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 ...
Marcus Müller's user avatar
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 ...
orchi_d's user avatar
  • 567
3 votes
Accepted

Group delay equalization for second order IIR notch filter

Yes if you have access to Matlab's arbitrary magnitude and phase tool, that is certainly a good bet. Other approaches if you want to get more into the design details are: As an IIR solution, see the ...
Dan Boschen's user avatar
  • 50.2k
2 votes
Accepted

LTE PSS Channel Estimation for coarse SSS Equalization

Every 5 ms it is sent an OFDM Symbol which carries a PSS. So by using the block based channel estimation it might be possible to interpolate these PSS channel responses over time to get a $ h_{x_u}(f,...
AlexTP's user avatar
  • 6,585
2 votes
Accepted

ISI and RRC basic concepts

The understanding may require some further explanation or clarification: Sinc pulses and similar “Nyquist Pulses” do not eliminate ISI but allow us to constrain bandwidth in transmission without ...
Dan Boschen's user avatar
  • 50.2k
1 vote
Accepted

Decision Feedback Equalizer initialization

How do I choose the number of taps (feedback and feedforward) to use in the equalizer? Long enough to reflect the channels you need to equalize. So, if your sample rate is 100 MS/s, and your channel ...
Marcus Müller's user avatar
1 vote

Separating an audio file into "N" frequencies

You can use Scipy.signal https://docs.scipy.org/doc/scipy/reference/signal.html or, Pyfar https://pyfar.readthedocs.io/en/latest/readme.html or, Librosa
Filipe Pinto's user avatar
1 vote
Accepted

Equalization with FSK

The LMS equalizer would perform equally well for "non-linear" modulations such as FSK. This is because the modulation itself does not come into play. We are using a linear equalizer to ...
Dan Boschen's user avatar
  • 50.2k
1 vote
Accepted

Numerical Stability for Channel Estimation

The problem is given by: $$ \arg \min_{\boldsymbol{h}} \frac{1}{2} {\left\| \boldsymbol{X} \boldsymbol{h} - \boldsymbol{y} \right\|}_{2}^{2} $$ Where $ \boldsymbol{X} $ is the convolution matrix (...
Royi's user avatar
  • 19.5k
1 vote

LMS algorithm: Training and tracking phase

This implementation assumes timing has already been properly established (as given by $t_{k,l}$) and $\hat{c}_k$ is the decisions made at the proper sampling locations for the symbol decisions at one ...
Dan Boschen's user avatar
  • 50.2k
1 vote

Least Squares Solution Using the DFT vs Wiener-Hopf Equations

This is not a complete answer but a companion simulation to the other answers showing that the two approaches when used for a practical application are not identical as concluded in some of the other ...
Dan Boschen's user avatar
  • 50.2k
1 vote

Least Squares Solution Using the DFT vs Wiener-Hopf Equations

This is not so much an answer as some observations that may help. Using Dan's notation, let: $A = $ the convolution matrix of $x$ s.t. $Ah = x*h$ $A^H = $ Hermitian transpose (or "adjoint") ...
Gillespie's user avatar
  • 1,738
1 vote

Least Squares Solution Using the DFT vs Wiener-Hopf Equations

My assertion is as following: Given a model: $ \boldsymbol{y} = \boldsymbol{h} \circledast \boldsymbol{x} $ where $ \circledast $ is the periodic / circular convolution operation the following are ...
Royi's user avatar
  • 19.5k
1 vote

Should we use Maximal ratio combining and an equalizer together?

The MRC technique is applied in the case of flat fading channels. In mathematical terms, this means that the channel coefficient between the Tx antenna and each Rx antenna is a single complex number $...
QMC's user avatar
  • 784

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