FPGA Central

Hi all!
I am a newbie to DSP. I have some basic questions. I will reall
appreciate if someone answers them.

1. Is it logical to perform 1024 point FFT on a vector of size less tha
1024 (say 150) in MATLAB ?
2. If yes, then -does MATLAB perform zero padding automatically in abov
case or do we need to do it manually ?
3. what kind of output will it give ?

"Rajan" <prasad6927373@rediffmail.com> skrev i en meddelelse
news:-JidnfJgtJHkbg_ZnZ2dnUVZ_s-dnZ2d@giganews.com...
>
> Hi all!
> I am a newbie to DSP. I have some basic questions. I will really
> appreciate if someone answers them.
>
> 1. Is it logical to perform 1024 point FFT on a vector of size less than
> 1024 (say 150) in MATLAB ?

It will increase the resolution of the spectrum and FFT of a 2^n vector is
easier/faster to calculate.

> 2. If yes, then -does MATLAB perform zero padding automatically in above
> case or do we need to do it manually ?

Use the help function in matlab and you will get an answer to some of your
questions.

>> help fft

FFT Discrete Fourier transform.
FFT(X) is the discrete Fourier transform (DFT) of vector X. For
matrices, the FFT operation is applied to each column. For N-D
arrays, the FFT operation operates on the first non-singleton
dimension.

FFT(X,N) is the N-point FFT, padded with zeros if X has less
than N points and truncated if it has more.

FFT(X,[],DIM) or FFT(X,N,DIM) applies the FFT operation across the
dimension DIM.

For length N input vector x, the DFT is a length N vector X,
with elements
N
X(k) = sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.
n=1
The inverse DFT (computed by IFFT) is given by
N
x(n) = (1/N) sum X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N.
k=1

See also IFFT, FFT2, IFFT2, FFTSHIFT.

Overloaded methods
help qfft/fft.m

> 3. what kind of output will it give ?

A small example could be:

subplot(1,3,1); plot(abs(fftshift(fft([1 2 3 4], 4))))
subplot(1,3,2); plot(abs(fftshift(fft([1 2 3 4], 16))))
subplot(1,3,3); plot(abs(fftshift(fft([1 2 3 4], 128))))

To reconstruct the signal ifft(fft([1 2 3 4])) you only need 4 points but
when you want to use the graph in a report then you could make a high
resolution graph by increasing N.

/Rune

"Rajan" <prasad6927373@rediffmail.com> wrote in message
news:-JidnfJgtJHkbg_ZnZ2dnUVZ_s-dnZ2d@giganews.com...
>
> Hi all!
> I am a newbie to DSP. I have some basic questions. I will really
> appreciate if someone answers them.
>
> 1. Is it logical to perform 1024 point FFT on a vector of size less than
> 1024 (say 150) in MATLAB ?
> 2. If yes, then -does MATLAB perform zero padding automatically in above
> case or do we need to do it manually ?
> 3. what kind of output will it give ?

1. Maybe, if that's what you want to do.
It will take longer than computing an fft over just 150 points.
The results will be an interpolated version of an fft that is 150 points but
add really no new information. So, the apparent increased resolution is a
bit illusory.

2. It depends. If you use fft(x) then no. If you use fft(x,n) then yes.

3. A complex vector of the length of x in the first case. A complex vector
of length n in the second case.

Fred Marshall wrote:
> "Rajan" <prasad6927373@rediffmail.com> wrote in message
> news:-JidnfJgtJHkbg_ZnZ2dnUVZ_s-dnZ2d@giganews.com...
> >
> > Hi all!
> > I am a newbie to DSP. I have some basic questions. I will really
> > appreciate if someone answers them.
> >
> > 1. Is it logical to perform 1024 point FFT on a vector of size less than
> > 1024 (say 150) in MATLAB ?
> > 2. If yes, then -does MATLAB perform zero padding automatically in above
> > case or do we need to do it manually ?
> > 3. what kind of output will it give ?
>
> 1. Maybe, if that's what you want to do.
> It will take longer than computing an fft over just 150 points.
> The results will be an interpolated version of an fft that is 150 points but
> add really no new information. So, the apparent increased resolution is a
> bit illusory.

It won't add information. But there will be an increase in
the resolution of the precise frequency of a well separated
sinusoidal component, more accurately than can be done
with using just the peak bins or even quadratic interpolation.
Essentially you get a high quality interpolator of lots
of intermediate points automatically in a much longer fft.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M