In this experiment,we performed linear convolution,circular convolution and linear convolution using circular convolution. We used the mathematical formula of convolution and observed the results. The length of the input signal in linear convolution was L=5 and M=3, the length of the output signal was N=L+M-1. In circular convolution as we increase the the length of signal, zeros are added to the output signal. The length of the signal was N=max(L,M).For linear convolution using circular convolution N>= L+M-1. Zero padding was observed.We studied aliasing effect.We also performed cross and auto correlation. The second case was the same input but delayed. In auto correlation the value at the center is largest and the signal is symmetric.
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Correlation
Circular
Linear
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Correlation
Circular
Linear
If both x[n] and h[n] are causal then the resultant y[n] is also causal.
ReplyDeleteConvolution gives the relation between the input signal, output signal and the response of the signal.Correlation is the optimal technique for detecting a known waveform in random noise. It has applications such as radar.
ReplyDeleteZero padding smoothens the curve giving better resolution of the spectrum.
ReplyDeleteCan you mention about the aliasing effect?
ReplyDeleteYes the last value of M-1 of y(n) wraps around and gets added with the first M-1 of y(n). This is called as aliasing.
ReplyDeleteIn the circular convolution aliasing takes place where the last few values get aliased with ones in the start.
ReplyDelete