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5

Formulation of the Problem I am solving the problem under the following assumptions: The blurring operator is Linear and Spatially Invariant (Hence applied by convolution). The blurring operator is known. There is a measurement noise. So the model is: $$\boldsymbol{y} = H \boldsymbol{x} + \boldsymbol{n}$$ Where $H$ is the matrix form of the blurring ...

4

Formulation of the Denoising Problem The problem is given by: $$\arg \min_{x} \frac{1}{2} {\left\| x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right) = \arg \min_{x} \frac{1}{2} {\left\| x - y \right\|}_{2}^{2} + \lambda {\left\| D x \right\|}_{1}$$ Where $D$ is the column stacked derivative operator. In the above I used the Anisotropic ...

3

I suspect the OP is referring to a frequency offset and not a static time offset. If the 1ppm is a frequency offset of the clock frequency and not a static time offset, this could be introduced with an numerically controlled oscillator (so in Matlab this is simply multiplying the datapath signal by $e^{j\Delta f t}$). If that clock is a reference to other ...

3

I wonder why the negative part and positive part of X axis is not symmetrical? The data is symmetrical. The problem is that you have an odd FFT length and hence your frequency grid does NOT include the Nyquist frequency and you construct the frequency vector incorrectly. It should be f1 = -(Fs/2-dF/2):dF:(Fs/2-dF/2);

2

I have done a bit of this myself and you'd need to adapt. There is a Douglas Rachford self implemented and a primal dual approach here implemented in Recovery of Fusion Frame Structured Signal via Compressed Sensing. Note that Clarice Poon (Bath University) had some nice tutorials on it. Another source is the Numerical Tours from Gabriel Peyre. See Denoising ...

2

This happens because when lowpass filtering, you remove the high-frequency content that gives the square pulses their sharp edges. Now, if you're not yet versed in Fourier analysis of signals this will be a bit tough, but I'll provide some graphs to show what I mean. Let's take a simple pulse and a sinusoid like the ones you have. We're going to filter them ...

2

Remark: This is adapted from How to Solve Image Deblurring with Total Variation Prior Using ADMM? Formulation of the Problem I am solving the problem under the following assumptions: The blurring operator is Linear and Spatially Invariant (Hence applied by convolution). The blurring operator is known. There is a measurement noise. So the model is:  \...

1

% create complex white normal noise noise = randn(size(Signal)) + 1i*randn(size(Signal)); % calculate the gain for the noise noiseGain = rms(Signal)./rms(noise)*exp(-SNR(i)*log10/20); % add it SignalN = Signal + noiseGain*noise;

1

If your error vector magnitude is below the decision threshold between adjacent symbols then there would be no impact on the BER. Thus there will be a point where you can continue to reduce the error vector while not see a change in BER. Ultimately our objective is to minimize the error vector regardless, to maximize performance in lower SNR conditions. Also ...

1

Your signal is 8 samples per symbol. After reviewing your eye diagram it also appears that the signal is only root-raised cosine filtered. It should go through one more root raised cosine filter before final decision (the matched filter in the receiver) for optimum performance in the presence of noise.

1

I´m not sure if this really applies to your problem since it may be another issue, but I can tell from my experience with acoustic impulse response measurements (only there you want to estimate the response from the input signal, but the deconvolution should be the same): In case your transfer function E is somehow bandlimited and has zero (or very low) ...

1

Are the plots correct? Mostly. Two things to consider: since your input signal is real (as it not complex), the spectrum is conjugate symmetric. So typically you would only plot the first half from 0Hz to 500Hz. If you want to plot the whole thing, it's better to circulate it and plot it from -500Hz to +500Hz. In most cases you would also use a logarithmic ...

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You have two signals of length $N = 220500$ and $L = 8821$ samples long, and you want to obtain their convolution $y[n]$ of length $K = N + L-1 = 229320$ samples long, by using a frequency-domain DFT//FFT method... Then you have to compute $K = N + L -1 = 229320$ sample long FFTs of both signals $x[n]$ and $h[n]$, and then multiply them, and then invert ...

1

You're looking for cluster detection. In your case, it's very basic: there's no more than one dimension along which to detect clusters. It's probably overkill, but 1-dimensional k-means is probably what you want. Matlab has good documentation on k-means. (Also, seriously, all this is wikipedia or textbook knowledge, there's very many free resources. You very ...

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I am not sure why the first 3 coefficients in python are always different than that of MATLAB. It's just a scaling. If you call Matlab's zp2sos without the second output argument, you will get the same three values as Python. If you need Python to match Matlab, use the first value of the sos as your "k" and divide the first three values in the sos ...

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