MATLAB Central Newsreader - fft for beginners

fft for beginners

JMMO MartinOlalla — Sat, 04 Jul 2009 06:44:02 -0400

Hi all,

I am just starting doing fft with MatLab. No previous experience.

I am working with 2^19 experimental data points extending over some 50hours arranged as a vector X whose length is 2^19. I am getting on the fft since I need to study correlations and convutions in sets of different experimental data (so ifft will be also needed)

Since the rate of time in the experimental data is known I can control easily what the index of X means: say, from X(1,i) to X(1,i+1) there are 0.11ms while, of course, the first datapoint is t=0.

Now, I got: W=fft(X), which is again a vector whose length is 2^19.

My question is how is the index of this vector W running in the frequency domain? Say, low index means low frequency? frequencies are equally spaced? on what basis?

Also, I would like to know what would I be doing if I fftshift the vector W.

Thanks in advance.

Re: fft for beginners

Luca Zanotti Fragonara — Sat, 04 Jul 2009 15:33:01 -0400

Low indexes means low frequencies?

Yes, but remember that the second half of W contains negative frequencies (which usually are useless, but depends from your field of applications).

Frequency are equally spaced?

Yes.

On what basis?

It depends from your sampling time. If you didn't choose the nfft option, the fft command uses the default option, which calculates a fft which has length equal the length of X (your array).
So in order to build your frequency axis, you will have to use:
f = Fs/2*linspace(0,1,NFFT/2+1);

Where Fs is your sampling frequency and NFFT is the length of your fft.

Greetings,

Luca

"JMMO MartinOlalla" <none@us.es> wrote in message <h2mtni$phl$1@fred.mathworks.com>...
> Hi all,
>
> I am just starting doing fft with MatLab. No previous experience.
>
> I am working with 2^19 experimental data points extending over some 50hours arranged as a vector X whose length is 2^19. I am getting on the fft since I need to study correlations and convutions in sets of different experimental data (so ifft will be also needed)
>
> Since the rate of time in the experimental data is known I can control easily what the index of X means: say, from X(1,i) to X(1,i+1) there are 0.11ms while, of course, the first datapoint is t=0.
>
> Now, I got: W=fft(X), which is again a vector whose length is 2^19.
>
> My question is how is the index of this vector W running in the frequency domain? Say, low index means low frequency? frequencies are equally spaced? on what basis?
>
> Also, I would like to know what would I be doing if I fftshift the vector W.
>
> Thanks in advance.

Re: fft for beginners

Greg — Sat, 04 Jul 2009 18:43:05 -0400

On Jul 4, 2:44 am, "JMMO MartinOlalla" <n...@us.es> wrote:
> Hi all,
>
> I am just starting doingfftwith MatLab. No previous experience.
>
> I am working with 2^19 experimental data points extending over some 50hours arranged as a vector X whose length is 2^19. I am getting on thefftsince I need to study correlations and convutions in sets of different experimental data (so ifft will be also needed)

N = 2^19 % 524288
tmax = 50*60*60 % 180000
dt = tmax/(N-1) % 0.3433

t = dt*(0:N-1);
T = N*dt
t = 0:dt:T-dt;

Fs = 1/dt
df = 1/T
Fs = N*df
f = df*(0:N-1);
f = 0:df:Fs-df;

> Since the rate of time in the experimental data is known I can control easily what the index of X means: say, from X(1,i) to X(1,i+1) there are 0.11ms while, of course, the first datapoint is t=0.

You lied. If

dt = 1.1e-4

% then

tmaxsec = (N-1)*dt % 57.6716 seconds

tmaxhr = tmaxsec/3600 % 0.0160 hours (NOT ~ 50)

did you mean tmax ~ 50 sec ???

Anyway, go back and recalculate all of the above quantities

> Now, I got: W=fft(X), which is again a vector whose length is 2^19.
>
> My question is how is the index of this vector W running in the frequency domain? Say, low index means low frequency? frequencies are equally spaced? on what basis?

See above formula for f

> Also, I would like to know what would I be doing if I fftshift the vector W.

Then the N index periodicity is used to shift all frequences
at the Nyquist frequency Fs/2 = N*df/2 and above to negative
frequencies

fb = df*(-N/2:N/2-1);

Hope this helps.

Greg

Re: fft for beginners

Greg — Sat, 04 Jul 2009 18:57:23 -0400

PLEASE DO NOT TOPPOST!

On Jul 4, 11:33 am, "Luca Zanotti Fragonara" <Luca_Zano...@libero.it>
wrote:
> Low indexes means low frequencies?
>
> Yes, but remember that the second half of W contains negative frequencies (which usually are useless, but depends from your field of applications).

In particular, if X is real, the frequency components
above the Nyquist freqency are redundant because of
conjugate symmetry about the Nyquist frequency.

Hope this helps.

Greg

Re: fft for beginners

Etaoin — Mon, 06 Jul 2009 08:53:01 -0400

Thank you very much to Greg and and Luca; much more clear now.

Yes, I 'lied', it was not 0.11ms. Actually it was 0.11111111111mh=4s.

Greg <heath@alumni.brown.edu> wrote in message <b03e0cd2-9bba-477e-b2d0-37431867c269@j32g2000yqh.googlegroups.com>...
> On Jul 4, 2:44?am, "JMMO MartinOlalla" <n...@us.es> wrote:
> > Hi all,
> >
> > I am just starting doingfftwith MatLab. No previous experience.
> >
> > I am working with 2^19 experimental data points extending over some 50hours arranged as a vector X whose length is 2^19. I am getting on thefftsince I need to study correlations and convutions in sets of different experimental data (so ifft will be also needed)
>
> N = 2^19 % 524288
> tmax = 50*60*60 % 180000
> dt = tmax/(N-1) % 0.3433
>
> t = dt*(0:N-1);
> T = N*dt
> t = 0:dt:T-dt;
>
> Fs = 1/dt
> df = 1/T
> Fs = N*df
> f = df*(0:N-1);
> f = 0:df:Fs-df;
>
> > Since the rate of time in the experimental data is known I can control easily what the index of X means: say, from X(1,i) to X(1,i+1) there are 0.11ms while, of course, the first datapoint is t=0.
>
> You lied. If
>
> dt = 1.1e-4
>
> % then
>
> tmaxsec = (N-1)*dt % 57.6716 seconds
>
> tmaxhr = tmaxsec/3600 % 0.0160 hours (NOT ~ 50)
>
> did you mean tmax ~ 50 sec ???
>
> Anyway, go back and recalculate all of the above quantities
>
> > Now, I got: W=fft(X), which is again a vector whose length is 2^19.
> >
> > My question is how is the index of this vector W running in the frequency domain? Say, low index means low frequency? frequencies are equally spaced? on what basis?
>
> See above formula for f
>
> > Also, I would like to know what would I be doing if I fftshift the vector W.
>
> Then the N index periodicity is used to shift all frequences
> at the Nyquist frequency Fs/2 = N*df/2 and above to negative
> frequencies
>
> fb = df*(-N/2:N/2-1);
>
> Hope this helps.
>
> Greg