# Complex exponential X delta function

1. Feb 22, 2012

### palex

1. Problem Statment:
Sketch the sequence x(n)=$\delta$(n) + exp(j$\theta$)$\delta$(n-1) + exp(j2$\theta$)$\delta$(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$\theta$)? Thanks very much.

Last edited by a moderator: Feb 22, 2012
2. Feb 22, 2012

### cepheid

Staff Emeritus
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.