1. ## I am taking a signals course but my math skills are a little rusty... please help

I am unsure on how to get this equation with complex j into the format prescribed. Can I get some help please. Thanks.

2. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by thatsmessedup
I am unsure on how to get this equation with complex j into the format prescribed. Can I get some help please. Thanks.

Well, by comparin the two forms we have A = 5 + j. So what is |5 + j|?

-Dan

3. ## Re: I am taking a signals course but my math skills are a little rusty... please help

sqrt(26) I suppose. So then how do I arrange the t and the complex j? Thanks!

4. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by thatsmessedup
sqrt(26) I suppose. So then how do I arrange the t and the complex j? Thanks!
Weird. I didn't look through the whole thing.

Compare forms for the exponential:
General:
$\displaystyle e^{j( \omega _0 t + \theta )}$

Yours:
$\displaystyle e^{-(2 + 3j)t}$

Now we can rewrite yours as $\displaystyle \sqrt{26} e^{j(-3t)} \cdot e^{-2t} = \left ( \sqrt{26} e^{-2t} \right ) e^{-3jt}$

It would appear that your signal has an extra time varying amplitude which has the effect of a decay term. (That or you could look at it as having a complex phase term.)

-Dan

5. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by topsquark
Weird. I didn't look through the whole thing.

Compare forms for the exponential:
General:
$\displaystyle e^{j( \omega _0 t + \theta )}$

Yours:
$\displaystyle e^{-(2 + 3j)t}$

Now we can rewrite yours as $\displaystyle \sqrt{26} e^{j(-3t)} \cdot e^{-2t} = \left ( \sqrt{26} e^{-2t} \right ) e^{-3jt}$

It would appear that your signal has an extra time varying amplitude which has the effect of a decay term. (That or you could look at it as having a complex phase term.)

-Dan
This isn't quite right. You neglected the phase factor that arises from $(5+j) = \sqrt{26}e^{j \arctan(1/5)}$

the actual form is

$\sqrt{26}e^{-2t}\cdot e^{j(-3+\arctan(1/5))t}$

and we can read off amplitude, frequency, and phase from that

6. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by romsek
This isn't quite right. You neglected the phase factor that arises from $(5+j) = \sqrt{26}e^{j \arctan(1/5)}$

the actual form is

$\sqrt{26}e^{-2t}\cdot e^{j(-3+\arctan(1/5))t}$

and we can read off amplitude, frequency, and phase from that
bit of a typo above...

$\sqrt{26}e^{-2t}\cdot e^{j(-3t+\arctan(1/5))}$

7. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Thanks for the help. The prof. gave us this answer. Also, what is a phase factor? I cant find that term anywhere in my book.

8. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by thatsmessedup
Thanks for the help. The prof. gave us this answer. Also, what is a phase factor? I cant find that term anywhere in my book.
if you have a sinusoid described by

$f(t) = A e^{j (2 \pi f t + \phi)}$

then

$A$ is the amplitude

$f$ is the frequency

$\phi$ is the phase factor

9. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Ya, but what is this phase factor thing. Why do I need to take the arctan?

10. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by thatsmessedup
Ya, but what is this phase factor thing. Why do I need to take the arctan?
this has more than the answer to your question but as an (I assume) an up and coming electronics engineer you need to know all of this.

https://www.electronics-tutorials.ws...x-numbers.html

Thanks!

12. ## Re: I am taking a signals course but my math skills are a little rusty... please help

I've looked over that tutorial and it was very helpful. I guess the very last thing that I am confused about is the e^-2t term. What is it and why is it not a part of the answer for the amplitude?

13. ## Re: I am taking a signals course but my math skills are a little rusty... please help

Originally Posted by thatsmessedup
I've looked over that tutorial and it was very helpful. I guess the very last thing that I am confused about is the e^-2t term. What is it and why is it not a part of the answer for the amplitude?
It's what's known as a decay term. It is part of the amplitude actually. In this case the amplitude is time varying.

If you have a sinusoidal signal $s(t) = |A|e^{j 2\pi f t + \phi}$

And a purely real function $e(t)$ then

$e(t)s(t) = |A e(t)|e^{j 2\pi f t + \phi}$

i.e. the real function contributes only to the amplitude, not to the phase.