Giacinto Gelli DSP Course – 1 / 5

Digital Signal Processing a.y. 2007-2008

Matlab Laboratory # 1Discrete-time signals and systems

Giacinto Gelli

gelli@unina.it

Discrete-time signals

Giacinto Gelli DSP Course – 2 / 5

• Discrete-time signal x[n] ⇒ represented by a pair of Matlab vectors n (time)and x (amplitude)

• Example: n = [-3,-2,-1,0,1,2,3]; x = [2,1,-1,0,1,4,3];

• Graphical representation: command stem(n,x) (not plot! check thedifference!)

• Exercises:

(a) Generate/plot x[n] = RN [n] (rectangular window in 0 ≤ n ≤ N − 1).

(b) Generate/plot x[n] = u[n].

(c) Generate/plot x[n] = δ[n].

(d) Generate/plot x[n] = A(α)nu[n] (the 6 cases on a single figure usingsubplot.

(e) Generate/plot x[n] = A cos(ω0n + φ) (check frequency/timeperiodicity).

Signal operations

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• Operations on two or more signals require that the signal be defined on thesame time interval.

• Time-shifting and reflection operates only on the vector n.

• Exercises:

(a) Given the signal x[n], write a Matlab function [y,n] =

time shift(x,n,n0) for evaluating y[n − n0] for arbitrary values ofn0 ∈ Z. Test it with the signal x[n] = (0.9)nu[n] for −5 ≤ n ≤ 20 andn0 = ±10, plot the results and comment.

(b) Given the signal x[n], write a Matlab function [y,n] =

time reverse(x,n) for evaluating y[n] = x[−n] (use the commandfliplr or flipud). Test it with the signal x[n] = R3[n], plot theresults and commment.

Discrete-time systems and convolution (1/2)

Giacinto Gelli DSP Course – 4 / 5

• Convolution y[n] = x[n] ∗ h[n] is performed using the command y =

conv(x,h).

• Limitations:

(a) x[n] and h[n] must be finite-length sequences or must be truncated ⇒

can be used only for FIR filters (for the general case use the commandfilter instead).

(b) The command conv does not allow one to specify the time-interval.

Discrete-time systems and convolution (2/2)

Giacinto Gelli DSP Course – 5 / 5

• Exercises:

(a) Write a Matlab script for evaluating the convolution betweenh[n] = RN (n) and x[n] = anu[n] for N = 4 and a = 0.8 (a criticalpoint is truncation of the infinite-length x[n], try to find an appropriatecriterion). Plot the results and comment.

(b) The command �conv can alos be used for poynomial multiplication. Use itto perform multiplication between the two polynomialsP1(z

−1) = 1 − 1

2z−1 and P2(z

−1) = 1 + 3

4z−1. Check with the

analytical solution.