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# Questions tagged [bilinear-transform]

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### my Butterworth lowpass formulas do not agree with Fisher webpage

I want to implement Butterworth low-pass filter. Thanks to this question, I have found out that the filter coefficients can be generated using Tony Fisher web-site or using his code. But the problem ...
• 155
4k views

### Bilinear transformation of continuous time state space system

I'm trying to understand the derivation of the bilinear transform for a set of continuous time state-space matrices. I've found plenty of websites which list steps to perform the conversion (here 1 or ...
1k views

### Mathematical question that comes out of using bilinear transform

So this is related to the Cookbook and I tried solving it maybe two decades ago, gave up, and was reminded of the unsolved problem. But it's pretty damn straight forward, but I still got slogged down ...
759 views

### A few conceptual questions about filter, pole, and bilinear

I am working on a school project on converting a 6th order butterworth high pass filter to digital filter using bilinear transformation. Just got a couple conceptual questions need to be clarified ...
• 133
699 views

### How to design digital Butterworth filter and return its zeros, poles and gain

I'm implementing digital Butterworth filter and encounter some numerical problem when filter order is high using direct form, so I wonder how to design the digital Butterworth filter and return its ...
• 527
1k views

### Prewarping both resonant frequency $f_0$ and bandwidth (or $Q$) when using bilinear transform

RBJ's Audio EQ cookbook takes into account only frequency prewarping when case Q is used for bandwidth. Why not $Q$ prewarping as well with some of those filter ...
• 917
1 vote
829 views

### How can I get the continuous-time transfer function coefficients (or poles and zeros) from the corresponding discrete-time TF and vice versa?

Let's say I have a continuous time transfer function which I know its numerator coefficients $(B^c = [b^c_m, ..., b^c_1, b^c_0])$ and denominator coefficients $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
• 338