Complex exponential X delta function

[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.

 

[cepheid]

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.