# How to correctly make FFT of sound set?

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Igor on 14 Jun 2011
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?

Rick Rosson on 17 Jun 2011
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

Igor on 17 Jun 2011
The best -- y=y(:) :-)
At zoom on figure I see 7 peaks symmetrically..
And I have to understand this result, and I shell push "Accept"-button!
Rick Rosson on 17 Jun 2011
Rick Rosson on 17 Jun 2011
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?

Daniel Shub on 15 Jun 2011
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 on 16 Jun 2011
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 Comment

Igor on 17 Jun 2011
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)