This experiment was performed in two parts which included Discrete Convolution and Discrete Correlation..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 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. The application of Convolution is to find the output of the system while that of Correlation is to find degree of similarity between two signals.
Correlation gives similarity of signals. It is used in Audio Feature Extraction to compare the extracted signal with the reference signal.
ReplyDeleteZero padding smoothen the curve giving better resolution of the spectrum.
ReplyDeleteIf both x[n] and h[n] are causal then the resultant y[n] is also causal.
ReplyDeleteOne of the key application of correlation is in radar systems.The transmitted signal is correlated with the echo signal to locate the position of the target.Convolution gives the relation between the input signal, output signal and the response of the signal.
ReplyDeletewe use Linear convolution for non periodic sequence and Circular convolution for periodic sequence.
ReplyDeleteConvolution is used for evaluating output of a filter in time domain. For frequency domain , transfer functions are used.
ReplyDeleteConvolve combines neighbouring points before and after the point being convolved, and at the ends of the waves not enough neighbouring points exist.
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