Skip to main content

Questions tagged [bilinear-transform]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
1 answer
104 views

For unit step $g(t) = u(t)$, why does $G(z) = \frac{z}{1-z}$, whereas $G(s) = \frac{1}{s}$?

Edit: The source of my confusion is over the existence of multiple s-z mappings. After researching these mappings and where they came from, I couldn't find why $z=e^{sT}$ can be ignored and replaced ...
ThePhysicsOverthinker's user avatar
0 votes
0 answers
51 views

Bilinear transformation with a high sampling rate (chebyshev filter)

I'm trying to design a digital Chebyshev filter of order 2. This gives the general transfer function If I transform this and simplify I get If I then expand the denominator and then normalize so ...
Johannes's user avatar
1 vote
1 answer
259 views

What exactly are the assumptions behind Tustin's formula? Application on state space models

I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple. You have a continuous time state space model : $$ \begin{split} \...
NokiYola's user avatar
  • 507
1 vote
0 answers
75 views

Bilinear Transformation in Audio EQ Cookbook

In the Audio EQ CookBook there is $$\omega_0 = 2\pi\cdot\frac{f_0}{f_s}$$so frequency warping will be $$\omega_r = \frac{2}{T}\tan(\frac{\omega_0}{2})$$ Then $$s \longleftarrow \frac{2}{T}\frac{1-z^{-...
arlen's user avatar
  • 21
2 votes
2 answers
235 views

Bilinear transform for a system in zero-pole-gain form

MATLAB's bilinear performs the following steps for a system in zero-pole-gain form If fp is present, it prewarps: ...
DSP novice's user avatar
2 votes
1 answer
747 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 ...
DSP novice's user avatar
0 votes
0 answers
56 views

Do we use calculator in radians or degree while calculating prewarping analog frequency in Bilinear Transformation?

Say $\omega_s=1.96\;,\omega_p=0.785$ For bilinear transformation-: $\Omega_p=2/T*tan(\omega_p/2)$ $\Omega_s=2/T*tan(\omega_s/2)$ Should I put my calculator in radian mode or degree mode. I believe it ...
achhainsan's user avatar
1 vote
2 answers
231 views

Digital IIR LPF Difference Equation from Transfer Function

I want a digital IIR filter with f0=225kHz and fs=53.125GHz. I can come up with the transfer function and plot it using Matlab. ...
capj's user avatar
  • 23
1 vote
1 answer
330 views

States transformation of the bilinear transform

I have used the bilinear (or tustin) transform for a while, have been though the derivation of it and also through the concept of frequency warping. Something that I still not understand that is ...
PidTuner's user avatar
2 votes
3 answers
1k views

Why must the order of a Band-Pass and Notch filter always be even?

My professor mentioned that the order of a band-pass and a notch filter must always be even, when showing an example of designing a digital filter using the bilinear transformation. Then he also ...
Kevin KZ's user avatar
0 votes
0 answers
136 views

How to break a second-order filter into two first-order filter

Let's assume the transfer function of a continuous-domain filter consists of two poles and one zero: $H(s) = \frac{k_c (s-\omega_{z_1})}{(s-\omega_{p_1})(s-\omega_{p_2})}$. Let's consider we do the bi-...
shampar's user avatar
  • 338
1 vote
1 answer
390 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 ...
user53751's user avatar
2 votes
2 answers
1k views

Justification of bilinear transform

I would like to understand the "justification" for the bilinear transform. The basic idea as I understand it is that by integration rule of Laplace transform we have for continuous $y(t)$: $$\mathcal{...
Dole's user avatar
  • 348
2 votes
1 answer
3k views

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 ...
oliver's user avatar
  • 266
1 vote
2 answers
1k 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. ...
oliver's user avatar
  • 266
1 vote
0 answers
298 views

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, ...
ackbar03's user avatar
1 vote
1 answer
3k views

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 ...
shampar's user avatar
  • 338
1 vote
1 answer
838 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 $(A^c = [a^c_m, ..., a^c_1, a^c_0])$. ...
shampar's user avatar
  • 338
0 votes
1 answer
560 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 ...
Aditya P's user avatar
  • 171
0 votes
1 answer
171 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 ...
kb4444's user avatar
  • 35
1 vote
3 answers
9k views

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 ...
Chika's user avatar
  • 93
1 vote
1 answer
732 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}...
VMMF's user avatar
  • 1,142
6 votes
2 answers
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 ...
Nicholas Appleton's user avatar
2 votes
1 answer
970 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=\...
Rohit's user avatar
  • 578
0 votes
1 answer
2k 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 ...
Akhilesh Rao's user avatar
11 votes
3 answers
27k views

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}}...
kando's user avatar
  • 353
2 votes
1 answer
245 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: ...
kando's user avatar
  • 353
11 votes
5 answers
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 ...
robert bristow-johnson's user avatar
0 votes
1 answer
568 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 ...
Peter's user avatar
  • 11
2 votes
1 answer
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 ...
Juha P's user avatar
  • 917
0 votes
1 answer
494 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 ...
Maks Piechota's user avatar
3 votes
1 answer
770 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 ...
DL72's user avatar
  • 133
0 votes
1 answer
1k 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 ...
peterjtk's user avatar
0 votes
2 answers
659 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 ...
John Smith's user avatar
3 votes
2 answers
184 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})}...
varunkr's user avatar
  • 233
15 votes
1 answer
920 views

Where did Arnold Tustin first introduce the bilinear transform?

It's well known that the bilinear transform is also known as Tustin's Method. As far as I know, Arnold Tustin really did introduce the idea into the control systems literature, so the name isn't just ...
datageist's user avatar
  • 4,897