Initially a four point and later an eight point signal was fed as the input to implement the Discrete Fourier Transform which basically converted any signal from time to frequency domain.Thus in simple words DFT was nothing but the frequency sampled version of DTFT(Discrete time fourier transform).The results produced in both cases were found to be periodic in nature.Magnitude spectrums were plotted for each case which highlighted the effect of increasing the input signal length on frequency spacing , approximation error and spectrum resolution.The most revealing observation however was that as we expanded the input in time domain we achieved a compressed spectra in frequency domain.
Short and simple
ReplyDeleteHad to be. Thank you
DeleteIs DFT computationally efficient?
ReplyDeleteDue to large number computations in DFT it is not computationally efficient
DeleteIf input signal is not periodic,how is output periodic in nature?
ReplyDeleteIn DFT we always assume the input signal to be periodic in nature with period = N.
DeleteDFT is practical implementation of DTFT. DTFT is continuous in nature viz defined for every value of frequency in which case we will have to deal infinite values and it doesn't seem feasible. DFT on other hand is discrete i.e defined only for discrete values of frequency which means finite values to deal with and hence the name practical implementation. So although we get approximate results in case of DFT, error can be reduced by increasing 'N'where 'N' is the period of input signal.
ReplyDeleteDFT produces periodic results
ReplyDeleteThat is correct and this is mainly due to the fact that we assume the input as periodic in nature when we perform DFT.
Deletefreq domain sampling is easy to analyse
ReplyDeleteDFT is used when designing fir filters
ReplyDelete