MATLAB

ELEG 320L: Signals and Systems Lab

LAB 5 – EXERCISES

Exercise 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.

Exercise 2

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

𝑐[𝑛] = 𝑥[𝑛] ∗ ℎ[−𝑛]

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.

Exercise 3

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

𝑎[𝑛] = 𝑥[𝑛] ∗ 𝑥[−𝑛]

Generate a random Gaussian noise signal 𝑥[𝑛] using the function randn. Use the

function crosscorrelation(x,h) of Exercise 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.