Nov 25th, 2014
IZMIR UNIVERSITY OF ECONOMICS
EEE 301 LABORATORY ASSIGNMENT III
In this assignment, you will learn to simulate the Continuous-Time Fourier Series (CTFS)
analysis and synthesis of continuous-time periodic signals in Matlab using its symbolic toolbox.
BACKGROUND:
For periodic (T) continuous-time signals, the continuous-time Fourier series synthesis and
analysis equations are given respectively as:
x(t ) 

a e
k  
ak 
jkw0 t
k
1
x(t )e  jkw0t dt

T
T
The continuous-time Fourier series representation converges for all periodic signals which have
finite energy over a single period. The energy in the approximation error approaches 0 as N goes
to inf. It can be shown that by using a finite number (N) of CTFS coefficients the Fourier series
synthesis gives the best (in mean-squared error sense) approximation to the original signal.
ASSIGNMENT:
1. Simulate the CTFS analysis equation above to compute the Fourier series coefficients of a
given periodic continuous-time signal (as a symbolic function of t):
T0=2; %fundamental period
N=5; %number of FS coefficients
k=[-N:N];
syms t
for kk = 1:length(k)
% CTFS
X1(kk) = int(xt*exp(-j*2*pi*k(kk)*t/T0), t, 0, T0)/ T0;
ak(kk) = subs(X1(kk)); %store as numeric value
w(kk) = k(kk)*2*pi/T0; %angular frequency
end
%plot CTFS coefficients
figure, stem(w,abs(ak),'x-');
2. For the given continuous-time periodic signal with fundamental period T=2, calculate and plot
the Fourier series coefficients ak for k=-5:5 using the symbolic CTFS simulation in step 1.
x(t )  et
for  1  t  1
3. Next, simulate the CTFS synthesis equation above to reconstruct an approximation to the
periodic continuous-time signal using a finite number (N) of CTFS coefficients. Compute and
plot the reconstructed approximation to x(t) using the 11 CTFS coefficients found in step 2.