Questions tagged [minimum-phase]

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Question about reducing phase delay in filters for microcontroller application

I am trying to design a filter to smooth out some of my sensor data. This is for a control systems application where I have limited phase margin. I am looking for a solution where I can maintain lower ...
Mr Phase Locked Loop's user avatar
2 votes
1 answer
188 views

Intuitive explanation of magnitude-phase-relationship for minimum phase filters

I know that, given the magnitude response $|H(e^{j \omega})|$ of a filter $H(z)$, it's minimum-phase response is given by $$ \phi(\omega) = -\mathscr{H}\Big\{ \log(|H(e^{j \omega})|) \Big\} \ . $$ I ...
herrzinter's user avatar
2 votes
1 answer
161 views

Why extracted minimum phase component have inverted phase?

I'm using Octave code to extract minimum phase, but this minimum phase has became inverted phase acording to original signal, What is goin wrong? Resault here I have shifted main signal about 48 ...
mohammadsdtmnd's user avatar
0 votes
1 answer
58 views

Finding impulse response/polynomial zero on the unit circle

The polynomial here is impulse coefficients of minimum phase FIR filter, or it's impulse response. A code somewhere tries to finding roots of polynomial on the circle. It have roots of polynomial <...
mohammadsdtmnd's user avatar
1 vote
1 answer
172 views

How to determine if a system is minimum phase or not?

I'm studying for an exam and this is an old exam question that I don't understand: Is the following system non-minimum phase? $$G(s) = \frac{e^{-2s}}{s+2}$$ I can see that the real part of the pole is ...
student's user avatar
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1 answer
252 views

What is the position of all zeros of a minimum phase, Type 1 Linear Phase FIR Filter?

Let me write down all the facts that I know of. In context of the z plane: Minimum phase system: All zeros and poles of such a system lie inside the unit circle. Linear phase FIR filter: For every ...
McSuperbX1's user avatar
0 votes
0 answers
58 views

Reconstruction of original signal after minimum phase filter

The question is pretty self explanatory. I want to know if it is possible to recover a signal originally injected into noisy data (coloured gaussian noise) after whitening the data with an AR minimum ...
GWSurfer's user avatar
1 vote
1 answer
90 views

How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response

I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
Heath's user avatar
  • 131
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1 answer
185 views

Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
Mark's user avatar
  • 369
4 votes
0 answers
227 views

How to solve Hilbert Transform with empirical discrete data in frequency domain?, from zero to infinity

I have a filter/LTI system frequency response in form of list of values in the frequency domain. I want to get the phase curve/data from magnitude data. Input data can have either linear spaced points ...
Leandro Alsina's user avatar
6 votes
1 answer
563 views

Getting phase response from magnitude. How to develop and solve this Hilbert transform?

I'm trying to generate phase data from magnitude data in a frequency function, assuming the system is minimum phase. Using Hilbert Transform. For instance, having this simple system: $G(s) = s$ $G(j\...
Leandro Alsina's user avatar
13 votes
4 answers
1k views

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 ...
Dan Boschen's user avatar
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1 vote
1 answer
93 views

inverting unstable zeros

Consider a dynamic system $$\dot{x}=Ax+Bu \text{ and } y=Cx$$ The transfer function is $$sX(s) = AX(s)+BU(s),$$ so $$(sI-A)X(s)=BU(s)$$ and $$Y(s)=CX(s)$$ combining the two transfer equations, we have ...
sunxd's user avatar
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3 answers
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On what it means for a system to be minimum phase

From my undestanding I get that when a system's poles and zeros are all inside the unit circle then it means that it's minimum phase. But I don't get how the location of zeros and poles are related to ...
Nyquist-er's user avatar
0 votes
2 answers
478 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 ...
d4898ty's user avatar
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1 answer
498 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 ...
d4898ty's user avatar
-1 votes
1 answer
81 views

Mininum phase question

I know in a minimum-phase system, any poles or zeros are reflected. How do I show that a minimum phase system is unique, or that only one system with that magnitude response can be minimum phased?
d4898ty's user avatar
0 votes
1 answer
346 views

Minimum phase conversion with Cepstrum method, how to scale the result?

I am trying to convert a zero phase spectrum (magnidue response curve with zero phases) to a minimum phase spectrum, because I need a totally causal impulse response for FFT spectral filtering, and ...
elena's user avatar
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1 vote
1 answer
327 views

Phase correction algorithm: minimisation phase error

Thank you for your participation in my discussion in advance. I am working on the implementation of a phase correction. Currently, I have finished the algorithm. I think it is a standard algorithm ...
Jang Lee's user avatar
3 votes
2 answers
790 views

minimum-phase phase via Hilbert transform returned values

Following my previous question: HRIR Minimum phase I managed to compute the minimum-phase phase of a FIR filter (in my particular case, HRTF filters). However I am not sure of the phase values ...
Mattia Surricchio's user avatar
3 votes
1 answer
693 views

Compute minimum phase version of a FIR

I am working with HRIR filters, in particular I am trying to interpolate them. One commod method in the literature to perform interpolation of HRIR is to use the minimum-phase decomposition and ...
Mattia Surricchio's user avatar
3 votes
1 answer
64 views

Validity of an argument that two transfer functions are minimum-phase based on their ratio being minimum-phase

Update I think the essence of my question below is this: If the ratio of two transfer functions may be represented exactly as a minimum-phase filter (MPF) plus a pure delay (in the title, I simply ...
Rahul's user avatar
  • 123
1 vote
1 answer
357 views

What does nonnegative zero-phase response mean?

I am not exactly sure what nonnegative zero-phase response means. If a filter is zero-phase (i.e. symmetric and non-causal), then what does nonnegative imply? And what are the conditions to satisfy it?...
dsp_guy2020's user avatar
3 votes
2 answers
337 views

When is the sum of two (parallel) minimum-phase filters also minimum-phase?

Say I have two minimum-phase filters: $$\frac{A(z)}{B(z)} \: \text{ and } \: \frac{C(z)}{D(z)}$$ That is, the roots of $A(z)$, $B(z)$, $C(z)$ and $D(z)$ are all in the stable region. If add them ...
cloudfeet's user avatar
  • 301
3 votes
1 answer
202 views

Algorithm to Count Zeros Outside Unit Circle for FIR Filter

As detailed in this post Can I set a constraint on the first tap of an FIR filter such that its inverse is stable? I show how Cauchy's Argument Principle can be used to easily confirm if an FIR filter ...
Dan Boschen's user avatar
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2 votes
1 answer
137 views

How to create matched "minimum phase" for a system of parallel FIRs?

Problem statement I have a collection of magnitude (only) responses I'd like to turn into FIR filter kernels that are matched in phase "minimal" in phase, with respect to the complete system have ...
Joseph Anderson's user avatar
1 vote
1 answer
328 views

Not able to reach minimum phase using Hilbert transform

My problem is pretty simple, I've designed a magnitude response and I would like to find the corresponding minimum phase filter. I'm using the code below and unless there is a bug my eyes don't want ...
Julie's user avatar
  • 11
1 vote
1 answer
762 views

How to prove these two definitions of the minimum phase transfer function are same?

There are so many definitions of the minimum phase transfer function, and these are two of them. The transfer function of the system which has no zeros or poles at right half plane. The transfer ...
Kim Jaewoo's user avatar
0 votes
1 answer
259 views

Finding the transfer function of a discrete signal described by two equations

A discrete time system is described by the following system of equations. $$q[n] = \big(x[n]-\frac k4q[n-1]\big)$$ $$y[n] = \big(q[n]-\frac k3q[n-1]\big)$$ Find the systen function and then find the ...
thelaw's user avatar
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1 answer
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Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?

I have been staring at this problem for a week now... Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
user avatar
3 votes
1 answer
2k views

Hilbert transformer and minimum-phase

I can't find out if it possible to compute the minimum-phase response corresponding to a given magnitude response using a Hilbert transformer. Is that possible? When I write Hilbert transformer I ...
greggo's user avatar
  • 33
2 votes
1 answer
844 views

Definition of minimum-phase system

I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them. The first definition I saw was: An invertible system which ...
Vegetal605's user avatar
0 votes
0 answers
181 views

Closed form solution for the minimum phase of a continuous magnitude response

Let's say I have a continuous real function $F(\omega)$ defined in the region $\omega = [-\pi, \pi]$. Let's also say that I have a minimum phase $z$-domain transfer function $H(z)$ defined as: $$\...
keith's user avatar
  • 906
1 vote
1 answer
570 views

Under what conditions do the phase margin and Nyquist criteria give the same results?

When designing feedback systems, I often evaluate stability by thinking about phase margin: the closed loop system $$T(s) = \frac{L(s)}{1+L(s)}$$ is stable if $L(s)$ has positive phase margin, i.e., $...
Max's user avatar
  • 352
10 votes
1 answer
2k views

What is the easiest, most straight-forward way to prove this about minimum-phase filters?

Using the "unitary" or "ordinary frequency" or "Hz" convention for the continuous Fourier Transform: $$ \begin{align} X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\...
robert bristow-johnson's user avatar
1 vote
1 answer
647 views

Transform minimum phase FIR into linear phase FIR

I've seen examples of transforming a linear phase FIR into a minimum phase FIR, but is there a simple process to transform a minimum phase FIR into a linear phase FIR? I would like to end up with a ...
keith's user avatar
  • 906
2 votes
1 answer
642 views

Decomposition of $H(z)$ as maximum-phase, minimum-phase

The frequency response is: $$H(z) = 2-7z^{-1}+7z^{-2}-2z^{-3}$$ I see that it has $3$ zeros: $z_{01} = \frac 12$, $z_{02} = 2$, and $z_{03} = 1$; and $3$ poles in: $$z_x = 0$$ Now, I have to write ...
Euler's user avatar
  • 183
4 votes
1 answer
2k views

Minimum phase FIR method

I am trying to make a minimum phase filter (in wxMaxima) according to these steps: first create a "normal" FIR (a simple sinc, wc=0.4, random example, but in the pictures a remez with Octave) ...
a concerned citizen's user avatar
2 votes
1 answer
251 views

Given Gain function, how to design a causal, stable and minimum phase IIR filter?

I am given $|H(\omega)|$, I wonder if minimum phase stable causal filter is unique and how to calculate it.
user40129's user avatar
  • 143
4 votes
2 answers
2k views

Minimum phase systems with pole at infinity

If a system is given by a transfer function in the $z$ domain that has all poles and zeros inside the unit circle except for a factor of $z^{-1}$ in the denominator (pole at infinity), can it still be ...
user3361675's user avatar
3 votes
2 answers
4k views

Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
SpeedCoder5's user avatar
36 votes
5 answers
39k views

What is the true meaning of a minimum phase system?

What is the true meaning of a minimum phase system? Reading the Wikipedia article and Oppenheim is some help, in that, we understand that for an LTI system, minimum phase means the inverse is causal ...
TheGrapeBeyond's user avatar