Questions tagged [allpass]
Use this tag for questions related to filters that change the phase relationship of a signal, but does not change the gain (amplitude) of the signals.
58 questions
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Deriving the Thiran Coefficients for order 2
Consider the transform function:
$$G(z) = \frac{b + az^{-1} + z^{-2}}{1 + az^{-1} + bz^{-2}}$$
If $\Delta$ denotes the low frequency value of the phase delay and if the phase delay is maximally flat. ...
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1
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Creating All pass filter directly in the frequency domain
I have a very particular problem for my research: I need to create two all pass filters, with very similar but not completely equal frequency (phase) responses. To do this I have created an allpass ...
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Phase equalization for a notch-like filter
Consider the following filter with DC-notch-like characteristics:
$H(z) = \frac{1-2z^{-1} + z^{-2}}{1+a_1z^{-1}+a_2z^{-2}}$
where $a_1= -1.99396970948671$ and $a_2=0.994002716421032$.
The magnitude ...
- 511
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Group delay equalization for second order IIR notch filter
A couple of second order notch filters seem to be appear regularly in the literature (see e.g., Tseng, Chien-Cheng, and Soo-Chang Pei. "Stable IIR notch filter design with optimal pole placement.&...
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Half-band IIR filter design with cascaded allpass structure
I am trying to design a simple half-band complementary filter bank following this paper.
I don't have a Matlab license at the moment, so I am trying to implement it in Python, but I'm running into ...
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2
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597
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First-order allpass filter coefficient calculation
Given the first-order IIR allpass filter depicted below, I would like to calculate the coefficient $a_1$ such that a phase shift of $\frac{\pi}{2}$ occurs at a desired frequency $f_\mathrm{c}$ (the ...
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102
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Allpass Filter with Sign Switch
I want to design a digital allpass IIR filter with the following transfer function.
$$
H(\omega) =
1 \textrm{ for } \omega < \omega_1 \textrm{ or } \omega > \omega_2
$$
and
$$
H(\omega) =
-1 \...
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Are allpass filters maximum-phase systems?
There are few notes online stating that an all-pass filter is a maximum phase filter (e.g., Link). The core of the claim is that an all-pass filter is a maximum phase filter since its zeros are ...
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IIR Allpass Filter Phase Response Plotting in Excel
Using formula on Audio EQ Cookbook I implemented biquad IIR filters in Excel.
As in my previous question Phase Response Function / Plotting in Excel (IIR Filter), Hilmar helped a lot with the phase ...
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2
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165
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Allpass filter with delay of $\pi/2$ for only negative frequencies
I would like to design a complex and causal allpass filter with delay of $\pi/2$, but only for negative frequencies. The positive frequencies should have a delay of 0. Is that possible and how I ...
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Cascading IIR filter with All pass filter (APF) for constant group delay and linear phase over the passband using MATLAB not working?
I've designed an IIR Low pass filter in MATLAB with the following parameters.
...
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2
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173
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Calculating and controlling the location and bandwidth of individual notches in an allpass phaser
I'm currently working on a phaser implementation with the intention of adding some parameters that generate unique effects, namely effects that involve the precise placement of the phaser notches (e.g....
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Does flat group delay bandwidth of a Thiran filter increase with increase in filter order?
Experimentally, it does seem that for a Thiran allpass delay filter of desired low-frequency group delay $D$ with filter order $N$, increase in filter order $N$ increases bandwidth of the frequency ...
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Stability of N-order Thiran delay filter when required passband delay is N+1
In this lecture note, on page 7 (or page 111, the same page), it is said that the Thiran allpass delay filter of order N with passsband delay N+1 reproduces samples with zero error. I find it hard to ...
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Understanding conversion of frequency-warped signal and its orignal signal
I'm reading an article Frequency-Warped Signal Processing for Audio Applications which is talking about frequency warping. An open access version of this artical is available here.
Say a signal or ...
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Minimum Phase - All Pass Decomposition For Large Linear Phase Filters
UPDATE:
I am looking for a robust approach to decompose linear phase FIR filters with 100s of coefficients into its minimum phase and all pass components.
I originally thought determining all the ...
