Line 1: Line 1:
 
Given the following periodic DT signal
 
Given the following periodic DT signal
  
<math>\,x(t)=\sum_{k=-\infty}^{\infty}\delta(n-4k) + \pi\delta(n-1-4k) - 3\delta(n-2-4k) + \sqrt[e]{\frac{\pi^j}{\ln(j)}}\delta(n-3-4k)\,</math>
+
<math>\,x[n]=\sum_{k=-\infty}^{\infty}\delta[n-4k] + \pi\delta[n-1-4k] - 3\delta[n-2-4k] + \sqrt[e]{\frac{\pi^j}{\ln(j)}}\delta[n-3-4k]\,</math>
  
 
which is an infinite sum of shifted copies of a non-periodic signal, compute its Fourier series coefficients.
 
which is an infinite sum of shifted copies of a non-periodic signal, compute its Fourier series coefficients.
Line 7: Line 7:
 
== Answer ==
 
== Answer ==
  
By inspection
+
The function has a fundamental period of 4 (it can be easily shown that <math>\,x(

Revision as of 13:14, 25 September 2008

Given the following periodic DT signal

$ \,x[n]=\sum_{k=-\infty}^{\infty}\delta[n-4k] + \pi\delta[n-1-4k] - 3\delta[n-2-4k] + \sqrt[e]{\frac{\pi^j}{\ln(j)}}\delta[n-3-4k]\, $

which is an infinite sum of shifted copies of a non-periodic signal, compute its Fourier series coefficients.

Answer

The function has a fundamental period of 4 (it can be easily shown that $ \,x( $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett