A Bilinear Transform example for converting a first order Butterworth filter with 1rad/s cutoff frequency into a digital filter with 20Khz cutoff frequency.
Great review of the bilinear transform. Last time I looked at the bilinear transform was in about 1983. A couple of suggestions - Although it's in your intro text that the first order butterworth had a cutoff freq of 1 rad/sec, it wasn't mentioned in the lecture. I didn't read the intro text, so didn't realize it. Looking at the S domain transfer function, it wasn't too tough to figure out though. You then went over frequency scaling an S domain filter by replacing S by S/w0 , but you didn't mention that it only works when the original filter had a cutoff frequency of one rad/sec, and by the way, that's exactly what we've got. I had to stop and think about all this for me to fill in the blanks. Not too tough. But it would have been a bit easier to follow if you had said something along the lines of "Our S domain filter has a cutoff frequency, w0, of 1 rad/sec. To scale an S domain filter with a cutoff freq of 1 rad/sed to a new w0, we replace S with S/w0. We want in our transformation to have the cutoff frequency prewarped to be at Omega rad/sec, so we'll replace S with S/Omega." I was eventually able to figure all this out, but I did have to stop the video a couple of times to reremember/think through all of this in order to follow the discussion.
Hey Jerry, Thanks that's really good feedback. I will try to get around to adding a card on the screen. In the meantime I hope that your comments helps anyone who is confused :)
When transforming from Z to S how do I apply the transform when I have 2nd or higher order equation. Do I keep the ^-1 ^-2 and so on and apply it to the whole S approximation equation, or I ignore the powers and write them to their corresponding "S" after I'm done with all the maths? Im really bad at algebraic problems.
