signals and systems help me please

Discussion in 'Homework Help' started by kralyaki, Jan 27, 2016.

1. kralyaki Thread Starter New Member

Jan 27, 2016
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h(t)=e^-3t u(t) impulse
x(t)=cos(3t) input signal

a-) Y(jw)=?
b-) y(t)= ?

2. Papabravo Expert

Feb 24, 2006
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So what does your best effort at a solution look like? You might start by explaining what Y(jω) and y(t) are supposed to be. A convolution perhaps?

3. thumb2 Member

Oct 4, 2015
90
4
I think that the exercise is asking you a) the Fourier transform and b) the convolution of the two signals.

Do you know how to proceed ?

4. Papabravo Expert

Feb 24, 2006
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Don't you have to have the convolution before you can get the Fourier Transform?

5. kralyaki Thread Starter New Member

Jan 27, 2016
4
0
Fourier transform

6. Papabravo Expert

Feb 24, 2006
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Do you know of a way to get the Fourier Transform before you get the convolution?
Is convolution in the time domain, equivalent to multiplication in the frequency domain?
This is your homework after all, and you need to show some effort.
Homework Help is not the same thing as homework done for you.

thumb2 likes this.
7. thumb2 Member

Oct 4, 2015
90
4
I don't have his paper down on my table, but a) is the Fourier Transform and b) should (or could) be the convolution.

Also:

X(iw)H(iw) = x(t) * h(t)

8. Papabravo Expert

Feb 24, 2006
10,340
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Ahhh....I thought I remembered a theorem to that effect. So you can compute the Fourier transforms of x(t), and h(t). Multiply them together to get Y(iω), and finally take the inverse Fourier Transform to get y(t). Did I get that right? Now the TS/OP really really has to do something so we can proceed. This is enough now with the hints.

9. thumb2 Member

Oct 4, 2015
90
4
$x(t)*h(t) = X(\mathrm i \omega)H(\mathrm i\omega)$

is the convolution property of the Fourier Transform.

I agree!

10. shteii01 AAC Fanatic!

Feb 19, 2010
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Yeah, remember, convolution in time domain (which is a pain in the butt) is simple multiplication in the frequency domain.

11. shteii01 AAC Fanatic!

Feb 19, 2010
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thumb2, I think the OP is supposed to use transformation identities, I remember my Signal and Systems textbook had a whole table where they would have time domain representation of a signal on one side and corresponding frequency domain representation on the other side. There was something like 8 or 10 entries in that table, impulse, step, ramp, sine and a few others. This way students can quickly work out their time domain signal into frequency domain signal, without doing the whole Fourier Transform.