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Questions tagged [bilinear-transform]

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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 ...
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2answers
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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. ...
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What are the differences between Gaussian down-sampling and bicubic down-sampling in Matlab? Which is more accurate for simulating low resolution?

I see in some of the technical papers, good practice for downsampling is to first pass the image through a Gaussian Filter and then take sampling to avoid problems like aliasing and so on. However, ...
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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 ...
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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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1answer
56 views

Low pass to low pass transformation coefficient?

I am unable to solve this question, 10.10 from GATE IN 2004 (a previous year question paper for an exam targeted at engineering graduates in India.) So I tried to solve the 10.10 by considering the ...
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1answer
58 views

Time-domain LPF not showing expected behavior

I am trying to implement a simple first-order Butterworth Low-Pass filter in Python. I have some code that makes use of scipy.signal.butter and scipy.signal.filtfilt. It works fine, but I wanted to ...
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2answers
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What is the difference between the sampling frequency of signal and sampling frequency of filter

I believe that there is no connection between the sampling frequency used for converting an analogue filter to digital filter and the one used to sample a signal that the filter will be used on. But I ...
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1answer
248 views

Butterworth low pass filter zeros location after bilinear transformation explanation

I am studying in a text book the transformation of a continuous time Butterworth low pass filter into a discrete time filter by means of bilinear transformation: $$ s = \frac{2}{T_d}*\frac{1-z^{-1}...
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1answer
550 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 ...
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1answer
506 views

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=\...
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1answer
707 views

Whats is the difference between FIR/IIR filters and Chebyshev/Butterworth filters

I am new to Signal Processing. From my understanding -- FIR/IIR just refer to the placement of poles and zeros in the z-domain helping us achieve convolution, if FIR and ??? in IIR. Chebyshev and ...
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3answers
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First order low pass filter

I am trying to better understand the first-order low pass filter: Summary: Per wikipedia, a first order low pass filter yields the following in discrete time: $$ \frac{Y(s)}{U(s)}= \frac{\omega_{c}}...
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1answer
124 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: ...
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5answers
768 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 ...
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1answer
256 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 ...
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1answer
704 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 ...
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1answer
344 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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1answer
314 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 ...
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1answer
524 views

Convert low pass continuous time filter design to bandpass, discrete time

I am trying to convert the continuous time transfer function of a second order lowpass Butterworth filter is given by: To a bandpass fourth order bandpass digital filter, I first apply the mapping to ...
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2answers
387 views

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 ...
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2answers
134 views

Confusion Regarding Bi Linear Transform

I was reading my book where the z-transform of a signal is derived to be ${1-e^{-2bT}z^{-1}}$ . Then it goes on to say that by applying the bilinear transform we can get $$\frac{2(1+bT+(bT-1)z^{-1})}...