# Questions tagged [linear-phase]

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### Time delay vs phase ramp, group delay and phase delay

I need to apply a phase ramp in the frequency domain to a signal in order to apply a delay to it in the time/digital domain. However, I am confused by the fact that if I convert the phase ramp into ...
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### Linear Phase in equiripple filters

How come equiripple filters are symmetric/anti-symmetric in time, but do not posses linear phase, but only piecewise-linearity? Do not all FIR+symmetric/anti-symmetric have Generalized linear phase?
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### 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 ...
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1 vote
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### 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 ...
• 13
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### FFT-Phase variation of a signal

I was studying the phase variation of a signal using sliding window FFT generated using below python code. The phase variation produced for my signal starts from somewhere in middle of the signal ...
159 views

### Derivation of the 4 types of real-valued linear-phase FIR filters

Is there any resource or literature where I can find derivations/proofs for all four linear phase filter types starting from an arbitrary real valued impulse response? I looked at some of the ...
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### 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. ...
• 726
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948 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 ...
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### 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 ...
1 vote
780 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, ...
• 279
2k 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 ...
• 23
762 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 ...
• 103
619 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 ...
104 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 ...
485 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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### 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 ...
1k 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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844 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, $h[n] =\delta(n-n_0)$ ...
• 307
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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 ...
2k 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 (...
1 vote
### 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(...