Questions tagged [minimum-phase]

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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 ...
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5 votes
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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\...
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4 answers
286 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 ...
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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 ...
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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 ...
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2 answers
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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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1 answer
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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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-1 votes
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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?
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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 ...
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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 ...
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2 votes
2 answers
310 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 ...
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1 answer
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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 ...
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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 ...
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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?...
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2 votes
2 answers
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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 ...
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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 ...
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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 ...
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1 vote
1 answer
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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 ...
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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 ...
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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 ...
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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 ...
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3 votes
1 answer
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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 ...
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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 ...
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0 answers
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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: $$\...
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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., $...
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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\limits_{-\infty}^{\infty} x(t) \, ...
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1 vote
1 answer
510 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 ...
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3 votes
1 answer
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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) ...
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2 votes
1 answer
209 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.
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4 votes
2 answers
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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 ...
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35 votes
4 answers
35k 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 ...
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