Discrete Fourier Transform

Discrete Fourier Transform

In this experiment, we calculated the discrete fourier transform of a N point sequence in time domain to obtain an N point sequence in Frequency domain. Hence, using DFT, discrete time data sets are converted into discrete frequency spectrum. DFT gives an approximate spectrum and is computationally slow. 

In the first case, the input signal was x[n] was an N point sequence. The output of DFT gave X[k] which was also an N point sequence.  

                      In the second case, the sequence was padded with zeros at the end. 

                    In the third case, the input signal was expanded by adding zeros in   between the signal values as shown.

All these cases showed that, as the length of signal increases by zero padding: Frequency spacing decreases, approximation error decreases and resolution of the spectrum increases. Hence, Expansion of a signal in time domain gives a compression of signal in frequency domain.