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15 votes
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could anybody explains me why IIR filters do not have linear phase?

Please tell me. Also I dont know why phase is linear with FIR filters. I would like quantitative analysis. And why linear phase is not achieved by IIR filters ?
hafsa's user avatar
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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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10 votes
3 answers
4k views

Downsampling lowpass filter for audio: FIR or IIR?

I'm working on a real-time audio processing project in which I have to downsample a 44.1 kHz to a yet-to-be-determined lower sampling rate essentially for reducing computational complexity. I'm ...
Phonon's user avatar
  • 5,216
9 votes
3 answers
5k views

Why do linear phase filters have symmetric impulse responses?

It was given as a fact that linear phase filters have symmetric impulse responses, but I don't see why that has to be true. Can somebody please explain or prove this?
CAJ's user avatar
  • 313
8 votes
4 answers
48k views

Group delay of the FIR filter

For an FIR filter, with symmetrical tap values $h[N-1-n]=h[n]$, why is the group delay $\frac{N-1}{2} T$ (where $N$ is the number of taps of the FIR filter and $T$ is the sampling time)? Why is ...
Jayesh Parmar's user avatar
7 votes
4 answers
2k views

Examples where non-linear phase filters are used

I stumbled apon this old question: Why is a linear phase important? There the explanation of why linear-phase processing (filtering) is important is very clear. Also the effects on waveforms due to ...
Todor Petkov's user avatar
6 votes
3 answers
1k views

Delay a signal in time vs in frequency

I have a signal h that I want to delay for a time t. I know that I could use two possible approaches: $h_{\text{delay}}[k] = \...
Mattia Surricchio's user avatar
5 votes
1 answer
1k views

Why can't realisable IIR filters have linear phase?

I am studying IIR Filter Design and came across this arbitrary statement in my textbook which says that 'physically realisable and stable IIR filters can not have linear phase'. Would really ...
Devesh Lohumi's user avatar
5 votes
1 answer
465 views

Group Delay for Hilbert Transformer and Resulting Dispersion

An ideal Hilbert Transformer shifts the phase for all positive frequencies by $-\pi/2$ and all negative frequencies by $+\pi/2$ while maintaining constant magnitude everywhere. Group Delay is the ...
Dan Boschen's user avatar
  • 51.9k
5 votes
1 answer
465 views

Filter design with a phase delay specification?

Given a desired filter magnitude response, plus acceptable linear phase and minimum phase FIR filter approximations, how can one design a filter with the given response and a delay specification of ...
hotpaw2's user avatar
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4 votes
2 answers
825 views

Linear phase FIR filter for impulse responses that don't appear symmetric

I would like to clarify some confusion I have about linear phase FIR filters of which do not seem to have symmetric impulse responses. Starting with a simple case, a delay, $ h[n] =\delta(n-n_0) $ ...
DarkLink's user avatar
  • 307
4 votes
2 answers
1k views

Are the 4 types of linear phase FIR filters the only linear phase FIR filters one can come up with?

Basically my question is the same as the title: Are the 4 types of linear phase FIR filters the only linear phase FIR filters one can come up with? And if so, then why? I'm pretty sure that they are ...
zer0square's user avatar
3 votes
5 answers
513 views

Linear phase with a non-integer delay?

Let's say you are given a frequency domain specification for a filter design. As a simple example, let's use an ideal (brickwall) LPF. Now the impulse response of an ideal LPF is a $\operatorname{sinc}...
Ahsan Yousaf's user avatar
  • 1,533
3 votes
2 answers
2k views

Matlab `filtfilt` provides excessive transient

I observed that filtfilt suffers from an undesired behavior when I provide IIR bandpass filters having steep transition bands. Specifically, the output signal exhibits excessive transient response; ...
ale83FiUni's user avatar
3 votes
1 answer
3k views

Differences between phase and group delay

Yet another group delay vs. phase delay question! Though this is a question that's been asked several times I don't feel like it's been fully discussed so I'll post an example that I can't quite seem ...
lerneaen_hydra's user avatar
3 votes
3 answers
269 views

Why make the phase of an FIR filter linear?

