Joe Mack
  • Member for 1 year, 8 months
  • Last seen more than a month ago
  • Maryland, United States
Why Cramér spectral representation and not DTFT for stochastic process
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4 votes

I will introduce some terminology and intuition that will be helpful when reading other references. It will be neither complete nor completely rigorous. The measures that we first encounter in real ...

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Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?
4 votes

I think that considering the DFT from a linear algebraic point of view has some value, so I will attempt to introduce the foundations. We will assume that our signal is a vector of $N$ complex ...

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Question about eigendecomposition, signal subspace and their properties
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3 votes

My first swing at the answer had some very incorrect claims. I do not have access to the article, so I am inferring some things from the portion posted in the question. NOTA BENE: My arguments ...

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Relationship between input and output sequence in Hartley transformation
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3 votes

Wikipedia's entry for the discrete Hartley transform shows states that the $\mathsf{DHT}$ is, up to a scaling, its own inverse. If $x$ is a vector with $N$ entries and $y$ is its discrete Hartley ...

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Circular Convolution Formula Deduction from DFT
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3 votes

Let $x$ and $y$ be signals of $N$ samples each, numbered as $x(0),\ldots,x(N-1)$. Then their DFTs are $X$ and $Y$, which also have $N$ entries each: \begin{eqnarray} X(k) &=& \sum_{n=0}^{N-1}x(...

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Wiener Khinchin theorem : struggle in the derivation
2 votes

Let me state at the beginning that the details that make this rigorous do not bring any extra understanding of the statistical behavior of signals, so the desire to use the Dirac delta distribution is ...

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Finding the linear prediction coefficients for a sampled sinusoid
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2 votes

In the absence of more details, I assume that the phase $\Theta$ is a random variable and $\Theta$ is uniformly distributed on the interval $[0,2\pi]$, so that its probability density function is $\...

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Scipy.signal noise with rfft compared to fft
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2 votes

The DFT of a real sequence is complex-valued. The array output by scipy.fftpack.rfft consists of the real part of the 0th entry, followed by the imaginary part of the 0th entry, followed by the real ...

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In computed tomography (CT), why is 'Inverse Problem of Radon transform' studied?
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1 votes

Note that the original mathematical back-projection method assumes that the value of the Radon transform is known for all lines. This is an infinite amount of information, so it is pure mathematics at ...

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Identify whether to have unique output in this ARMA system
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1 votes

As I mentioned in my comment, I think there is a typographical error in the equation. I think it is supposed to be \begin{equation} y[k] = \sum_{i=1}^{M}a_iy[k-i] + \sum_{j=1}^{N}b_jx[k-j]. \end{...

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Steady state variance of a stochastic differential equation - relation between the frequency and time domains
1 votes

BOTTOM LINE UP FRONT: I think the exponential decay growth in $\left<|x(t)|^2\right>$ can be shown in the frequency domain only if the "boundary terms" are nonzero when we compute the ...

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Stationarity, discrete-translation operator, and the power spectral density matrix
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1 votes

Given the definition of the correlation matrix $\mathbf{R}_{\mathbf{x}}$ here, I am assuming that $\mathsf{E}[\mathbf{x}] = \mathbf{0}$. I do this because the correlation matrix is usually defined as $...

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Conceptually confused by LPC for speech: Do we synthesize by the inverse filter (FIR)?
1 votes

Given speech samples, the LPC computation yields linear prediction coefficients $a_1,\ldots,a_p$. These describe a dependence model for a few samples. It is assumed that for short-enough collections ...

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Optimal pulse shape for minimal interference in adjacent frequencies
1 votes

The root-raised-cosine pulse-shape is widely used because using the root-raised-cosine as both pulse shape and as matched filter yields the raised-cosine pulse-shape, and the root-raised-cosine and ...

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Cross correlation and cross power spectrum for signal + noise
1 votes

Previous answers have already discussed some of the mathematical issues that arise after the Fourier transforms in the question, so I will try to impart some more easily earned intuition. Even if we ...

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Downsampling, shifting, high pass and low pass filter commutativity
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0 votes

I am suspicious due to the claim that $\mathcal{R}_0$ is the inverse of $\mathcal{D}_0$. Decimation is not invertible. Once samples/entries are deleted, those values are forgotten. They cannot be ...

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