How to correctly make FFT of sound set?

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Igor
Igor 2011-6-14
评论： Danilo Persico 2021-7-9
During 7 sec 7 tones plays with frequences (all in Hz), one tone -- one sec. Code:
Fs=44100;f=[261.63 293.67 329.63 349.23 392.00 440 493.88];
duration=7;octava=2;f=f/octava;Df=duration*Fs;FF=2*pi/Fs*f;
len = length(f);tau=Df/len;
n=1:Df;y=zeros(1,Df);
for i = 1:len
amplitude=(n>(i-1)*tau)&(n<i*tau);
y = y + sin(FF(i)*n).*amplitude;
end
soundsc(y, Fs);
This question rather for mathematicians. Now I have to see Fourier tranformation. Perhaps it will not accurate vertical Dirac bars but what?
Code:
Y1=fft(y);plot(abs(Y1))
Two bar on edges? How to make beauty picture? And what frequencies will be?

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采纳的回答

Rick Rosson
Rick Rosson 2011-6-17
Maybe this will help:
%%Parameters:
playAudio = false;
%%Time domain:
Fs = 44100;
dt = 1/Fs;
StartTime = 0;
StopTime = 1;
t = (StartTime:dt:StopTime-dt)';
%%Cosine waves:
Fc = [261.63 293.67 329.63 349.23 392.00 440 493.88];
y = cos(2*pi*t*Fc);
N = size(y,2);
%%Reshape signal to a single column vector:
y = y(:);
%%Reformulate time domain:
StopTime = N*StopTime;
t = (StartTime:dt:StopTime-dt)';
M = size(t,1);
%%Frequency domain:
dF = Fs/M;
f = -Fs/2:dF:Fs/2-dF;
Y = (N/M)*fftshift(fft(y));
%%Play the music:
if playAudio
sound(y,Fs);
end
%%Plot time domain:
figure;
plot(t,y);
%%Plot frequency domain:
figure;
plot(f,abs(Y));
HTH.
Rick
  4 个评论
显示 2更早的评论
Rick Rosson
Rick Rosson 2011-6-17
Also, there are a few things about this script that are not quite optimal. Can you figure out what they are and how to fix them?
Danilo Persico
Danilo Persico 2021-7-9
Hello Mr. Rosson, I would like if you could give an explaination of the code, thank you!

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更多回答（2 个）

Daniel Shub
Daniel Shub 2011-6-15
The fft assumes that the signal is cyclical. You need to match up your edges (or zero pad) to get delta functions. The fft also returns both positive and negative frequencies. I would read the documentation about fft and fftshift.
Rick Rosson
Rick Rosson 2011-6-16
Please try the following:
dt = 1/Fs;
len = duration*Fs;
n = dt*(0:len-1);
Df = Fs/len;
f = -Fs/2:Df:Fs/2-Df;
Also:
Y1 = fftshift(fft(y));
plot(abs(Y1));
HTH.
  1 个评论
Igor
Igor 2011-6-17
Not clear...
1st part -- replace my 2nd row? but what is the sense of *f*?
how does the 2nd part refer to 1st part?
(because of, y-array is unchanged data)

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