# Tag Info

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Important Information : Sampling at $f_{s}$ will map $[-\frac {f_{s}}{2}, \frac {f_{s}}{2}]$ to digital frequency $\omega=[-\pi, \pi]$, and similarly sampling at $2f_{s}$ will map $[-f_{s}, f_{s}]$ to digital frequency $\omega=[-\pi, \pi]$. Also, we need to look only at digital frequency $\omega = [-\pi, \pi]$ as the digital spectrum is a $2\pi$-periodic ...

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The ZF equalizer, $f[n]$, is a filter (I'm assuming a FIR filter) that tries to force, $f[n]*h[n]$, to be $\delta[n-d]$, where $d$ is the sample delay introduced by the filter (I choose $d=2$ below) and $h[n]$ is the channel impulse response. You can use this convolution equation to solve for the filter weights. I assume that both $f[n]$ and $h[n]$ are zero ...

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The fourier transform of the two dimensional autocorrelation function should do it.

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The noise of interest would ultimately be over the bandwidth of your signal and specifically all filtering done prior to ultimately making a decision over which symbol was transmitted- which would typically be the bandwidth of your matched filter. So given a noise density in $dBm/Hz$ you can translate that to the total noise in the signal to noise ratio of ...

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See "ePeriodicity: Mining Event Periodicity from Incomplete Observations" by Zhenhui Li, Jingjing Wang, and Jiawei Han (2013); preprint at https://faculty.ist.psu.edu/jessieli/Publications/tkde14.pdf

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Yes, you will need to make a 50Hz notch filter. I would suggest you to look at this post. If you tell what type of program you use (Python, R, etc) I could try to provide you some code aswell.

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I just don't think you're thinking this through all the way, and using the toolbox in MATLAB before you understand the basics. SNR is signal-to-noise ratio and is defined as $\text{SNR}=\frac{\text{Signal Power}}{\text{Noise Power}}$. When you call snr(signal, noise) in MATLAB, all it is doing is calculating the signal power, mean(abs(signal).^2), and the ...

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Below is a function which I wrote long back, when I needed to generate AWGN time-domain samples given Noise PSD in dBm/Hz. AWGN_NOISE() : Generates Additive White Gaussian Noise of PSD power in dBm/Hz AWGN has Gaussian PDF with 0 mean and $\sigma^{2} = N_{o}/2$ Noise Spectrum in $dBm/Hz = 10*log_{10}(BW*N_o/2)$, hence $\sigma$ = $\sqrt{No/2} = \sqrt{10^{... 3 Dirac delta function has a continuous argument, but Kronecker delta function has a discrete argument. Your example is a discrete signal so Kronecker delta is used. 0 Let us say you detected noise level power at -100dBm. You keep additional 10dB threshold to detect energy. Means if you detect >= -90dBm power, you try to detect preamble of Wifi packet. If you detect -95dBm power, you ignore it assuming it may not be a valid Wifi packet. This really works assuming you are very far from base station/access point(AP). Now ... 3 I assume you are working with discrete-time, since continuous-time white noise has infinite power ($\sigma^2$). First, remember that the power of a stationary process is always equal to the autocorrelation at 0 ($P_x = R_x[0]$); and the variance is the autocovariance at 0 ($\sigma^2_x = \rm{Cov}_x[0]\$). These 2 expressions are equal for processes with 0 ...

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