Contents
Example of Computation of Fourier series of a CT SIGNAL
A practice problem on "Signals and Systems"
Signal
Compute the Fourier series coefficients of the following signal: $ x(t) = 3cos(7t) + 11sin(4t)\! $
Fourier series
$ x(t) = 3cos(7t) + 11sin(4t)\! $
$ x(t) = 3\frac{e^{i7t}+ e^{-i7t}}{2} + 11\frac{e^{i4t}- e^{-i4t}}{2i} $
$ x(t) = \frac{3}{2}e^{i7t}+ \frac{3}{2}e^{-i7t} + \frac{11}{2i}e^{i4t}- \frac{11}{2i}e^{-i4t} $
Coefficients
$ w_0=1\! $
$ a_4= \frac{11}{2i} $
$ a_{-4}= -\frac{11}{2i} $
$ a_7=a_{-7}= \frac{3}{2} $
$ a_k = 0\! $ for all other $ k \in \mathbb{Z} $
