Hi,
I'm having trouble with a homework question.

Suppose I'm given a signal x[n], which is obtained by sampling at
a frequency of 2kHZ.Using matlab I plotted its spectrum (vs. frequency)
and got the following:
http://img141.imageshack.us/my.php?image=dft1cc2.jpg

The question is (quote): "Can you retrieve any information about the distribution of
frequencies as a function of time?"

What can I say about the signal except that it has 2 sinusoids?

S Alex-

> I'm having trouble with a homework question.
> 
> Suppose I'm given a signal x[n], which is obtained by sampling at
> a frequency of 2kHZ.Using matlab I plotted its spectrum (vs. frequency)
> and got the following:
> http://img141.imageshack.us/my.php?image=dft1cc2.jpg
> 
> The question is (quote): "Can you retrieve any information about the distribution of
frequencies as a function of time?"
> 
> What can I say about the signal except that it has 2 sinusoids?

You can say that you can't determine where in the input time domain frame the two
sine waves occurred; i.e. their relative position.  A single FFT does not offer "time
resolution".  You could also say that assuming no time domain window (like a Hamming
window) was applied, that neither of the two sinusoids were at the beginning of the
time frame (because there is no dc energy in the spectrum).

How many points were in the FFT?  Was the FFT size longer than the time frame size
(i.e. zero-filled)?  Did you apply a window prior to the FFT?

-Jeff

Hello,

You could try using the specgram function in matlab. It gives you the time-frequency
distribution of the signal. Remember, you can never estimate accurately the frequency at a
given time instant because of the uncertainty principle.

Regards,
Nik.

Hi,
>I'm having trouble with a homework question.
>
>Suppose I'm given a signal x[n], which is obtained by sampling at
>a frequency of 2kHZ.Using matlab I plotted its spectrum (vs. frequency)
>and got the following:
>http://img141.imageshack.us/my.php?image=dft1cc2.jpg
>
>The question is (quote): "Can you retrieve any information about the distribution of
frequencies as a function of time?"
>
>What can I say about the signal except that it has 2 sinusoids?

Hi Dear

You might be aware of the 'spectrogram' in MATLAB which plots the frequency
v/s time.

To my knowledge it could help in determining the frequency spectrum and its
time length. Well, it all depends which type of signal you are processing
for such analysis.

In my analysis, i analyse if there is any reflection of wave in first few
microseconds of the (raw) ampitude-time signal or not, and found that
frequency spectrum changes for direct waves compared to reflected waves in
first 20 microseconds. since your sampling rate is low, you may find
reflection in milli-seconds, not in microseconds.

such analysis is also useful in source location, etc.

from the plot you have mentioned, it shows that the source does have
dominating frequency spectrum between 650 to 750 Hz, and another one with
less dominating at 250 to 350 Hz.

if you plot the frequency v/s time, for first few data, you would be able to
find exactly at what time the signal is popping-up different frequency
spectrum.

other way, you can plot the band pass signals (650 to 750 Hz & 250 to 350
Hz) with different color and see the features in the amplitude-time plots.

i hope it helps.
cheers
Nadimul Haque Faisal

On 26/03/2008, s...@gmail.com <s...@gmail.com> wrote:
>
>   Hi,
> I'm having trouble with a homework question.
>
> Suppose I'm given a signal x[n], which is obtained by sampling at
> a frequency of 2kHZ.Using matlab I plotted its spectrum (vs. frequency)
> and got the following:
> http://img141.imageshack.us/my.php?image=dft1cc2.jpg
>
> The question is (quote): "Can you retrieve any information about the
> distribution of frequencies as a function of time?"
>
> What can I say about the signal except that it has 2 sinusoids?
>

Hi Dear
 
You might be aware of the 'spectrogram' in MATLAB which plots the frequency v/s time. 
 
To my knowledge it could help in determining the frequency spectrum and its time length. Well,
it all depends which type of signal you are processing for such analysis. 
 
In my analysis, i analyse if there is any reflection of wave in first few microseconds of the
(raw) ampitude-time signal or not, and found that frequency spectrum changes for direct waves
compared to reflected waves in first 20 microseconds. since your sampling rate is low, you may
find reflection in milli-seconds, not in microseconds. 
 
such analysis is also useful in source location, etc. 
 
from the plot you have mentioned, it shows that the source does have dominating frequency
spectrum between 650 to 750 Hz, and another one with less dominating at 250 to 350 Hz. 
 
if you plot the frequency v/s time, for first few data, you would be able to find exactly at
what time the signal is popping-up different frequency spectrum.
 
other way, you can plot the band pass signals (650 to 750 Hz & 250 to 350 Hz) with
different color and see the features in the amplitude-time plots. 
 
i hope it helps.
cheers
Nadimul Haque Faisal
Hi,
>I'm having trouble with a homework question.
>
>Suppose I'm given a signal x[n], which is obtained by sampling at
>a frequency of 2kHZ.Using matlab I plotted its spectrum (vs. frequency)
>and got the following:
>http://img141.imageshack.us/my.php?image=dft1cc2.jpg
>
>The question is (quote): "Can you retrieve any information about the distribution of
frequencies as a function of time?"
>
>What can I say about the signal except that it has 2 sinusoids?