zero padding - increase sampling rate in freq domain

hi

i have a doubt like how is that the zero padding in time domain resulting in the increase of the sampling rate in Fourier Domaini mena i have seen so many books which gives finer spectrum by padding zeros. How is it possible by just adding zeros will give good resolution in the other domain? will it be the same even if padd zeros in Freq domain will result in upsampling of the time domain signal.?
pls help me in this regard

thnx

purna

zero padding can not increase sampling rate in freq domain, it increase resolution of frequency domain.

I would think of it as an extrapolation (the zero padding) or interpolation (inreased resolution/"sampling rate). It is not exact/perfect.

hi purnapragna,
Zero padding decreases the interval between two samples in the DFT as the N point DFT is calculated as compared to M point DFT earlier without zero padding, where N>M.Hence it gives finer spectrum by padding zeros.
happy learning..........

decrease of interval between the samples in DFT domain? It is nothing but the increase of sampling rate in freq domain right? Is the finer spectrum means gud resolution?

I mean what is exact definition of frequency resolution?

thnx

purna

Frequency resolution: Once the signal in time domain becomes discrete, the freqeuncies can only be represented in the range of 0 to 2*pi.

now, let us say we have a signal x[n] which is represented by 10 samples and you take 10 point DFT on it, this will result in 10 frequency components called bins, with frequency resolution of (2*pi/10).

now, if the same signal is sampled at ten times the previous sampling rate so that you have 100 samples of the same signal for the same time duration. now if you take a 100 point DFT of this signal, you will get frequency bins spaced at (2*pi/100).

as you can see from the above example the frequency resolution has increased (meaning the spacing between adjacent frequency components has decreased) so that you can see even minor variations in the frequency characterstics of the signal x[n]..

i hope the concept of frequency resolution is clear now..

hi so now can i say that i have increased the sampling rate in frequency domain and has filtered the signal in time domain to get the samples of the signal (freq domain) . i..e., i mean i have done fltering ing the time domain?

pls clarify me

regards

purna

first let me make some things clear, according to you, does sampling rate in the frequency domain refer to sampling of the DTFT of the signal in order to obtain the DFT. if this is true, then we are speaking of two diferent things.
as for ur second question, increasing the frequency resolution doesnt result in time domain filtering as far as i know..

see as we know that time and frequency domains both are dual of each other we can say th at increase of frequency resolution which is same as increase of sampling rate in freq domain, there shd be something called time domain filtering which we can call as windowing effect. I think i m yet to be clarified thourouhly

thnx

purna