# Questions tagged [bilinear-transform]

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### Get the discrete-time poles and zeros from continuous-time poles and zeros

How do you implement the following function: $$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$ where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
36 views

### Is the sampling period arbitrary for a bilinear transform, and why?

I have been given the specifications for a digital highpass filter (stopband, passband, stopband attenuation and maximum passband ripple). I am expected to design a prototype lowpass filter in the ...
361 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 $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
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### Bilinear Transform (Tustin's Method) applied to the Derivative

I hope that I have not misunderstood something terribly wrong, but the continuous derivative $D=d/dt$ can be considered a transfer function in Laplace space $D(s) = s$, right? So when I try to ...
557 views

### Bilinear transform with pre-warping for systems other than classical filters

I only seem to be able to find online information about applying bilinear transform + pre-warping to filters (like butterworth, etc.) with only one edge frequency that is purposely 'designed' into it. ...
404 views

### Analog butterworth to digital - bilinear transform

In my previous question I've designed analog butterworth filter (poles own calculated). But now I would like to transform it to digital domain. I'm using bilinear transformation but not all is clear ...
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### Bilinear transformation confusion

Wikipedia says in bilinear transformation from \$s\$ domain to $z$ domain relation is $$\boxed{s \longleftarrow \frac{2}{T}\frac{z-1}{z+1}}$$ But here this relation is given like this \boxed{w=\...
896 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 ...
159 views

### Bilinear Transformation Comparison

If I have transfer function coefficients, I can analyze the transfer function in the s-plane and/or the z-plane. If I wanted to demonstrate that the z-plane and s-plane responses are equivalent: ...
345 views

### DSP filter. Is prewarping performed when discretizing using Forward/Backward?

I am trying to derive the coefficients used for a IIR implementation for the lowpass portion of a SVF filter. I've seen finished expressions for the coefficients (smith (p.8) and victor), their ...
### 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 ...