Nov 12th, 2014
IZMIR UNIVERSITY OF ECONOMICS
EEE 301 LABORATORY ASSIGNMENT II
In this assignment, you will learn to compute the Discrete-Time Fourier Series (DTFS) analysis
and synthesis of discrete-time periodic signals in Matlab.
BACKGROUND:
For periodic (N) discrete-time signals, the discrete-time Fourier series synthesis and analysis
equations are given respectively as:
x[n] 
a e
k N
ak 
jk ( 2 / N ) n
k
1
x[n]e jk ( 2 / N ) n

N n N
The discrete-time Fourier series representation is a finite series with N terms since there are only
N distinct complex exponentials that are periodic with period N. The spectral coefficients ak
repeat periodically with period N.
ASSIGNMENT:
The following code in Matlab simulates a discrete-time periodic square-wave signal:
% Specify x[n] as discrete-time periodic square-wave with N1=2, N=8
N=8;
xn=[0 1 1 1 1 1 0 0];
% plot one period
k=-3:4;
% “stem plot” the original function
figure, p = stem(k,xn,'k','filled');
set(p,'LineWidth',2','MarkerSize',4);
xlabel('n'),ylabel('x[n]'),title('periodic square wave'); % label the
original function axis
axis([-4 4 0 2])
1. Simulate the DTFS analysis equation above to compute and plot the Fourier series coefficients
of a given periodic square-wave signal:
% DTFS analysis equation: ak = (1/N)*sum_{n=<N>}(x[n]*exp(-jk(2pi/N)n))
% signal period (in samples)
N = length(xn);
n = [0:(N-1)]';
% allocate space for N DTFS coefficients
ak = zeros(N,1);
% loop over all coefficients
for k=0:(N-1)
% DTFS anaysis equation here
end
2. Next, simulate the DTFS synthesis equation above to construct the periodic square-wave signal
as a weighted (by coefficients ak) sum of N harmonically related complex exponentials:
% DTFS synthesis equation: x[n] = sum_{n=<N>}(ak*exp(jk(2pi/N)n))
k = [0:(N-1)]';
% allocate space for synthesized x[n]
xns = zeros(N,1);
% loop over all signal samples
for n=0:(N-1)
% DTFS synthesis equation here
end
3. Recompute and plot the Fourier series coefficients of a given periodic square-wave signal for
the following period values, N=16, 32, 64.