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Prove the following property of All-Pass Filters
If A(z) is an all-pass filter given by
$$A(z)=\frac{z^{-1}-d_1}{1-d_1 z^{-1}}$$ where $d_1$ is a real coefficient
Then prove that
$$ |A(z)|\left\{
\begin{aligned}
&<1 &|z|>1 \\
&=1 &...
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answer
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Fine tuning LPF responses from cascading APFs
I would use this post to outline my question since the post had laid down the groundwork:
how to design LPH and HPF from APF
So if want to fine tune overall LPF response with more cascading allpass ...
2
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2
answers
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Design of all pass filter with desired phase response
I want to design an all pass filter with a desired phase response in MATLAB. But in MATLAB, all pass filters are designed either by specifying the all pass filter coefficients or from a transfer ...
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Phase Response of $N$-th order Digital All-Pass Filter
I am having trouble reconciling my derivation of the phase response of an N-th order all-pass filter with those I am finding in the literature, and I figured someone here could help me.
Real Version:
...
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Why does the volume increase when I reduce the gain of an all-pass filter connected in series?
I am using the colorless allpass-filter proposed by Schroeder Manfred R to create a reverberator.
It consists of about 8 colorless allpass-filters connected in series, each with a different delay ...
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Is the Schroeder Allpass implementation in Freeverb incorrect?
I've been looking into the venerable Freeverb and I see that CCRMA state that it uses 4 Shroeder Allpass filters in series, but when I look at the source code I see:
...
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602
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Get minimum phase from function
Why is it that reflecting any poles or zeros of a rational function across the unit circle gives a minimum phase system? Here's an example, it seems reflecting any poles or zeros would result in the ...
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635
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Minimum phase All-pass
Why is it that reflecting any poles or zeros of a rational function gives a minimum phase system? And why is doing that make a unique minimum phase system?
I understand the all-pass function absorbs ...
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3
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3
answers
956
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Linkwitz-Riley Crossover Sum as Allpass Filter
I was curious about crossover filter design, so I did some reading on Linkwitz-Riley filters. Seems to me that the general idea is that if you add HP and LP filters and they are properly designed, ...
- 1,038
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341
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All-pass phase compensation only in a specific frequency range
I am trying to design an all-pass filter in order to compensate the phase distortion at the output of an equalizer. To do so, I take the phase vector of the output, compute the real and imaginary part ...
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300
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Linkwitz-Riley Allpass filters of Nth order from cascaded SVF second order sections
I am in the process of implementing a Linkwitz-Riley filter of 16th order. (LR-16, 96dB/oct) I am using 2nd order SVF sections with three modal outputs on each section. (LP, BP, HP) I am looking to ...
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451
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Design of discrete time second order all pass filter
I want to design a second order digital all pass filter with the transfer function given by
$$H(z)=\frac{a_2 +a_1 z^{-1}+z^{-2}}{1+a_1 z^{-1}+a_2 z^{-2}}$$
The input to this filter has frequencies ...
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Phase correction using second order all pass filters/LMS with Wiener-Hopf equations
I am working on phase correction algorithms. Can anyone help me understand how can the following diagram be used for phase correction:
Additionally, for a channel function suggested How determine the ...
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Plotting Frequency Response Magnitude and Phase for first order all pass filter
Having trouble plotting the frequency response characteristics for first order all pass filter. The Magnitude is expected to be constant across entire freq and Phase is expected to be only decreasing (...
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Is there a simpler way to calculate the amplitude response of the following filter
I would like to calculate the amplitude response $|H(z)|$, $z=e^{j\omega}$, of the following filter:
$$H(z)=\frac{\frac{b}{2}+z^{-2}}{2+bz^{-2}}$$
and I would like to avoid using Euler's formula and ...
- 103
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Getting a single feedback peak from a basic 4 stages phaser
I try to set a very basic 4 stages phaser (two 2-pole all-pass filters), with a particular feedback path where only one peak is raised at center frequency when the feedback is above 0.
The following ...
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3
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How do you calculate the group delay in samples of a Biquad Filter at a given frequency from the coefficients?
If I have a BiQuad all-pass filter with a given set of coefficients such as:
g: 0.903228
a1: -1.88142
a2: 0.903228
B1: -2.08299
B2: 1.10714
And my operation per ...
