MATLAB —— 信号处理工具箱之fft的案例分析

mytomorrow · 发表于 2019-11-26 14:06

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上篇：MATLAB —— 信号处理工具箱之fft的介绍和相关案例分析介绍了MATLAB信号处理工具箱中的信号变换 fft 并分析了一个案例，就是被噪声污染了的信号的频谱分析。

这篇博文继续分析几个小案例：

Gaussian Pulse
这个案例是将高斯脉冲从时域变换到频域，高斯脉冲的信息在下面的程序中都有注释：

clc
clear
close all
% 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)|')
$ f$ ^2 A2 J+ C+ j

高斯脉冲在时域的图像：

高斯脉冲在频域的图像：

Cosine Waves

这个例子比较简单，就是不同频率的余弦波在时域以及频域的比较：

clc
clear
close all
% 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.
& f) T: Z4 G9 I3 q* v2 Q
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.
8 X4 H5 d# U. o/ w# y
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
% v' O V9 E2 F6 ^- {
X = [x1; x2; x3];
% Plot the first 100 entries from each row of X in a single figure in order and compare their frequencies.
! g; i$ ?( T( z, f0 [/ |9 [2 E
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
+ W' w+ i$ n1 _6 d
% 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.
# W+ G) z" a$ y0 t+ H8 y
n = 2^nextpow2(L);
% Specify the dim argument to use fft along the rows of X, that is, for each signal.
$ \8 _+ Z/ @4 K% t9 ^, d
dim = 2;
% Compute the Fourier transform of the signals.
7 a) i% F, s! ?2 `0 N1 w- e
Y = fft(X,n,dim);
% Calculate the double-sided spectrum and single-sided spectrum of each signal.
) a/ _1 P! H T$ h
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.
$ m- ?+ ^! o" r, S6 n& a
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'])
end7 x; O5 L$ x, o& Q" a2 T

下图是频率为50Hz，150Hz以及300Hz的余弦波在时域的图像：

下图分别为其fft：

从频域图中可以清晰的看到它们的频率成分位于何处。

ddny · 发表于 2019-11-26 16:00

看看，学习一下

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MATLAB —— 信号处理工具箱之fft的案例分析

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