Questions tagged [linear-phase]
The linear-phase tag has no usage guidance.
50
questions
0
votes
1answer
43 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 ...
0
votes
1answer
21 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 ...
4
votes
1answer
118 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 ...
0
votes
1answer
52 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 ...
0
votes
1answer
99 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
$$q_{1,2} = -2 \pm 2j$$
$$q_{3} = -\...
2
votes
1answer
65 views
Linear phase FIR filter for impulse responses that don't appear symmetric
I would like to clarify some confusion I have about linear phase FIR filters of which do not seem to have symmetric impulse responses.
Starting with a simple case, a delay, $ h[n] =\delta(n-n_0) $ ...
0
votes
1answer
341 views
How to prove a filter has linear phase response?
I have designed an FIR filter to have linear phase response using odd-symmetry design. The coefficients of this filter are {2,1,3,1,0,-1,-3,-1,-2}. I am now being asked to prove it has linear phase ...
0
votes
0answers
116 views
Determine phase response from pole-zero plot
I know how to determine the frequency response from the pole-zero diagram given the following formula:
$\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
0
votes
1answer
467 views
Is ideal band pass filter (brick wall filter) linear phase? [duplicate]
I'm very new in digital signal processing.
I have multiple sensors and the way I filters the signals in post processing is:
take FFT of the signals.
put zero on out range of interesting frequency (...
1
vote
1answer
63 views
Phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$
I want to find the phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$ for the interval $0\leq \omega \leq \pi$.
Method 1:
$H(e^{j\omega})=1-\left(...
1
vote
1answer
474 views
Downsampling impact on complex phase
For my application, I have to downsample a bandpass complex signal which spectrum is located on the second Nyquist zone.
Knowing that this processing will cause a spectrum inversion, what would be ...
2
votes
2answers
381 views
Mean delay for a M tap harmonically weighted filter
I am trying to derive the mean delay for $M$ filter taps harmonically weighted:
$$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 ...
0
votes
0answers
122 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
1answer
144 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
116 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 ...
-1
votes
1answer
45 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....
3
votes
2answers
988 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
187 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?
1
vote
1answer
134 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 ...
0
votes
2answers
100 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]$$ We also know that it has linear phase with group delay of $n_0$
.
In general, a FIR filter with symmetric (or anti-...
1
vote
1answer
73 views
Filters using equiripple approximations (different from type I lowpass)
In Oppenheim & Schafer's Discrete-Time Signal Processing, only type I lowpass filters are explained in detail in the chapter "Optimum Approximations of FIR filters".
I want to know what happens ...
0
votes
3answers
774 views
Effect of zero padding an odd symmetric FIR filter in the time domain
I have a symmetric lowpass FIR filter with 1149 time domain taps (all real coefficients). For implementation purposes, it would be easier if the filter had 1200 taps.
Since it has an odd number ...
2
votes
1answer
208 views
Regarding the advantages of generalized linear phase filters
I know that for a linear-phase filter with frequency response given by
$$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] $$
where $s[...
8
votes
2answers
3k views
Why do linear phase filters have symmetric impulse responses?
It was given as a fact that linear phase filters have symmetric impulse responses, but I don't see why that has to be true. Can somebody please explain or prove this?
1
vote
1answer
2k views
Differences between phase and group delay
Yet another group delay vs. phase delay question! Though this is a question that's been asked several times I don't feel like it's been fully discussed so I'll post an example that I can't quite seem ...
2
votes
1answer
533 views
FIR to linear-phase FIR
I am trying to convert an FIR impulse into linear-phase FIR impulse, I need to remove the phase response, so when it is applied to a sound it only changes the amplitude response.
Here is my code ...
1
vote
1answer
360 views
Transform minimum phase FIR into linear phase FIR
I've seen examples of transforming a linear phase FIR into a minimum phase FIR, but is there a simple process to transform a minimum phase FIR into a linear phase FIR?
I would like to end up with a ...
3
votes
1answer
874 views
Why is there little emphasis on phase distortion?
I have a question regarding the frequency response of digital filters. Specifically the phase aspect of the frequency response.
Why do we not seem to care about the nonlinear phase response in ...
2
votes
1answer
575 views
Transform linear-phase FIR to minimum-phase FIR
Given a FIR filter (non-causal) with phase zero and real coefficients given by $$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
0answers
642 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 ...
3
votes
2answers
634 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 ...
1
vote
3answers
143 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 $...
0
votes
1answer
4k 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
395 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 ...
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 ...
0
votes
1answer
131 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 ...
1
vote
0answers
415 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
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
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
1answer
602 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, ...
0
votes
1answer
273 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
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 ...
3
votes
3answers
27k 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 ...
1
vote
2answers
424 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 ...
0
votes
1answer
456 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
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
3answers
653 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 ...
14
votes
3answers
14k 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 ?
5
votes
1answer
411 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 ...
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 ...
