The aim of this experiment was to perform Discrete Fourier Transform(DFT) of N point signal. We found out the DFT of input signal x(n), zero padded x(n) and expanded signal. We also plotted the magnitude spectrum of these signals. We also performed Inverse Discrete Fourier Transform(IDFT) to verify our original input signal.
We observed that, as the length of the signal increases by zero padding, frequency spacing decreases, approximation error decreases and resolution of spectrum increases. DFT gives approximated spectrum. Expansion of signal in time domain gives compressed spectra in frequency domain. Also, DFT is computationally slow. We found out the total number of real additions and multiplications using the code and verified it with the formulae available for these parameters.
We observed that, as the length of the signal increases by zero padding, frequency spacing decreases, approximation error decreases and resolution of spectrum increases. DFT gives approximated spectrum. Expansion of signal in time domain gives compressed spectra in frequency domain. Also, DFT is computationally slow. We found out the total number of real additions and multiplications using the code and verified it with the formulae available for these parameters.
So as a remedy for better computation we can use Fast Fourier Transform
ReplyDeleteWhat happens when the length of the signal increases?
ReplyDeleteAs the length of signal increases, frequency spacing decreases, approximation error decreases and resolution of spectrum increases.
DeleteDFT results obtained are periodic you see...the reason would be due to multiplication of twiddle factor..which is periodic.
ReplyDeletefreq domain sampling is easy to analyse
ReplyDeleteNicely written
ReplyDeleteDFT produces periodic results
ReplyDeleteDft assumes input signal to be periodic
ReplyDeleteWhen the signal is expanded in time domain it is compressed in the frequency domain.
ReplyDeleteDFT is slow
ReplyDeleteDft is slow as compared to fft
ReplyDelete