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The OP clarified in comments that his real question/concern is with the transient response of the reflections that occur in a 1/4 wavelength transformer. In any typical application given the relativel …

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 " …

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 intro …

They are the common choice for time domain equalization for frequency selective channels with deep frequency nulls. …

For "blind" equalization using this approach, I would use receiver decisions to recreate the expected transmitted signal (including any pulse shaping etc). …

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 …

Showing both cases to show that the approach handles both cases without aliasing issues: First for a real result after equalization: f1 = 800 f2 = 1500 N = 5000 mask = np.zeros(N) mask[f1:f2+1] = 1 mask …

If an RRC is used in the filter, and then an RRC in the receiver would be the "matched filter" (although other filtering/ equalization for channel distortions which also cause ISI may be needed). …

$\hat{c}_k$ are the decisions which are used to keep the equalizer converged during "Tracking" mode, and can also be used for Decision-Directed approaches for blind equalization when sufficient SNR allows … In this case the hard limit decisions on the real and imaginary portions of the signal map to what the desired output would be if the equalization was 100% effective (resulting in zero error $\hat{e}(k …

This appears to be a homework problem so I will avoid providing the complete solution here, but the following should suggest a path toward a solution: Typically this problem is done when the channel i …

The entire waveform in time will be delayed by the group delay of your frequency domain equalization, which may not necessarily match the group delay of the channel distortion. … If you applied no equalization (by multiplying in frequency by your frequency domain equalization); the IFFT would recover your time domain waveform in its original form with the noise and channel distortion …

In this case the equalization as a single filter is rather straightforward- we can treat the speaker as a black-box single system and drive the equalization based on the response as measured characterized …

The way it is drawn suggests that $\hat{c}[k]$ samples are the complex decisions for the demodulated symbols. This assumes correct timing to only use the samples for demodulation. Instead, assuming a …

The pulse shaping is only required if you are concerned with spectral efficiency, as the pulse shaping will convert what would otherwise be a Sinc function in frequency to a spectrum that is much clos …

The training sequence should be at the same spacing as the equalizer when considering its sampling at the input to the equalizer. Adaptive algorithms converge to the least square solution based on the …