aliasing in frequency domain problem
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Hello ,i am trying to show frequency domain transform of 3 sinuos signal.I samples it twice the frequency of the highest frequency in the signal.
Althogh i get 3 harmonics but i dont get them at the 10,30,70 Hz and their amplitude is not 10(As shown in the code bello)
Where did i go wrong?
Thanks.
t=0:0.001:1
f1=10;
f2=30;
f3=70;
y1=10*sin(2*pi*f1*t);
y2=10*sin(2*pi*f2*t);
y3=10*sin(2*pi*f3*t);
y4=y1+y2+y3;
% twice the sampling rate
Fs=2*70;
Ts=1/Fs;
Tn=0:Ts:1;
fft_L=length(Tn);
y4_samples=10*sin(2*pi*f1*Tn)+10*sin(2*pi*f2*Tn)+10*sin(2*pi*f3*Tn);
%stem(Tn_new,y4_samples);
ff=fft(y4,fft_L);
plot(abs(ff));
采纳的回答
Ameer Hamza
2020-4-1
编辑：Ameer Hamza
2020-4-1
First, you are taking fft of y4 which is sampled at 1000Hz. Check the following code to see how it can be dome properly
f1=10;
f2=30;
f3=70;
% twice the sampling rate
Fs=2.05*70; % sampling frequency is a bit above 2 times to get all the peaks.
Ts=1/Fs;
Tn=0:Ts:1;
fft_L=length(Tn);
y4_samples=10*sin(2*pi*f1*Tn)+10*sin(2*pi*f2*Tn)+10*sin(2*pi*f3*Tn);
%stem(Tn_new,y4_samples);
ff=fft(y4_samples);
ff1 = abs(ff/fft_L);
fft2 = ff1(1:floor(fft_L/2)+1);
f = Fs*(0:fft_L/2)/fft_L;
plot(f, fft2);
See this example for more detail: https://www.mathworks.com/help/matlab/ref/fft.html#buuutyt-7
5 个评论
fima v
2020-4-1
Ameer Hamza
2020-4-1
As an example check this
f1=10;
f2=30;
f3=70;
% twice the sampling rate
Fs=1.5*70; % sampling frequency is a bit above 2 times to get all the peaks.
Ts=1/Fs;
Tn=0:Ts:1;
fft_L=length(Tn);
y4_samples=10*sin(2*pi*f1*Tn)+10*sin(2*pi*f2*Tn)+10*sin(2*pi*f3*Tn);
%stem(Tn_new,y4_samples);
ff=fft(y4_samples);
ff1 = abs(ff/fft_L);
fft2 = ff1(1:floor(fft_L/2)+1);
fft2(2:end) = 2*fft2(2:end);
f = Fs*(0:fft_L/2)/fft_L;
plot(f, fft2);
The sampling frequency is 135 less than the Nyquist frequency for 70 Hz signal. So you will see that it is shifted back by the amount of this new sampling frequency (105-70=35) Hz.
Ameer Hamza
2020-4-1
Sorry, I don't have much knowledge about this stuff. Since this question is specifically related to signal to process, I think you will have a better chance of getting an answer on an appropriate forum: https://dsp.stackexchange.com/
fima v
2020-4-2
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