Umal-qura university

-------------------------TASK 04--------------------------

Determine the complex conjugate of the exponential signal given in above example and plot its real and imaginary portions.

-------------------------TASK 05--------------------------

Generate the complex valued signal
y(n) = exp ^{(-0.2 + j0.5)n}, ‐10≤n≤10
and plot its magnitude, phase, the real part, and the imaginary part in separate subplots.

Lab # 6

OBJECTIVES OF THE LAB
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In this lab, we will cover the following topics:

• 
  Generating Sinusoids
  
• 
  Addition of Sinusoids with Variation in Parameters and their Plots
  
• 
  Linear Phase Shift Concept When Dealing With Sum of Sinusoids
  

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1. GENERATING SINUSOIDS

Sinusoidal sequences are implemented using sin() & cos() functions.


Example: Continuous‐Time Sinusoid

clc;
clear all;

close all; f0 = 3;
A = 5;
t = -1:0.005:1;
y = A*cos(2*pi*f0*t); figure, plot(t, y,'*:');
xlabel('Time, sec'), ylabel('Amplitude'); title('Graph of sinusoid');


Program: Discrete‐Time Sinusoid

clc; clear all;

close all;
M=10; %samples/sec n=-3:1/M:3; A=2;
phase=0; f=1;
x=A * sin(2*pi*f*n + phase);
stem(n,x,'linewidth', 2)
title('Discrete-Time Sine Wave: A sin(2*\pi*f*n + \phi)') xlabel('Time Index')
ylabel('Signal Amplitude') axis([n(1) n(end) -A A]) grid

2. CREATING PHASE SHIFT

Phase shift can be created by adding an angle to 2πft for a sinusoid.


Example

clc; clear all; close all; fs=1000;

t=-3:1/fs:3; A=2;
phase=0; f=1;
x=A * sin(2*pi*f*t + phase);

plot(t,x, 'linewidth', 2)

title('Continuous-Time Sine Wave: A sin(2*\pi*f*t + \phi)') xlabel('Time Index')
ylabel('Signal Amplitude') axis([t(1) t(end) -A A]) grid