Bandwidth Filtering: Get Help Solving Last Problem

[snatchingthepi]

Homework Statement

Determine the 3dB bandwidth of the filters

$$ H_1(z) = \frac{1-a}{1-az^{-1}} $$

$$ H_2(z) = \frac{1-a}{2} \frac{1+z^{-1}}{1-az^{-1}} $$

if 0<a<1

Relevant Equations

Not sure.

Hi everyone

I am finishing the last problem for a DSP problem set and just frankly have no idea where to start this one. I'm thinking I could compute the magnitude of each filter and then compare, but again am not sure. Can anyone point me in the right direction?

Thanks

 

[Jody]

Try that first. Plot the magnitude like you were saying. You have to show some work or attempt before people can help you here.

edit:

When you plot it: Are you going to plot as a function of $z$ or as something else? Did the professor use anything else or give you an equation where $z$ was some function of something else that had $\Omega$ in it?

 

[berkeman]

Homework Statement:: Determine the 3dB bandwidth of the filters

$$ H_1(z) = \frac{1-a}{1-az^{-1}} $$

$$ H_2(z) = \frac{1-a}{2} \frac{1+z^{-1}}{1-az^{-1}} $$

if 0<a<1
Relevant Equations:: Not sure.

I am finishing the last problem for a DSP problem set and just frankly have no idea where to start this one. I'm thinking I could compute the magnitude of each filter and then compare, but again am not sure. Can anyone point me in the right direction?

You can just figure out where the upper and lower -3dB frequencies are from each transfer function...

 

[snatchingthepi]

These posts were enough to encourage me to find a good answer. Thank you both.