We performed Discrete Fourier Transform and Inverse Discrete Fourier Transform and studied the magnitude spectrum of the output obtained by Discrete Fourier Transform. We took two cases with input signals of lengths 4 and 8. It was observed that as the length of the input signal was increased the quality of the output magnitude spectrum improved. This was because the frequency spacing reduces which increases the approximation error in the spectrum representation.
Discrete Fourier Transform : https://drive.google.com/open?id=0BwzFGc0wvjNvdTF2ZG91Y1V5MGs
Inverse Discrete Fourier Transform : https://drive.google.com/open?id=0BwzFGc0wvjNvYW5pV1lVOFlYRWc
Discrete Fourier Transform : https://drive.google.com/open?id=0BwzFGc0wvjNvdTF2ZG91Y1V5MGs
Inverse Discrete Fourier Transform : https://drive.google.com/open?id=0BwzFGc0wvjNvYW5pV1lVOFlYRWc
Very precise
ReplyDeleteWith zero padding, the length of signal increases, the number of points per unit length in the spectrum increases, and so the resolution of the spectrum increases and hence the the approximation error reduces.
ReplyDeleteby appending more zeroes, the missing values in less point DFT are present in the DFT with more point.
ReplyDeleteDiscrete Fourier Transform is used to convert a time domain signal into frequency domain. It helps us in analyzing a signal.By increasing the length of N, the spacing between the values on the magnitude spectrum can be reduced thereby improving the quality of the spectrum.
ReplyDeleteFFT is faster compared to DFT and it is easier to implement FFT. But programming wise DFT is much simpler....
ReplyDeleteThank you for the additional information.
ReplyDelete