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Questions tagged [minimum-phase]

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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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0answers
26 views

How can I test a finite sequence to see if it is minimum phase other than by finding its zeros?

I want to test finite (but long - up to 400 elements) sequences to see if they are minimum phase. Is there a test other than computing the zeros of the z-transform of the sequence? Something like ...
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1answer
64 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 ...
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0answers
101 views

Determine phase response from pole-zero plot

I know how to determine the frequency response from the pole-zero diagram given the following formula: $\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
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0answers
73 views

Excess phase component of a signal

I have a signal that I would like to separate to its minimum phase and excess phase components. If I understand correctly any speech signal can be represented by the convolution of these components, ...
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1answer
108 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 ...
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1answer
54 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 ...
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1answer
71 views

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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1answer
670 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 ...
1
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1answer
270 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 ...
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0answers
128 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: $$\...
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1answer
265 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., $...
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1answer
763 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\limits_{-\infty}^{\infty} x(t) \, ...
1
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1answer
348 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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1answer
154 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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2answers
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 ...