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Presenting an all-pass filter of a high order as a cascade of all-pass filters of the 1-st order
Are all-pass filter of the n-th order just a cascade of N all-pass filters of the 1-st order?
There are some nice statements regarding zeros, poles, and gain for the 1-st order. Can those statements ...
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309
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How to calculate an All-Pass filter quantization coefficients
Given
$$H(z) = \frac{z^{-1}-0.8}{1-0.8z^{-1}}\text,$$
does the filter stay an All-Pass filter after quantization of coefficients?
If so, how can I prove it mathematically?
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answer
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How to calculate the delay generated by a 2nd order all-pass filter
I'm trying to simulate the dispersion effect of a stiff string in a digital waveguide system, by using second-order all-pass filters.
I use a second order all-pass filter with this transfer function:...
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All pass filter design for group delay compensation
I've designed an IIR bandpass elliptic filter in Scilab with the following parameters.
Sampling Frequency = 25000 Hz
Lower cutoff frequency = 100 Hz
Upper cutoff frequency = 150 Hz
Pass band ripple = ...
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174
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Calculating Stability of Phaser Feedback Loop
I have been doing some experiments with phaser programs. I really like setting the phaser feedback to really high levels, such that the effect is really metallic and resonant, almost like a physical ...
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218
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Why these cross-connections in the allpass filter?
Why these cross-connections in the allpass filter?
and what do negative and positive $k_1$ really refer to?
Is it when the signal is going downwards or is it when the signal is below the zero line?
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Allpass Filters - Causal and Stable
So I have been learning about how to test systems for causality and stability but I am confused about the implications on their unit circle representation.
Would it be safe to say that a causal and ...
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Given a causal LTI system with a transfer function, determine if the system is an all-pass filter
We are given a transfer function of a causal LTI system and must determine if it is an all-pass filter:
$$ H(z) = \frac{1 + 4z^{-2}}{4 - z^{-2}} $$
To the best of my recollection to determine if a ...
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IIR Hilbert Transformer
I'm beginning to explore discrete Hilbert transformers - ways to achieve 90°. phase shift across a band of perhaps 6 kHz at a 44.1 kHz sampling rate. I'm trying to stick with IIR filters in order to ...
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A property of all-pass filters
Let $G(z)$ be a real coefficient stable all-pass transfer-function with
degree greater than zero. Then it can be shown that $|G(z)| < 1$ for
$|z| > 1$: Given that the poles occur in complex ...
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215
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how to design LPH and HPF from APF
I came across a concept that says we can design LPH and HPF from APF when the transfer function of the two APFs given as
$$\begin{align}A_0(z)&=1\\
A_1(z)&=\frac{-a+z^{-1}}{1-az^{-1}}\\\\
H_{...
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Finding minimum-phase/allpass of transfer function
I am trying to find the minimum-phase system of the transfer function $H(z) = \frac{2 + 3.125z^{-2}}{1-0.9z^{-1}+0.81z^{-2}}$.
I know I need to find and remove the allpass (basically reflect the two ...
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filtering in frequency domain
I am performing decorrelation of two channels of audio using all pass filtering. The two all pass filters for two channels are of very high order (>1000 but with not all coefficients non zero). I have ...
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All pass systems- Poles and Zeros
If an All Pass system has poles at $0.8\exp\left(-j \dfrac{\pi}{4}\right)$ and $0.8\exp\left(j \dfrac{\pi}{4}\right)$, There would be $2\pi$ jumps in the phase (principal value) at angular frequency $\...
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Allpass filter feedforward/feedback design and code
I want to design/implement a simple feedforward/feedback all-pass filter, and I am having some troubles and questions with it.
From Shroeder design (based on J. Smith article here):
I came up ...
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3 Band Crossover with Linkwitz Riley Filter
I would like to write a 3 Band "EQ" with BiQuad Filters but for some reason, I get some phase distortion.
The problem already got discussed here.
I found out that I need to work with Allpass filters ...
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390
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Unstable Cascade of Allpass Filters
I'm working with cascaded second-order allpass filters. Each filter is characterized by conjugate pole/zero pairs. In a long (>50) cascade of identical filters, the pole locations of the overall ...
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