Questions tagged [linear-phase]

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Design FIR with linear phase response

What is the best way to design a FIR filter with a given linear phase response, such that each frequency inside the passband is phase shifted according to: $$H(f)=e^{i2\pi f k}$$ where $k$ is factor ...
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2answers
143 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 ...
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1answer
61 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 ...
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1answer
21 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?
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1answer
333 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 ...
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1answer
81 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?
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1answer
66 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 ...
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1answer
27 views

Constraints for Type 3 Linear Phase Filter

This might be a strange question - but most of the Type 3 LPF I'm seeing are having this in common for $h[n]$, assuming $h[n]$ is real: We cannot have outermost element of h[n] lower than middle ...
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2answers
111 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}...
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1answer
47 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, ...
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4answers
427 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 ...
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2answers
100 views

How does one make a Zero Latency, Linear Phase, or Natural Phase filter?

Looking at FabFilter's ProQ3 plug-in, they have an option at the bottom of the window to switch between Zero Latency and Linear Phase modes (and I think a Natural Phase option too). I'm familiar with ...
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4answers
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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 ?
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1answer
46 views

Is this phase response linear phase?

Would the following frequency response be considered linear phase? I know that linear phase is when the phase response is a linear function of frequency. However, the phase response is only linear ...
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1answer
80 views

FIR Linear Phase Condition

This is the linear phase condition for FIR filters as expressed by my prof: I don't understand why $G(f)$ can be negative. Isn't the Fourier transform expressed in polar form ? So the magnitude is ...
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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,...
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1answer
154 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 ...
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1answer
80 views

How to Determine if FIR has a Linear_Phase Response w/o Matlab

Given the FIR transfer function: h(z) = $ .36 + .384z^{-1} + .1608z^{-2} +.9712z^{-3} + .352z^{-4} + .18z^{-5} - .2z^{-6} $ How do you determine if this transfer function has a linear - phase ...
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1answer
289 views

Finding remaining zeros of linear phase FIR filter

Question given is: if $h(n)$ is a linear phase causal FIR of order $10$ with real coefficients, find the remaining zeros of this filter if the zeros given are $$q_{1,2} = -2 \pm 2j$$ $$q_{3} = -\...
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1answer
137 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) $ ...
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1answer
755 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 ...
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1answer
1k 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 ...
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1answer
721 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 (...
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1answer
65 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(...
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1answer
720 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 ...
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2answers
414 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 ...
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1answer
165 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 ...
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1answer
48 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....
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0answers
154 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....
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3answers
31k 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 ...
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2answers
1k 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; ...
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1answer
78 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 ...
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1answer
2k 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 ...
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1answer
412 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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3answers
201 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?
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2answers
108 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-...
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1answer
163 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 ...
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3answers
943 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 ...
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1answer
261 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[...
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2answers
3k 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?
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1answer
579 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 ...
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1answer
687 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 ...
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694 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 ...
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2answers
712 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 ...
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3answers
154 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 $...
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1answer
5k 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 ...
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2answers
461 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 ...
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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 ...
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1answer
143 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 ...
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0answers
452 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 ...