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?image1cc2.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?

# DFT spectral analysis

Started by ●March 26, 2008

Reply by ●March 27, 20082008-03-27

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?image1cc2.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

> 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?image1cc2.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

Reply by ●March 28, 20082008-03-28

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?image1cc2.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 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?image1cc2.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?

Reply by ●March 28, 20082008-03-28

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 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?image1cc2.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 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 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?image1cc2.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?

>

Reply by ●March 28, 20082008-03-28

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?image1cc2.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 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?image1cc2.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?