Lab Rubrics DSP Lab
Lab #: 05
Lab Title: Discrete time Fourier transform
Submitted by:
Names Registration #
Saman Nosheen FA17-BEE-012
Maryum Zafar FA17-BEE-006
Faiz ur Rehman FA17-BEE-031
Ali Sajjad FA17-BEE-001
Rubrics name & number Marks
In-Lab Post-Lab
Engineering R2: Use of Engineering Knowledge and follow Experiment Procedures:
Knowledge Ability to follow experimental procedures, control variables, and record
procedural steps on lab report.
R3: Interpretation of Subject Knowledge: Ability to interpret and explain
mathematical and/or visual forms, including equations, diagrams, graphics,
figures and tables.
Problem R5: Data/Evidence Measurements:
Analysis Ability to record raw data / evidence.
R6: Experimental Data Analysis:
Ability to interpret findings, compare them to values in the literature, identify
weaknesses and limitations.
Design R7: Implementing Design Strategy: Ability to execute a solution
taking into consideration design requirements and pertinent
contextual elements. [Block Diagram/Flow chart/Circuit Diagram]
R8: Best Coding Standards:
Ability to follow the coding standards and programming practices.
Modern R9: Understand Tools: Ability to describe and explain the principles behind
Tools Usage and applicability of engineering tools.
R11: Tools Evaluation:
Ability to simulate the experiment and then using hardware tools to verify the
results.
Individual R12: Individual Work Contributions: Ability to carry out individual
and responsibilities.
Teamwork
R13: Management of Team Work:
Ability to appreciate, understand and work with multidisciplinary team
members.
Rubrics to follow
Rubrics# R2 R3 R5 R6 R7 R8 R9 R11 R12 R13
In –Lab
Post- Lab
Lab 05 Discrete Time Fourier Transform
1. Objectives:
To become familiar with DTFT and its properties.
To find the DTFT of signal in MATLAB.
2. Introduction:
Discrete Time Fourier Transform (DTFT) is a frequency analysis tool for a periodic discrete
time signals The DTFT of x[n] , X(e^jw) is given by following equation :
∞
X(e )= ∑ x [n¿ ]e− jwn ¿
jw
n=−∞
Fourier transform, X(ejw) is also called spectrum and is a continuous function of the
frequency parameter. To convert X(ejw) to x[n] , we use inverse DTFT equation which is given
by:
π
1
x[n]= ∫ X ( e jw )e jwn
2 π −π
DTFT Properties:
We can compute DTFT in following three ways
a) DTFT Using exact transformation (Analytic form)
b) DTFT using definition/formulae (Numerical computation form)
c) DTFT using function
3. In Lab Tasks:
Task 01: Compute DTFT of a one-sided exponential:
CODE
a=1.5
w = linspace(-pi,pi,2^8);
X = exp(1j*w)./(exp(1j*w) - a);
subplot(2,1,1)
plot(w/pi,abs(X));grid
xlabel('frequency in \pi');
ylabel('|X|')
title('Magnitude Part')
subplot(2,1,2);
plot(w/pi,angle(X));grid
xlabel('frequency in \pi');
ylabel('radians')
title('Angle Part')
Task 02: Compute DTFT of a following signal:
4. Post Lab Tasks:
Task 01: Compute DTFT of a following triangle:
n=-15:15
m=12
x=[zeros(1,m) 1 2 3 4 3 2 1
zeros(1,m)]
N = 100;
k = -N:N-1;
w = (pi/N)*k;
X = x*(exp(-1j*pi/N)).^(n'*k); %
DTFT
magX = abs(X); angX = angle(X);
subplot(2,1,1); plot(w/pi,magX);grid
xlabel('frequency in \pi'); ylabel('|X|')
title('Magnitude Part')
subplot(2,1,2); plot(w/pi,angX);grid
xlabel('frequency in \pi');
ylabel('radians')
title('Angle Part')
Task 02: Prove frequency shift property of DTFT.
CODE title('Magnitude of X')
clc subplot(2,2,2);
n=1:15 plot(w/pi,angX);grid
m=12 xlabel('frequency in \pi');
x=[ 4 3 1 ones(1,m)] ylabel('radians')
N = 100; title('Angle of X')
k = -N:N-1; subplot(2,2,3);
w = (pi/N)*k; plot(w/pi,magY); grid
X = x*(exp(-1j*pi/N)).^(n'*k); % xlabel('frequency in \pi');
DTFT of x title('Magnitufe of Y');
y=exp(j*pi*n/4).*x ylabel(' Magnitude')
Y=y*(exp(-j*pi/100)).^(n'*k) %DTFT subplot(2,2,4);
OF y plot(w/pi,angY); grid
magX=abs(X); angX = angle(X); xlabel('frequency in \pi');
magY=abs(Y); angY = angle(Y); title('Angle of Y');
subplot(2,2,1); ylabel(' Radians')
plot(w/pi,magX);grid
xlabel('frequency in \pi');
ylabel('Magnitude')
5. Conclusions:
Through this lab, I came to know about DTFT and its properties. It is computed for the
frequency response analysis of a signal. . I also came to know about how to implement code in
MATLAB to compute DTFT in three different ways.
