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How to Calculate Frequency "X values" from a FFT/DFT Transformation

What you have heard about the sampling frequency/rate and the number of samples/data points is correct. When you take $n$ samples in the time-domain representation of the signal and "Fourier ...
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Does a .wav file created from a .mp3 file have better quality than the .mp3 file itself?

Changing an MP3 to wave file does not effect the content of the file If you wish to remaster or adjust the file content then changing the file to wave will give results Such as: changing to a wave ...
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calculate the normalized angular frequencies

The normalized angular frequency for $x_1[n]$ is $2\pi3.5/64$. $n$ is the sampling index so would not be included in the angular frequency. The units of normalized angular frequency are radians/sample,...
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How does one interpret an element of the "transfer matrix" used to calculate frequency domain granger causality (via VAR models)?

If you take the Fourier Transform of your AR equation, you get $$\begin{align} Y(f) &= \sum_{k=1}^p A(k)e^{-j2\pi f k} Y(f) + U(f)\\ \left(I - \sum_{k=1}^p A(k)e^{-j2\pi f k}\right) Y(f) &= U(...
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Autocorrelation and the dot product of complex signals

The autocorrelation value at zero lag is a positive real number regardless of whether the sequence is real-valued or complex-valued, except in the trivial case of the sequence being the all-zeroes ...
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Why would the emitted signal from repeating binary data over a wire appear at a frequency lower than the bit frequency?

The highest possible fundamental frequency to be emitted is when we send the binary pattern 10101010…. Note that we send each bit at the data rate but the repetition of the pattern will be half the ...
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Why would the emitted signal from repeating binary data over a wire appear at a frequency lower than the bit frequency?

If you send the same pattern again and again, you have a periodic signal which has a line spectrum and the fundamental frequency is the inverse of the time period. If you send a random bit pattern at ...
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