The aim of this experiment was to study mathematical operations. In the first part of this experiment,we studied discrete convolution .Under this part we studied methods like linear convolution,circular convolution and linear convolution using circular.We used C language for coding.We observed outputs for different inputs to the system for result analysis.
The length of linear convolution output signal was one less than addition of two input signal. Also,if both input signals are causal then output resultant signal was also causal. In circular convolution,the length of input signals should be maximum of two input signals.Circular convolution gives aliased output.
Discrete correlation was second part of this experiment ,under which we studied auto-correlation,cross-correlation for input signals and delayed input signals.We observed that auto-correlated signal is even signal and auto-correlation of delayed signal is same as original signal. Also cross-correlated signal of input signal and delayed input signal is auto-correlated input signal.
The length of linear convolution output signal was one less than addition of two input signal. Also,if both input signals are causal then output resultant signal was also causal. In circular convolution,the length of input signals should be maximum of two input signals.Circular convolution gives aliased output.
Discrete correlation was second part of this experiment ,under which we studied auto-correlation,cross-correlation for input signals and delayed input signals.We observed that auto-correlated signal is even signal and auto-correlation of delayed signal is same as original signal. Also cross-correlated signal of input signal and delayed input signal is auto-correlated input signal.
It's good that we got to know the basics behind the DSP applications from this experiment
ReplyDeleteWe also got to know how to code for specific operation and implement it .
DeleteLength of output signal in autocorrelation will be N=L+M-1 where L and M are lengths of input signals
ReplyDeleteYes,for circular convolution length of output signal will be maximum of L and M.
DeleteWe can also perform Linear convolution using Circular Convolution.
ReplyDeleteYeah.
DeleteThese are important operations in signal processing.
ReplyDelete