ECE 350 – Signals and Transforms
Spring 2009
Homework #6
The following problems are to be completed and turned in at the start of class on Friday 6
March 2009.
Problems:
1) A continuous-time periodic signal x(t) is real valued and has a fundamental
period T=4. The non-zero Fourier series coefficients for x(t) are
a0 = 10, a1 = a-1 = 1.5, a2 = a-2* = 6
4
5
π
j
e, a3 = a-3* = 2j
Express x(t) in the form
∑
∞
=
+=
0
)cos()(
k
kkk tAtx
φω
2) Text problem 3.22 (a) –Figure (c)
Verify your calculations of the Fourier Series coefficients with
fourier_series.m. Turn in your plot and your code.
3) Text problem 3.22 (a) – Fig (f)
Use the table of Common Fourier Series and Table 3.1 (Properties of Fourier
Series) instead of the analysis integral.
Verify your calculations of the Fourier Series coefficients with
fourier_series.m. Turn in your plot and your code.
4) (a) Given x(t) as in problem 1, sketch the Fourier series coefficients on the
following axis (label the axis fully):
(i)
Re(ak)
k
Im(ak)
k
(ii)
|ak|
k
∠
ak
k
(iii)
Re(ak)
ω
Im(ak)
ω
