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Number of samples required for FFT

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lordsathish

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Hi all...
Suppose i have a band pass signal and i have sampled it at greater than the nyquist rate, then how many samples should i take from the sampled signal to take FFT of the given signal such that i have the info of all frequencies in the band pass signal...?
will this be different for a low pass signal...
 

such that i have the info of all frequencies in the band pass signal...?
To have the info of all frequencies, the number of samples has to be infinite.

A finite sequence also has a finite frequency resolution in FFT. It's up to you to define the requirements.
 

    lordsathish

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FvM said:
such that i have the info of all frequencies in the band pass signal...?
To have the info of all frequencies, the number of samples has to be infinite.

A finite sequence also has a finite frequency resolution in FFT. It's up to you to define the requirements.

And if we have N input samples for DFT (FFT) then we have resolution df ~ Fs/(2*N) for real input signal
Fs - sampling frequency
 

The resolution is Fs/N or Fs/2N...?
 

well, Fs/N

The frequency range is ( 0 - Fs/2) It is devided on N/2 bins, so Fs/N ))
Other N/2 are derivatives

But usually we also use windowing to prevent artifacts, so resolution is not so good
 

fft is all about to compute dft,it is simply an algorithum,it depends upon how much point dft u want to compute
 

Ok then suppose i have a 3KHz sinusoidal signal, I sample it at 23KHz.
I take FFT of 1024 points of this sampled signal.
Then frequency domain values of the FFT are given by Fs*k/N
Fs here is 23KHz and N is 1024.
So then this 3Khz impulse in the FFT should appear at 133.56522th point.
Since this point is in between two values i.e not discrete, does this mean that the FFT will not have the frequency content of the 3KHz sinusoid...?
 

lordsathish said:
Ok then suppose i have a 3KHz sinusoidal signal, I sample it at 23KHz.
I take FFT of 1024 points of this sampled signal.
Then frequency domain values of the FFT are given by Fs*k/N
Fs here is 23KHz and N is 1024.
So then this 3Khz impulse in the FFT should appear at 133.56522th point.
Since this point is in between two values i.e not discrete, does this mean that the FFT will not have the frequency content of the 3KHz sinusoid...?

There is no perfection. It represents content in such a discret way

By the way, if you have singular sinusoid (a priory knowledge about singular content) you could use interpolation to get "frequency content" more accurate. Look at this matlab models

**broken link removed**
 

lordsathish said:
Ok then suppose i have a 3KHz sinusoidal signal, I sample it at 23KHz.
I take FFT of 1024 points of this sampled signal.
Then frequency domain values of the FFT are given by Fs*k/N
Fs here is 23KHz and N is 1024.
So then this 3Khz impulse in the FFT should appear at 133.56522th point.
Since this point is in between two values i.e not discrete, does this mean that the FFT will not have the frequency content of the 3KHz sinusoid...?

Then something called leakage happens. The points around the 133.56522th get the energy of this point. The 134th and the 133th will have high peaks. The 135th and the 132th points will have peaks less then the 134th and 133th points. All points in FFT gets influenced by this effect and will show a peak.
 

You need to take samples in the frequency domain according to the nyquist critrain and do sampling the frequency axis. It will be the fft
 

It depends on the resolution u want for your signals. If you just want to know what all frequencies are there, then even a 128 point FFT will do.. Go for longer N only if you wish to resolve frequencies at the output.
 

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