Through this experiment, we have aimed to comprehend the Convolution
and Correlation of Discrete signals by programming for the same in
C-language and tallying them with their mathematically verified outputs.
Results obtained for the following were analyzed to derive legitimate conclusions:
1. Linear Convolution
2. Circular Convolution
3. Linear using Circular Convolution
4. Auto-correlation
5. Cross-correlation
In convolution, we have taken varied lengths of the two input signals to get different results for linear and circular convolution and have observed an aliasing effect in circular convolution.
In Correlation, we have found auto-correlation and cross-correlation in combinations of original, delayed and scaled values of the same signal in order to find degree of similarity between two signals.
Results obtained for the following were analyzed to derive legitimate conclusions:
1. Linear Convolution
2. Circular Convolution
3. Linear using Circular Convolution
4. Auto-correlation
5. Cross-correlation
In convolution, we have taken varied lengths of the two input signals to get different results for linear and circular convolution and have observed an aliasing effect in circular convolution.
In Correlation, we have found auto-correlation and cross-correlation in combinations of original, delayed and scaled values of the same signal in order to find degree of similarity between two signals.
Which is better, convolution or correlation?
ReplyDeleteAs convolution gives the output of the system with the input signals and correlation gives the degree of similarity between the signals, we cannot draw a comparison on what is better without a specific requirement given
DeleteWhat are the applications of each of the methods?
ReplyDeleteConvolution has applications in domains like probability, image processing and statistics.
DeleteCorrelation too has applications in similar domains of signal processing, face recognition etc
What is the significance of the output of Auto correlation?
ReplyDeleteThe output of autocorrelation helps us determine the energy of the signal by the y(0) value.
ReplyDeleteIn 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)
ReplyDeleteCan you mention about the aliasing effect?
ReplyDeleteYes she last value of M-1 wraps around and gets added with the first M-1 values of y(n). This is called aliasing
DeleteCan you give some real time applications?
ReplyDeleteCorrelation can be used in radar systems and also in speech processing etc
Delete