Questions tagged [linear-phase]

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14
votes
3answers
13k views

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 ?
8
votes
3answers
3k 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 ...
8
votes
2answers
2k 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?
5
votes
1answer
394 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 ...
3
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2answers
853 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; ...
3
votes
3answers
166 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?
3
votes
3answers
24k 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 ...
3
votes
1answer
748 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 ...
2
votes
1answer
471 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 ...
2
votes
2answers
551 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 ...
2
votes
2answers
312 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 ...
2
votes
1answer
167 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[...
2
votes
1answer
480 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 ...
1
vote
1answer
1k 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 ...
1
vote
1answer
326 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 ...
1
vote
1answer
329 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 ...
1
vote
3answers
135 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 $...
1
vote
2answers
382 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 ...
1
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1answer
57 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(...
1
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1answer
120 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 ...
1
vote
1answer
1k 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 ...
1
vote
1answer
67 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 happens ...
1
vote
0answers
575 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 ...
1
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0answers
384 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 ...
0
votes
1answer
423 views

Do antisymmetric FIR filters preserve the shape of their input waveforms?

For antisymmetric FIR windows, the phase response is of the form $a\omega+b$, where $b$ is $\pm\frac{\pi}{2}$, so it is not strictly linear. Does the waveform of the signal gets retained?
0
votes
3answers
639 views

Effect of zero padding an odd symmetric FIR filter in the time domain

I have a symmetric lowpass FIR filter with 1149 time domain taps (all real coefficients). For implementation purposes, it would be easier if the filter had 1200 taps. Since it has an odd number ...
0
votes
1answer
260 views

Phase is not linear in frequency domain after delay in time domain

When impulse response is symmetric around sample zero phase entirely zero. in = 0 , 0 , 0 , 0 , 1 , 1 , 1 , 1 , 0 , 0 , 0 -> This gives zero phase result As I know if I apply a delay in time ...
0
votes
1answer
97 views

If group delay is a constant for all $\omega$, Does this system have a linear phase response?

I want to know if a system has a linear phase response using frequency response of this system. So I got phase response of it and also group delay. and after that I got to know that if group delay ...
0
votes
2answers
88 views

Why does a simple delay system with $h[n]=\delta[n-n_0]$ have a linear phase?

Let's consider a simple delay system with impulse response $$h[n]=\delta[n-n_0]$$ We also know that it has linear phase with group delay of $n_0$ . In general, a FIR filter with symmetric (or anti-...
0
votes
2answers
1k views

linear phase and generalised linear phase filters

I know that for linear phase filters, all frequency components have equal delay times. That is, there is no distortion of signal due to the time delay of frequencies relative to one another. However,...
0
votes
1answer
320 views

Is ideal band pass filter (brick wall filter) linear phase? [duplicate]

I'm very new in digital signal processing. I have multiple sensors and the way I filters the signals in post processing is: take FFT of the signals. put zero on out range of interesting frequency (...
0
votes
1answer
123 views

Sketching Phase Spectra Using Group Delay and Magnitude Spectra Informations

I have only magnitude spectra and group delay information and I need to sketch phase spectra from this information. For example, group delay is given like this: $\tau_{g}(\omega) = c$ where c is a ...
0
votes
2answers
1k 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 ...
0
votes
2answers
81 views

Help me understand the phase of an FIR filter

I'm going over an exercise of designing an simple FIR filter, I have the solution in front of me, but I struggle to understand some parts of it. I'm asked to have an FIR filter with only 3 ...
0
votes
1answer
109 views

How to prove a filter has linear phase response?

I have designed an FIR filter to have linear phase response using odd-symmetry design. The coefficients of this filter are {2,1,3,1,0,-1,-3,-1,-2}. I am now being asked to prove it has linear phase ...
0
votes
1answer
3k 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 ...
0
votes
2answers
354 views

Fourier transform of a sum

I have a function : \begin{equation} C(t)=\left(1.42*\exp^{-1.192t}- 12.44*\exp^{-1.192t} +11.02 \right) u(t) \end{equation} where u(t) is a unit-step function What is its fourier transform? a step by ...
0
votes
1answer
51 views

what is the relation between a minimum phase system and a FIR system? [closed]

I want to see whats the relation between being an FIR system and a minimum phase system and when an FIR system can be minimum phase too with respect to have linear phase
0
votes
3answers
641 views

importance of symmetric windows for STFT for practical applications

I am wondering why is the linear phase property of filters with symmetric coefficients important for some practical applications of short time fourier transform, such as image processing? I have read ...
0
votes
0answers
46 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^{...
0
votes
0answers
87 views

Bandpass Fractional Delay Filter

I am designing a fractional delay filter, I found this code for lagrange FIR fractional delay filter, The fractional delay filter acts as a low pass filter, it passes low frequencies from 0 to 0.25*fs....
0
votes
2answers
90 views

How do I show an impulse response leads to a zero-phase frequency response?

I'm trying to understand how to show that with real coefficients, the phase response of a filter is 0. Here is the impulse response $h[n] = b_1d[n+1] + b_0d[n] + b_1d[n-1]$ How should I approach ...
0
votes
1answer
559 views

matlab fft phase response square wave

I am new to phase analysis, recently I have been trying compare the phase between the input signal and output signal of a system. From the code below, I simulated a square wave and plotted the phase, ...
-1
votes
1answer
44 views

Phase response approaches towards the zeros

Phase response is the relationship between the phase of a sinusoidal input and the output signal passing through any device that accepts input and produces an output signal, such as filter.https://en....