# signals and systems help me please

#### kralyaki

Joined Jan 27, 2016
4
h(t)=e^-3t u(t) impulse
x(t)=cos(3t) input signal

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

#### Papabravo

Joined Feb 24, 2006
13,565
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?

#### thumb2

Joined Oct 4, 2015
122
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 ?

#### Papabravo

Joined Feb 24, 2006
13,565
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 ?
Don't you have to have the convolution before you can get the Fourier Transform?

#### kralyaki

Joined Jan 27, 2016
4
Fourier transform

#### Papabravo

Joined Feb 24, 2006
13,565
Fourier transform
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

Joined Oct 4, 2015
122
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)

#### Papabravo

Joined Feb 24, 2006
13,565
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)
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.

#### thumb2

Joined Oct 4, 2015
122
$$x(t)*h(t) = X(\mathrm i \omega)H(\mathrm i\omega)$$

is the convolution property of the Fourier Transform.

papabravo said:
Now the TS/OP really really has to do something so we can proceed. This is enough now with the hints.
I agree!

#### shteii01

Joined Feb 19, 2010
4,644
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.
Yeah, remember, convolution in time domain (which is a pain in the butt) is simple multiplication in the frequency domain.

#### shteii01

Joined Feb 19, 2010
4,644
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)
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.