The aim of this experiment was to study linear convolution, circular convolution and linear convolution using circular convolution and correlation of signals.
Convolution is an mathematical expression used to express the relation between input and output of a system.
Mathematically, Linear convolution is expressed as y[n]=x[n]*h[n]
Where x[n] is the input to the system and h[n] is the impulse response of the system.
Linear convolution is use to find the output of the system.
The length of the output signal obtained was the one less than the addition of the length of the 2 input signals.
In case of Circular convolution the length of the output signal is chosen as maximum length of both the signals.
Circular convolution gives alliased output.
Correlation is use to find the degree of similarity of two signals.
Auto-correlation is an Even signal.
Convolution is an mathematical expression used to express the relation between input and output of a system.
Mathematically, Linear convolution is expressed as y[n]=x[n]*h[n]
Where x[n] is the input to the system and h[n] is the impulse response of the system.
Linear convolution is use to find the output of the system.
The length of the output signal obtained was the one less than the addition of the length of the 2 input signals.
In case of Circular convolution the length of the output signal is chosen as maximum length of both the signals.
Circular convolution gives alliased output.
Correlation is use to find the degree of similarity of two signals.
Auto-correlation is an Even signal.
In circular convolution,Length 2 signals should be exactly same. To obtain this zero padding is done.
ReplyDeleteYes circular convolution requires the length of two input signals to be exactly same. However as mentioned above the disadvantage of Circular convolution is that it provides alliased output.
DeleteWhat are the applications of co-relation?
ReplyDeleteCo-relation is basically used in applications such as speech processing, image processing and radar systems.
DeleteIn radar system, the transmitted signal is correlated with the ehco signal to locate the position of the target.
informative blog.
ReplyDeleteCircular convolution is used only for periodic signals
ReplyDeleteYes. And in case of circular convolution the length of output signal is chose as max of the two input signals
DeleteConvolution is used to find output in time domain. For evaluating output in frequency domain,transfer functions are used.
ReplyDeleteYes thanks for the information
DeleteThe output of the convolution has the length L+M-1 (where L = Length of x[n] , M = Length of h[n] ).
ReplyDeleteYes thanks for the information
Deletecorrelation is widely used for speech recognition, image processing.
ReplyDeleteYes as it basically provides the similarity between two signals
Delete