ECE250 Signals and Systems Assignment 1 -Solved

Programming Problems: 
• Use Matlab to solve the programming problems. 
• For your solutions, you need to submit a zipped file on Google classroom with the following: 
– program files (.m) with all dependencies. 
– a report (.pdf) with your coding outputs and generated plots. The report should be self-complete 
with all your assumptions and inferences clearly specified. 
• Before submission, please name your zipped file as: “A1 GroupNo RollNo Name.zip”. 
• Codes/reports submitted without a zipped file or without following the naming convention will NOT 
be checked. 
1) [CO1] A discrete signal x[n] is given as shown in Fig. 1. Using x[n], two more signals y[n] and 
z[n] are generated, as per the following definitions: 
• Even{y[n]} = x[n] for n ≥ 0 and Odd{y[n]} = x[n] for n < 0 
• Even{z[n]} = x[n] for −∞ < n < ∞. Assume that z[n] = 0 for n < 0 
i)  Find and sketch y[n] and z[n]. 
ii)  For the three signals i.e. x[n], y[n], and z[n], check and justify whether any of these are 
odd/even functions. 
Figure 1: Signal x[n] 
2) [CO1 For the signal g(t) = (√ 2 + √2j)e jπ/4e(−1+j2π)t , sketch the following: 
1i)  Real{g(t)} 
ii) Imag{g(t)} 
iii) (g(t + 2) + ¯
g(t + 2), where ¯
g(t) denotes the complex conjugate of g(t). 
3) [CO1]Two students of the Signal and Systems course are instructed to generate periodic 
signals of period T seconds using triangular pulses. Student-A generated a signal of the form s1(t) = at/T 
for 0 ≤ t < T as depicted in Fig. 2 (left), where a is a positive quantity that denotes the amplitude of the 
signal. In comparison, student-B generated a signal s2(t) as shown in Fig. 2 (right). 
i)Write the mathematical expression of signal s2(t) for 0 ≤ t < T. 
ii) For both the signals, compute the following signal parameters: 
a)Peak or maximum value 
b) Energy 
c) ) Power 
d) Root-mean-square (RMS) value 
RMS{s(t)} = T1 Z 0T 
s(t)2 dt! 1/2 
(1) 
e) (1 pt) Mean or average value 
Avg{s(t)} = T1 Z 0T 
s(t)dt! 
(2) 
f) (1 pts) Mean absolute value 
MAV{s(t)} = T1 Z 0T 
|s(t)|dt! 
(3) 
g) ( Sketch the derivate of the signal s1(t). 
Figure 2: Signals s1[t] and s2[t] 
4) [CO2] ( A system S is described by the relation y(t) = x(at + b), where x(t) is the input signal 
and y(t) is the output signal. 
i) Determine the values of b for which the system remains memoryless. Take a = 100. 
ii)  Will the system be memoryless if b = −t2 yielding the system of form y(t) = x(at − t2 )? Take 
a = 97. 
iii) If the input x(t) = cos(t), will the system be causal? Justify. 
iv) Another system S2 is described by the relation y(t) = ex(at+b) . Is it stable? Justify. 
Note: Each part of this problem is to be solved individually.Programming Problems: 
5) [CO1]  Generate and plot each of the following sequences over the indicated intervals. 
i) ( x[n] = n[u[n] − u[n − 10]] + 10e−0.3(n−10)[u[n − 10] − u[n − 20]], 0 ≤ n ≤ 20 
ii) ( y[n] = cos[0.03πn] + u[n], 0 ≤ n ≤ 50 
6) [CO1] ( Let z[n] = u[n] − u[n − 10]. Decompose 
z[
n] into its even and odd components and plot 
these in three individual subplots for the interval −
20 ≤ n 
≤ 
20.