how can i plot the amplitude spectrum of these signals

Question

Samuel Molinari 2021-7-12

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https://ww2.mathworks.cn/matlabcentral/answers/877038-how-can-i-plot-the-amplitude-spectrum-of-these-signals

编辑： Scott MacKenzie 2021-7-12

i need to plot the amplitude spectrum of this signals

and

g(t)=

the first fourier transform is:

and the second one is :

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Answer 1

Sulaymon Eshkabilov 2021-7-12

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在 MATLAB Online 中打开

Fs = ...    % Sampling freq
t  = ...    % Time  
    
F = 0.25+cos(2*pi*50*t);
L = length(F);
N = 2^nextpow2(L);
Y = fft(F, N);
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;
plot(f,P1) 
title('Single-Sided Amplitude Spectrum of S(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')

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Answer 2

Scott MacKenzie 2021-7-12

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https://ww2.mathworks.cn/matlabcentral/answers/877038-how-can-i-plot-the-amplitude-spectrum-of-these-signals#answer_745213

编辑：Scott MacKenzie 2021-7-12

在 MATLAB Online 中打开

Do you want the FFT of the combination of the 20 Hz and 50 Hz signals? If so, then this might be the sort of plot you are after:

duration = 1; % seconds
sRate = 8192; % default
sInterval = 1/sRate;
% vector for values of t at each sample point
t = 0:sInterval:duration;
n = length(t); % number of samples
% build the first wave vector, as per question (20 Hz)
y1 = 0.25 + sin(2*pi * 20 * t); 
% build the second wave vector, as per question (50 Hz)
y2 = cos(2*pi * 50 * t);
% combine waveforms
y = y1 + y2;
% constrain samples to +/- 1
y = rescale(y, -1, 1);
% perform fast fourier transform 
Y = fft(y); 
% get amplitude vs. frequency spectrum
P2 = abs(Y/n);
P1 = P2(1:n/2+1);
P1(2:end-1) = 2*P1(2:end-1);
tiledlayout('flow');
% plot signals 
nexttile;
plot(y);
set(gca,'ylim', [-1.2 1.2]);
title('Signal');
% plot fft of signals (up to 200 Hz only)
f = sRate*(0:(n/2))/n;
nexttile;
plot(f(1:200),P1(1:200));
title('Frequency Spectrum');