Define cross correlation of two discrete-time signals

Reference no: EM132454867

Discussion 1

Write a function that convolves two sequences of arbitrary lengths without using the built-in convolution function: conv(a,b). Using time markers tic and toc, compare the performance of your code with the built-in conv function.

Discussion 2

Cross correlation of two discrete-time signals is defined by:

??[??] = ??[??] ∗ h[-??]

Write a function crosscorrelation(x,h) to find the cross-correlation of two signals of arbitrary length and arbitrary starting points. Using time markers tic and toc, compare the performance of your code with the built-in xcorr function.

Discussion 3

The auto-correlation of a discrete-time signal is defined by:

??[??] = ??[??] ∗ ??[-??]

Generate a random Gaussian noise signal ??[??] using the function randn. Use the function crosscorrelation(x,h) of discussion 2 to find the auto-correlation of the noise signal. Determine the effect of the length of the noise signal on the auto- correlation of the signal.

Reference no: EM132454867

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