對應的原始時域信號、頻域信號、濾波器、濾波後的頻域信號分別爲：

用adobe audition查看，即可看到頻率被減小了，即實現了高通濾波器。
注：紅色爲原來的頻率，黃色爲濾波後的。

2. 時域濾波

f1=5;%第一個點頻信號分量頻率
f2=15;%第二個點頻信號分量頻率
fs=100;%採樣率
T=2;%時寬
B=10;%FIR截止頻率
n=round(T*fs);%採樣點個數
t=linspace(0,T,n);
y1= cos(2*pi*f1*t);
y2=cos(2*pi*f2*t);
y=y1+y2;

%%
figure;
plot(t,y);
title('原始信號時域');
xlabel('t/s');
ylabel('幅度');

figure;
plot(t,y1);
title('原始信號時域');
xlabel('t/s');
ylabel('幅度');

figure;
plot(t,y2);
title('原始信號時域');
xlabel('t/s');
ylabel('幅度');

%%
figure;
fft_y=fftshift(fft(y));
f=linspace(-fs/2,fs/2,n);
plot(f,abs(fft_y));
title('原始信號頻譜');
xlabel('f/Hz');
ylabel('幅度');
axis([ 0 50 0 100]);

figure;
fft_y=fftshift(fft(y1));
f=linspace(-fs/2,fs/2,n);
plot(f,abs(fft_y));
title('原始信號y1頻譜');
xlabel('f/Hz');
ylabel('幅度');
axis([ 0 50 0 100]);

figure;
fft_y=fftshift(fft(y2));
f=linspace(-fs/2,fs/2,n);
plot(f,abs(fft_y));
title('原始信號y2頻譜');
xlabel('f/Hz');
ylabel('幅度');
axis([ 0 50 0 100]);

%%
b=fir1(80, B/(fs/2),'high');                    %濾波產生指定帶寬的噪聲信號
figure;
freqz(b);

%%
 y_after_fir=filter(b,1,y);

 %%
 figure;
 plot(t,y_after_fir);
 title('濾波後信號時域');
 xlabel('t/s');
 ylabel('幅度');
 fft_y1=fftshift(fft(y_after_fir));

 figure;
 f=linspace(-fs/2,fs/2,n);
 plot(f,abs(fft_y1));
 title('濾波後信號頻譜');
 xlabel('f/Hz');
 ylabel('幅度');
 axis([ 0 50 0 100]);
 

具體濾波結果如下圖