# Questions tagged [linear-phase]

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44 questions
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Fourier transform of a sum

I have a function : $$C(t)=\left(1.42*\exp^{-1.192t}- 12.44*\exp^{-1.192t} +11.02 \right) u(t)$$ where u(t) is a unit-step function What is its fourier transform? a step by ...
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### 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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### 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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### 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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### 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 ...
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### 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
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...