Complex exponential X delta function

  • Thread starter palex
  • Start date
  • #1
6
0
1. Problem Statment:
Sketch the sequence x(n)=[itex]\delta[/itex](n) + exp(j[itex]\theta[/itex])[itex]\delta[/itex](n-1) + exp(j2[itex]\theta[/itex])[itex]\delta[/itex](n-2) + ...

3. Attempt at the Solution:
The angle theta is given in this case Can someone remind me of how to multiply a complex exponential by a delta function? This sequence represents impulse signals. Such multiplication yields a real and imaginary component. Would I ignore the imaginary component and essentially keep the cos(k[itex]\theta[/itex])? Thanks very much.
 
Last edited by a moderator:

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38
Okay, so the terms in your sequence are complex valued. So the only way to really represent that is as two separate sequences. You can just use the Euler equation:

exp(jθ) = cos(θ) + jsin(θ)

So you could draw two separate sequences, each one representing the real part and the imaginary part x(n) respectively.

Alternatively, I suppose you could try to draw points in the complex plane.
 

Related Threads on Complex exponential X delta function

  • Last Post
Replies
3
Views
7K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
869
Replies
1
Views
4K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
3
Views
3K
Top