I am new to DSP and filter design. It is easy to design an FIR filter with linear phase by making the coefficient sequence symmetric. However, why make the phase linear?
K.n90's user avatar
  • 141
3 votes
1 answer
832 views

FIR to linear-phase FIR

I am trying to convert an FIR impulse into linear-phase FIR impulse, I need to remove the phase response, so when it is applied to a sound it only changes the amplitude response. Here is my code ...
skyisfalling's user avatar
3 votes
1 answer
437 views

Applications for the Maximum Phase Filter

A maximum phase digital filter has all zeros outside the unit circle, and has the maximum phase and therefore longest delay for a given magnitude response. Besides the possibility of needing a ...
Dan Boschen's user avatar
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3 votes
1 answer
462 views

Regarding the advantages of generalized linear phase filters

I know that for a linear-phase filter with frequency response given by $$H(e^{j\omega}) = |H(e^{j\omega})|e^{j\phi(\omega)} $$ if the input of the system is $$x[n] = s[n]\cos[\omega_0 n] $$ where $s[...
diegobatt's user avatar
  • 268
3 votes
1 answer
2k views

Why is there little emphasis on phase distortion?

I have a question regarding the frequency response of digital filters. Specifically the phase aspect of the frequency response. Why do we not seem to care about the nonlinear phase response in ...
Izzo's user avatar
  • 872
3 votes
1 answer
2k views

FIR filter phase response

With reference to the diagram below, is it correct to say that at the pass band the phase response is linear. It also remains linear in the stop band but it get chunks of π. These jumps happen when ...
dritech's user avatar
  • 35
2 votes
1 answer
227 views

Phase response of non-symmetric FIR filters

FIR filters are said to have linear phase when the filter coefficients are symmetric or antisymmetric with respect to time instant n=0. I am trying to design a ...
Deepa's user avatar
  • 315
2 votes
1 answer
777 views

How should we read FIR filter phase response graph?

What should we see from the FIR phase response graph, as an example for a linear phase? And what does this straight line at $0.5\pi$ mean?
Ece Su Ildiz's user avatar
2 votes
1 answer
2k views

Downsampling impact on complex phase

For my application, I have to downsample a bandpass complex signal which spectrum is located on the second Nyquist zone. Knowing that this processing will cause a spectrum inversion, what would be ...
M.FAKHFAKH's user avatar
2 votes
1 answer
7k views

Phase response of moving average filter -- how to interpret?

There are many articles on the frequency response of the moving average filter but they all seem to focus on magnitude. However the phase response is intriguing and I find it hard to interpret. The ...
barnhillec's user avatar
2 votes
1 answer
105 views

subquestion 2 : original Q "Difference between MSK and GMSK?"

if we talk about a modulation, we mention a linear and nonlinear modulation. GMSK is nonlinear modulation, but it can be derived from a linear modulation as MSK, PAM and we talk about a linear ...
FrimHart64's user avatar
2 votes
1 answer
919 views

What is the reason behind complex conjugate pairs in Linear Phase FIR filter analysis from the Pole Zero plot

When we say that a Generalized Linear Phase System must satisfy the pole zero plot with the condition that a complex zero not on the unit circle exist's in a pair of 4. Then I understand that I need ...
Power Surge's user avatar
2 votes
2 answers
578 views

Mean delay for a M tap harmonically weighted filter

I am trying to derive the mean delay for $M$ filter taps harmonically weighted: $$y[n] = \frac{M\,x[n] + (M-1)x[n−1]... + 1 \cdot x[n−M+1]}{\tfrac12 M (M + 1)}$$. For a uniformly weighted filter, I ...
Srilakshmi Alla's user avatar
2 votes
1 answer
1k views

Transform linear-phase FIR to minimum-phase FIR

Given a FIR filter (non-causal) with phase zero and real coefficients given by $$H(z) = \sum_{n=-M}^{M}h[n]z^{-n}$$ with ripple $\delta_2$. How can I obtain a filter $H_{{\rm min}}(z)$ of minimum ...
Euler's user avatar
  • 183
2 votes
1 answer
136 views

Combination of type I FIR linear-phase systems

Let $h_1[n]$ and $h_2[n]$ be impulse responses of type I FIR linear-phase systems with lengths $M$ and $N$. What can be said about the phase response of the following filters? $h_3[n] = h_1[n] + h_2[...
S.H.W's user avatar
  • 726
2 votes
0 answers
118 views

Equivalence between the linear phase of FIR filters and the (anti)symmetry of the coefficients

According to the Matt L.'s answer to this question, real-valued and causal FIR filters have a (generalized) linear phase response if and only if their coefficients satisfy (anti)symmetry condition. ...
S.H.W's user avatar
  • 726
1 vote
2 answers
156 views

Frequency Sampling Filters (FSFs) NOT the Frequency Sampling Method

A class of digital filters called Frequency Sampling Filters (FSF) has been mentioned in a side note by Richard Lyons in another related question comparing IIR digital filter design using mapping ...
Dan Boschen's user avatar
  • 51.9k
1 vote
2 answers
89 views

Turning non-symmetric filter into a symmetric filter

I would like to ask if there is a systematic way to turn a non-symmetric filter into a symmetric equivalent with the same frequency response. For example, let's say I have a finite length filter with ...
AAM's user avatar
  • 13
1 vote
1 answer
601 views

Matlab: How to design digital equivalent for a lowpass Bessel filter (Thiran filter)?

