【 MATLAB 】信号处理工具箱之 fft 案例分析

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 % Convert a Gaussian pulse from the time domain to the frequency domain.
    
 % 
    
 % Define signal parameters and a Gaussian pulse, X.
    
  
    
 Fs = 100;           % Sampling frequency
    
 t = -0.5:1/Fs:0.5;  % Time vector 
    
 L = length(t);      % Signal length
    
  
    
 X = 1/(4*sqrt(2*pi*0.01))*(exp(-t.^2/(2*0.01)));
    
 % Plot the pulse in the time domain.
    
 figure();
    
 plot(t,X)
    
 title('Gaussian Pulse in Time Domain')
    
 xlabel('Time (t)')
    
 ylabel('X(t)')
    
  
    
 % To use the fft function to convert the signal to the frequency domain, 
    
 % first identify a new input length that is the next power of 2 from the original signal length. 
    
 % This will pad the signal X with trailing zeros in order to improve the performance of fft.
    
  
    
 n = 2^nextpow2(L);
    
 % Convert the Gaussian pulse to the frequency domain.
    
 % 
    
 Y = fft(X,n);
    
 % Define the frequency domain and plot the unique frequencies.
    
  
    
 f = Fs*(0:(n/2))/n;
    
 P = abs(Y/n);
    
  
    
 figure();
    
 plot(f,P(1:n/2+1)) 
    
 title('Gaussian Pulse in Frequency Domain')
    
 xlabel('Frequency (f)')
    
 ylabel('|P(f)|')
    
  
    
  
    
  
    
    
    
    
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 % Compare cosine waves in the time domain and the frequency domain.
    
 % 
    
 % Specify the parameters of a signal with a sampling frequency of 1kHz and a signal duration of 1 second.
    
  
    
 Fs = 1000;                    % Sampling frequency
    
 T = 1/Fs;                     % Sampling period
    
 L = 1000;                     % Length of signal
    
 t = (0:L-1)*T;                % Time vector
    
 % Create a matrix where each row represents a cosine wave with scaled frequency. 
    
 % The result, X, is a 3-by-1000 matrix. The first row has a wave frequency of 50, 
    
 % the second row has a wave frequency of 150, and the third row has a wave frequency of 300.
    
  
    
 x1 = cos(2*pi*50*t);          % First row wave
    
 x2 = cos(2*pi*150*t);         % Second row wave
    
 x3 = cos(2*pi*300*t);         % Third row wave
    
  
    
 X = [x1; x2; x3];
    
 % Plot the first 100 entries from each row of X in a single figure in order and compare their frequencies.
    
  
    
 figure();
    
 for i = 1:3
    
     subplot(3,1,i)
    
     plot(t(1:100),X(i,1:100))
    
     title(['Row ',num2str(i),' in the Time Domain'])
    
 end
    
  
    
 % For algorithm performance purposes, fft allows you to pad the input with trailing zeros. 
    
 % In this case, pad each row of X with zeros so that the length of each row is the next higher power of 2 from the current length. 
    
 % Define the new length using the nextpow2 function.
    
  
    
 n = 2^nextpow2(L);
    
 % Specify the dim argument to use fft along the rows of X, that is, for each signal.
    
  
    
 dim = 2;
    
 % Compute the Fourier transform of the signals.
    
  
    
 Y = fft(X,n,dim);
    
 % Calculate the double-sided spectrum and single-sided spectrum of each signal.
    
  
    
 P2 = abs(Y/L);
    
 P1 = P2(:,1:n/2+1);
    
 P1(:,2:end-1) = 2*P1(:,2:end-1);
    
 % In the frequency domain, plot the single-sided amplitude spectrum for each row in a single figure.
    
  
    
 figure();
    
 for i=1:3
    
     subplot(3,1,i)
    
     plot(0:(Fs/n):(Fs/2-Fs/n),P1(i,1:n/2))
    
     title(['Row ',num2str(i),' in the Frequency Domain'])
    
 end
    
  
    
  
    
    
    
    
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