2.2. Solved exercises
EXERCISE 2.1.
The MATLAB code below generates and plots some basic discrete-time signals.
subplot (3,3,1); stem([1;zeros (49,1)]); title('Dirac pulse') subplot(3,3,2); stem(ones(50,1)); title(' Step function') subplot (3,3,3); stem ([ones (1,5),zeros(1,3)]) title(' Rectangular pulse') subplot (3,3,4); stem(sin(2*pi/8*(0:15)) ) title('Sinusoidal signal') subplot (3,3,5); stem(sinc(0:0.25:8)) ; title('“Sinc” signal') subplot (3,3,6); stem(exp(- (0:15))); title('e^-^n signal') subplot (3,3,7); stem(pow2(-0.5*(0:15))) title('2^-^0^.^5^n signal') subplot(3,3,8); stem(3.^(0:15)); title('3^n signal') subplot(3,3,9); stem (randn(1,16)); title('Gaussian random signal')
Figure 2.1. Examples of discrete-time signals
EXERCISE 2.2.
Generate the following signal:
x(n) = K · exp[c · n],
where: K = 2, c = −1/12 + jπ/6, n N and n = 0..40 .
c = -(1/12) + (pi/6)*i; K = 2; n = 0:40; x = K*exp(c*n); subplot (2,1,1); stem(n, real(x)); xlabel('Iime index n'); ylabel('Amplitude'); title('Real part'); subplot (2,1,2); stem, (n, imag(x)); xlabel('Time index n'); ylabel('Amplitude'); title('Imaginary part');
Figure 2.2. Real and imaginary parts of a complex discrete-time signal
K
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