Why is Digital Butterworth lowpass?

[karen03grae]

This is a homework question. However, here is what I have thought about.
Here is my formula for the output filtered signal:

Yk = a*Uk + (1-a)Yk-1

Where "a" is coeffiecient that "weights" the current value of the unfiltered signal. And Yk-1 is the previous output signal. For some reason, low frequencies signals can pass through while high ones get attenuated. My job is to explain why.

Now this is for a lab where we had a random noise generator that gets added to a sine wave. The ONLY thing I can guess is that the high frequencies are so random that they get averaged out by the equation. But if the noise generator gave off low freq. while my original signal was high, then the Butterworth would be highpass.

I've been all over the web to figure this out. If anyone can point me in the right direction, that would be great.

 

[karen03grae]

Maybe would determining a transfer function help?

 

[doodle]

I suppose you can z-transform the equation and rearrange to obtain the transfer function Y(z)/U(z) of the filter; the transfer function should shed some light on the nature of the filter.

You can assume the output of the random noise generator to be fairly distributed over the entire frequency spectrum. The filter (if it is lowpass) would thereby discard the noisy signals with higher frequency content.

 

[berkeman]

Which DSP textbook are you working out of, Karen?

 

[karen03grae]

I'm not. That question came from my mechanical engineering lab. In that class we are given a broad overview of everything including DSP. I just found out when I went to my professor that my question was too deep for the answer expected. So that's over. I was wondering if anyone knows of a good Principles and Applications of EE. I'm using a book by Hambley right now and it is horrible. I need a good one that covers node voltage analysis, ac signals, transfer funtions, and maybe some transient response stuff. Any recommendations would be great! :)

 

[berkeman]

The best basic electronics book IMO is "The Art of Electronics" by Horowitz and Hill. It doesn't cover nodal analysis much, but it is a very practical introduction to everything from basic circuits to transistors to opamps to filters to power supplies to digital logic, etc.

My (very old) basic EE text is "Basic Electrical Engineering" by Fitzgerald, Higgenbotham and Grabel. It's okay, but not stellar. I still refer to it occasionally, though.

The best basic/intro DSP book I've found is "Designing Digital Filters" by Williams. There are some great discussions in the book that really helped my understanding of digital filters, and really all filters in general.

Maybe see if your technical library has these books so you can skim them to see if they would be good to have.

 

[phantom_photon]

I was wondering if anyone knows of a good Principles and Applications of EE.

Well, Rizzoni's book "Principles and Applications of Electrical Engineering" comes to mind! It is written for the non-electrical engineer and covers a broad range of topics with lots of relevant examples. I don't think it has anything on digital filters though...

 

[karen03grae]

Hey, thanks guys! I'm going to check those out today at the library. I have to take my EE test this friday.