Digital Signal Processing and Processor

In this experiment, we performed Discrete Fourier Transform of 4-point sequence, zero padded signal (zero padding done to the 4 point sequence signal). Magnitude spectrum of the two case was drawn and observed that DFT coefficients are defined for w=2pik/n. Also the spectrum is discrete in the range 0 to pi.From the two cases when the signal was zero padded the length of the signal increased due to which frequency spacing got decreased which increases the Resolution the spectrum.We also observed that DFT produces periodic Results.Computations in DFT which included real Multiplication and Additions was also Calculated and we found that Discrete Fourier Transform is slow.   

We performed this experiment in two parts which included Discrete Convolution (expo 1 a) and Discrete Correlation (expt 1 b).We calculated the output manually in journal and with a c program which was executed and run on Linux os and we observed that the length of Linearly Convolved output signal was N=L+M-1 while that of Circularly Convolved output signal was Max(L,M) where L & M are length of input signals.Also circular convolution gives aliased(overlapped) output. In Discrete Correlation when the input signals are delayed auto-correlation of delayed input signal is same as that of original signal while Cross-Correlation of input with delayed input signal is same as that of auto correlated  delayed input signal. In Convolution we find the output of the system while in Correlation we find similarity between two signals.