8
votes
do digital equalizers use Fourier transforms?
Fourier transform technology
Well, Fourier theory is behind every kind of equalizer. We wouldn't know what "equal" means without; the Fourier transform is how we know how to describe a ...
- 29.6k
6
votes
Accepted
Why are equalizers moving average model (FIR)
The reason why almost all linear adaptive equalizers are implemented as FIR filters is that FIR filters are always stable and that there exist relatively simple and effective adaptation algorithms. ...
- 88.9k
5
votes
Accepted
Given an FIR filter coefficients, how can I find coefficients of its equalizer filter?
Assuming that you also want to equalize the filter's phase response (not only its magnitude response), you need an equalizer with a transfer function $E(z)$ that is the inverse of the FIR filter's ...
- 88.9k
5
votes
Accepted
OFDM time vs. frequency domain channel estimation/equalization
Traditionally, OFDM became popular in WiFi and LTE because the channel model consisted of multi-path. That is, the radio signal transmitted in 1-6GHz frequencies bounced from various obstacles (walls, ...
- 2,213
5
votes
Group delay compensation for non coincident drivers
For the first question, given the linear process, what you do to the sum with regards to filtering is equivalent to what you do to each and then sum.
For the second question, the dip is in the ...
- 48.9k
5
votes
Why do inverted impulse responses sound awful when applied to an audio system?
For simplicity we assume that the room and the source are fixed.
A room's impulse response depends on a LOT of different factors which include the exact position, directivity and orientation of the ...
- 42.6k
5
votes
Least Squares Solution Using the DFT vs Wiener-Hopf Equations
Following Royi's derivation, we want to show that,
$$\begin{align} \hat{h} = \arg \min_h||Xh - y||^2 = (X^T X)^{-1} X^H y = IDFT(Y \oslash X) \end{align}$$
where $X$ is a circular convolution matrix ...
- 537
4
votes
Accepted
Design of equalizer for wireless communication
Ok, there is some misconceptions in your question. I strongly recommend you to read a little more about the topics, but I will try to help you a little. My answers and some comments:
...linear ...
- 677
4
votes
Accepted
Matlab: What should be the BER performance for BPSK using Constant Modulus Algorithm equalizer
Well, I took a look at your code, and spent a lot of time on it, and I have discovered some mistakes, some practicals and some theoretics. Here are my answers:
(1) You can use the function filter. ...
- 677
4
votes
Accepted
What is the difference between an equalizer and a channel estimator?
In communication systems, transmitted signals are distorted by the physical medium (the channel) charactheristics.
The channel estimator tries to identify the transmission channel characteristics, by ...
- 28k
4
votes
Group delay compensation for non coincident drivers
I'm not sure whether this is a purely academic exercise or supposed to do something useful in the real world. Assuming it's the later, there are a few additional points to consider
Typically when ...
- 42.6k
3
votes
CMA Equaliser and FSK
The confusion comes from the fact that what is tagged as "transmitted" isn't the real transmitted waveform but its baseband representation, which are $\left\{+1,-1\right\}$ symbols in 1 dimension. For ...
- 1,792
3
votes
Why do the OFDM training (and payload) symbols have silent sub-carriers (aka virtual carriers)?
From the first to the sixth OFDM-Symbol you have spread virtual carriers equally across [0,..,51] with a distance of 3. With this way you have spread your 'energy' loss over a wide spectrum. In ...
- 31
3
votes
Accepted
Histogram Equalization
Assuming that in your question $T(r)$ denotes a map $:\mathbb{R}\to[0,1]$ and assuming that it is continuous and strictly increasing, then it is obviously an isomorphism among $r\in[0,1]$ onto its ...
- 768
3
votes
Remove a frequency and all its multiple (harmonics)
The choice of algorithm depends on your application scenario - i.e. there is no best solution per se. If your focus is on minimum computational requirements, a comb filter will probably be optimum. If ...
- 647
3
votes
Accepted
What is the difference between pulse shaping and equalizers when used to cancel Inter-symbol Interference (ISI)?
1.
This is a question investigated by many researchers decades ago. They discovered that the bandwidth limitation of R/2 Hz is not a fundamental limit set by nature. It is just a criterion if we don't ...
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3
votes
Accepted
how to set Equalizer's coefficient using generalized eigenvector.
The generalized eigenvalue problem is given by
$$Bw=\lambda Cw\tag{1}$$
where $\lambda$ is the generalized eigenvalue of the matrices $B$ and $C$. Multiplying $(1)$ from the left with $w^H$ (with $^...
- 88.9k
3
votes
Accepted
Adaptive equalization vs inverse of transfer function
Inverting a channel can only be done when the channel is a minimum phase system (trailing echos only). A minimum phase system is characterized as having all zeros in the left half plane (for the s ...
- 48.9k
3
votes
Accepted
The use of LS estimation with Vector OFDM
Sorry for late reply .. I was little bit busy.
you have mistakes in your code. Although mythology is right, you have mistakes in some parameters.
Check this paper "Low-Complexity Equalization of ...
- 1,056
3
votes
Accepted
Distortion of OFDM signal when using RRC filter
I checked your code in my PC, you need just to delete the delay added before the filter. For example, you can use:
U_aft_fil = U_aft_fil(fil_delay+1:end);
Then ...
- 1,056
3
votes
Why construct a minimum phase filter from measurements?
Room Equalization for listening purposes is NOT the same as equalization for, say, acoustic echo cancellation or data transmission purposes.
Inverting the measured impulse response or transfer ...
- 42.6k
3
votes
Why do inverted impulse responses sound awful when applied to an audio system?
One thing that I remember from a Brüel & Kjær application note from the 1980s or 90s is that for a room impulse response, you wanna separate the frequency response (and therefore the impulse ...
- 20.1k
2
votes
Why are equalizers moving average model (FIR)
Most of the books/articles on adaptive filters use the squared error as the optimization criterion. For FIR filters, the solution for the filter coefficients can be found using traditional least ...
- 2,841
2
votes
Fractional spaced equalizer + timing (clock) recovery
The answer is to NOT down-select to one sample per symbol until after using the Gardner Timing recovery since the TED requires 2 samples per symbol. If the equalizer is running at 2 samples per symbol,...
- 48.9k
2
votes
Accepted
MP3 equalization
The usual approach to achieve your goal would indeed consist in decoding the MP3 file to a series of uncompressed time-domain samples and then filtering this PCM signal. As you are building a player, ...
- 647
2
votes
Equalizing frequency response in software
Whilst I am not well versed in Scipy, or how the firwin2 function works that you have quoted, this is a very complicated problem that you propose, and there is a lot more to think about than you may ...
- 53
2
votes
Accepted
How to equalize an ISI channel when the transmitted symbols are unknown?
The classic approach is to include a "training sequence" along with the data. The training sequence is known to both transmitter and receiver, so it can play the role of $\mathbf{x}$ in your question.
...
- 14.9k
2
votes
What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?
All three are Estimators / Predictors.
All of them try to estimate the coefficients of Linear Filter which minimizes an MMSE Cost Function.
The Wiener filter assumes all data is given and sets the ...
- 19.3k
2
votes
Accepted
Constant modulus algorithm - performance poor?
The constant modulus algorithm does not work for QAM because the amplitude of QAM at the symbol decisions is not constant (therefore not a constant modulus signal), such as BPSK and QPSK.
SIR is the &...
- 48.9k
2
votes
Accepted
spectral factorization method
The question is not so clear. I am not sure what other types of examples you consider. In this particular case, if you didn't get the hint notice that:
$$\begin{align}
c(1+\alpha D)(1+\alpha D^{-1}) &...
- 4,225
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