Defining a Signal. periodic, bounded finite etc.

1. Oct 17, 2011

Evo8

Im having a little trouble about how to go about defining this signal. It has a sqrt(-1) in it raised to a power so this is where i get confused. No doubt my poor algebra skills may be holding me back from understanding this problem.

The signal is x(k)=j^-k u(k)

I need to determine:
A. Whether or not the signal is periodic or aperiodic. If periodic what is the period?
B. Is it bounded or unbounded?
C. Finite or Infinite?
D. Calculate the power of x(k)

Im starting off with A. I know the definition of a periodic signal is if I can replace "k" with "K+N" and get the same signal. The value of N that achieves this is my period. I don't even know how to go about that with the j in there. j=square root(-1).

For a bounded signal im not sure how to really go about this one either but since there is no "bounds" defined for k i would say its bounded with a bound of 1? Im not really sure on this though.

C. I would say this is a finite signal? I think because there are no operators to make the signal reach infinity?

D. I havent attempted this yet.

I feel ill be able to deal with this problem a little bit better if i fully understand what to do with the imaginary number.

Any ideas?

Thanks,

2. Oct 18, 2011

rude man

Not sure either, but I would certainly start with the Euler relation.

3. Oct 18, 2011

Evo8

Good point. I think your on to something here. I just cant really see how eulers identity fully applies.

However since ive posted this question ive tried taking x(k)=j^-k*u(k) --> x(k)=1/j^-k. If k=2 then we get x(k)=-1u(k)?

4. Oct 18, 2011

rude man

How about j = exp(jπ/2)? Can you take it from there?

5. Oct 18, 2011

Evo8

Im not really sure if that helps me or not. I dont see it anyway. There is still a j in there. Thats exp(j*pi/2) correct?

6. Oct 18, 2011

rude man

Correct.

Just because there is still a j in there doesn't mean the signal doesn't exist, does it? What about phasing?

BTW I assume k are integers?

7. Oct 18, 2011

Evo8

Yes K are integers. I think the signal does exist. Im not super familiar with eulers identity (unfortunately) But it seems like it could be on the right track...I dont know...

8. Oct 18, 2011

rude man

Your signal is certainly periodic: +1, -j, -1, +j, +1, ....

Is this a course in digital signal processing? If so, doesn't your textbook cover this business?

Take a look at the appropriate section of this:

http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch30.pdf

According to that, cos(wt + φ) --> exp(-jφ). I assume the complex Fourier series for this signal will also enable you to determine its power.

I'm no expert in this field myself, unfortunately. Hopefully I did kick-start you.

9. Oct 18, 2011

rude man

Last edited: Oct 18, 2011
10. Dec 4, 2011

Evo8

Thanks for the help guys