matlab 求傅里叶变换（fft 模板）

柔光的暖阳◎ 2023-06-12 09:11 18阅读 0赞

总结：求傅里叶变换，通常必须用函数fft(),   但是求出来的是双边谱，需要转换为单边谱。这个时候有一标准化的动作：

y=fft(s);
    p2=abs(y/L);
    p1=p2(1:L/2+1);
    p1(2:end-1)=2*p1(2:end-1);

完整代码如下：

%% Noisy Signal
    % Use Fourier transforms to find the frequency components of a signal buried 
    % in noise.
    % Specify the parameters of a signal with a sampling frequency of 1 kHz and
    % a signal duration of 1 second.
    % Copyright 2015 The MathWorks, Inc.
    Fs = 1000;            % Sampling frequency                    
    T = 1/Fs;             % Sampling period       
    L = 1000;             % Length of signal
    t = (0:L-1)*T;        % Time vector
    %% 
    % Form a signal containing a 50 Hz sinusoid of amplitude 0.7 and a 120 Hz 
    % sinusoid of amplitude 1.
    
    S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);
    %% 
    % Corrupt the signal with zero-mean white noise with a variance of 4.
    
    X = S + 2*randn(size(t));
    %% 
    % Plot the noisy signal in the time domain. It is difficult to identify 
    % the frequency components by looking at the signal |X(t)|. 
    figure(1);
    subplot(311)
    plot(1000*t(1:50),X(1:50));
    title('Signal Corrupted with Zero-Mean Random Noise');
    xlabel('t (milliseconds)');
    ylabel('X(t)')
    %% 
    % Compute the Fourier transform of the signal. 
    Y = fft(X);
    %%
    % Compute the two-sided spectrum |P2|.  Then compute the single-sided
    % spectrum |P1| based on |P2| and the even-valued signal length |L|.
    P2 = abs(Y/L);
    P1 = P2(1:L/2+1);
    P1(2:end-1) = 2*P1(2:end-1);
    %% 
    % Define the frequency domain |f| and plot the single-sided amplitude
    % spectrum |P1|.  The amplitudes are not exactly at 0.7 and 1, as expected, because of the added 
    % noise. On average, longer signals produce better frequency approximations.
    f = Fs*(0:(L/2))/L;
    subplot(312)
    plot(f,P1);
    title('Single-Sided Amplitude Spectrum of X(t)');
    xlabel('f (Hz)');
    ylabel('|P1(f)|');
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Y = fft(S);
    P2 = abs(Y/L);
    P1 = P2(1:L/2+1);
    P1(2:end-1) = 2*P1(2:end-1);
    subplot(313);
    plot(f,P1);
    title('Single-Sided Amplitude Spectrum of S(t)')
    xlabel('f(Hz)');
    ylabel('|P1(f)|');
    grid on;

运行结果：

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjUyODA4OQ_size_16_color_FFFFFF_t_70][]

后来发现太麻烦了，还是有一个自己写得fft函数比较顺手：

function [f, spectrum ] = gan_fft(s,Fs,L)
    %GAN_FFT 此处显示有关此函数的摘要
    %   此处显示详细说明
    y=fft(s);
    p2=abs(y/L);
    p1=p2(1:L/2+1);
    p1(2:end-1)=2*p1(2:end-1);
    f = Fs*(0:(L/2))/L;
    spectrum=p1;
    
    end

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