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# 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.

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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 ...
• 501
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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.&...
• 501
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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 ...
• 754
1 vote
400 views

### 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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1 vote
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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 ...
2k views

### 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 ...
• 325
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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: ...
• 632
1 vote
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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 ...
• 13
280 views

### 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: ...
• 423
555 views

### 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 ...
551 views

### 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 ...
838 views

### 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
1 vote
323 views

### 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 ...
284 views

### 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 ...
399 views

### 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 ...
• 325
344 views

### 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 ...
• 41
713 views

### 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 (...
• 33
2k views

### 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
255 views

### 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 ...
1 vote
1k views

### 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 ...
296 views

### 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?
1 vote
1k views

### 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 = ...
164 views

### 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 ...
• 151
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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?
• 1,414
1k views

### 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 ...
575 views

### 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 ...
4k views

### 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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1 vote
588 views

### 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 ...
208 views

### 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_{...
2k views

### 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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