In the process of applying a lowpass Bessel filter to my signal, I realized that besself function does not support the design of digital Bessel filters and the bilinear function can be used to convert ...
Amy 's user avatar
  • 53
1 vote
1 answer
649 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
1 vote
2 answers
2k views

Causal and minimum phase

I have couple of questions? Is there a relationship between a FIR filter being minimum phase/mixed phase and being causal? Is there a relationship between a FIR filter being minimum phase/mixed phase ...
user915783's user avatar
1 vote
1 answer
202 views

Slope of phase function

Would appreciate some help understanding if I take the phase function of some transfer function and derivative it in the linear part of it which is around the resonant frequency what does this slope ...
wonder3's user avatar
  • 13
1 vote
1 answer
519 views

What is the significance of the linear phase in the phase response of an M-point moving average filter?

I have plotted the magnitude and the phase responses of an M-point moving average filter, the following are the plots when M = 10: We can observe that corresponding to every lobe in the magnitude ...
Aditya's user avatar
  • 165
1 vote
1 answer
92 views

What is the phase response of SRRC/NRZ/RZ pulse shapping filters and does it matter?

So I would like to know if filters usually used for pulse shaping (like SRRC) have a linear phase response, and if not, what this response looks like and does it matters in any circumstances?
graille's user avatar
  • 57
1 vote
2 answers
1k views

How to properly smooth the phase of a spectrum (or any unit-complex function)

I want to smooth the phase of a measured (transfer) spectrum without destroying unit-complexity of the phase factor. Suppose $$f:\mathbb{R}\to \mathbb{C}\qquad , \qquad f(\omega)=r(\omega)\cdot {\rm e}...
oliver's user avatar
  • 266
1 vote
3 answers
236 views

Transfer function of linear phase filter & its frequency domain representation

Text of my exercise request: Determine the transfer function $H(z)$ of a causal linear phase FIR filter with zeros at $z= \frac{1}{3}$ and $z=-2$. The value of the impulse response at $n=0$ equals $...
P_B's user avatar
  • 57
1 vote
2 answers
965 views

Causality of Linear Phase Filter

If a digital LTI filter has phase response on the form $arg[H(e^{jw})] = -\alpha\omega$, what could one say about it's causality (and consequently, the causality of it's impulse response)? Also is ...
Thiago's user avatar
  • 285
1 vote
1 answer
657 views

Resampling FIR coefficients

I have received from a client a 32-coefficient FIR filter running at 1 kHz. I would like to adapt the filter to a 24-coefficient FIR filter running at 750 Hz while preserving the 0-375 Hz frequency ...
Ben's user avatar
  • 3,777
1 vote
1 answer
745 views

FMCW radar: Linear phase change determination with sinusoidal decomposition

I am struggling to understand how linear phase shift can be determined with a transform whose main purpose is to determine frequencies rather than rate of change of a function. In FMCW radar, ...
Raj's user avatar
  • 279
1 vote
1 answer
202 views

Phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$

I want to find the phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$ for the interval $0\leq \omega \leq \pi$. Method 1: $H(e^{j\omega})=1-\left(...
Narendra Deconda's user avatar
1 vote
1 answer
299 views

Why are linear phase filters called so, if they provide Constant delay instead of linear

Linear phase filters delay all frequencies by the same amount. Why aren't they called Constant phase filters instead of Linear phase? As I understand, if there is an input signal with two components ...
Naveen's user avatar
  • 53
1 vote
0 answers
116 views

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. ...
Md. Hasan Rahman's user avatar
1 vote
1 answer
91 views

Filters using equiripple approximations (different from type I lowpass)

In Oppenheim & Schafer's Discrete-Time Signal Processing, only type I lowpass filters are explained in detail in the chapter "Optimum Approximations of FIR filters". I want to know what ...
Tendero's user avatar
  • 5,020
1 vote
0 answers
780 views

When do you use a minimum-phase filter over a linear-phase filter

Q1) I have understood that linear-phase filters have more delay time whereas minimum phase filters implement a lesser delay time but introduce phase distortion artifacts which linear-phase filters ...
Akhilesh Rao's user avatar
1 vote
0 answers
646 views

Phase Linearization

Does anyone know of some simple algorithms to linearize the phase response of a filter. I have a notch filter with a non-linear phase response. I basically need an all pass filter (so that the ...
user1832413's user avatar