Lab 2 - Digital Signal Processing. FIR Filtering.

Appropriate report, code files, functions and figures are added together into the archive.

Exercise 1.1: Filtering a random signal by direct convolution
Write a MATLAB program to
(a) Generate a random input signal of 50 samples whose amplitude is uniformly distributed between -2
and 3 (see the rand function documentation);
(b) Process the input signal by direct convolution1 with the filter impulse response h(n) ...
(c) Plot the input and output signals on the same graph and explain what the filtering effect is.
Exercise 1.2: Step response of a FIR filter
Consider the impulse response filter. Its step response is denoted y(n), knowing that y(n) ... is the definition of the step response of any filter.
(a) Determine the expression of y(n) , as function of Lambda and a, using the geometric series formula.
(b) Use this result to find the expression of Lambda that leads to 1 for n >15.
(c) Write a MATLAB function Y = Lab2P1E2_NU(L, a) that calculates, with the filter function, the L first samples of a collection of step responses. Each response, associated to a given value of a , is stored as a column vector in the output matrix Y. The input parameter, a, is a row vector containing the collection of a values.
(d) Test your function for a = [0.25 0.5 0.75] and plot the collection of step responses on the same graph (use the legend function to reference each step response).
(e) By interpreting the graph, explain how the value of a modifies the step response.
Exercise 2.1: Filtering a multi-frequency signal
Let’s consider the following analog signal ...
Write a MATLAB program to
(a) Sample the analog signal at 60 kHz for a duration of 6 msec.
(d) Process the input signal by the sample processing method with the filter impulse response
(e) Filter the input signal by the block processing method using the filter function.
(f) Verify that the sample and block processing methods produce identical results. The sum of absolute
differences ... between the two filtered signals can be used for this verification.
(g) Plot the input and output signals (as function of time) on the same figure using the subplot function. Draw your conclusions from this figure.
Note!
fir_NU function should be updated, be careful.