# Tagged Questions

Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

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### When studying 2D gabor functions why is a gaussian called elliptical?

Consider $$G(x,y)=\frac{1}{2\pi\sigma\beta}e^{-\pi\left[\frac{(x-x_0)^2}{\sigma^2}+\frac{(y-y_0)^2}{\beta^2}\right]}e^{i[\xi_0x+\nu_0y]}.$$ This is the product of a complex plane wave and what this ...
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### Specific question about downsampling in frequency domain

I'm confused about why Equation 4.74 can be expressed as Equation 4.76 after the summation index is expressed as in Equation 4.75. Could somebody please explain? Thanks! Downsampling DTFT
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### Signal processing and algebraic geometry

Signal processing is a pretty huge branch of what I would (maybe wrongly) call electrical engineering. I have heard here and there whispers of interesting connections between signal processing - in ...
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### How to sketch frequency response obtained from H(z)?

How to sketch frequency response obtained from H(z)? I'm adding an example and its solution below. I did not understand some of the things for question 7.4, part D. Any help is appreciated! There ...
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### Convolution Problem

while working on a signal processing problem i've reached to the following: So my aproach was: Am I doing something wrong? Is it valid Y(f)=[X(f) x H(f)]*W(f)=X(f) x [H(f)*W(f)] If you could ...
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### Fast evaluation of an integral convolution with an “expanding kernel”

Suppose I have a 1-D integral convolution transform like this: $$g(x) = \int_{-\infty}^{+\infty} dy\, f(y)\, K(x-y). \qquad (1)$$ Say the kernel $K(x)$ is a known analytic function, and say we have ...
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### Find the inverse z transform of $H(z)=\frac{1}{8-6z^{-1}+z^{-2}}$

This question was on a homework assignment, and the solutions have been distributed but I'm having trouble reproducing the solutions. Given the initial conditions $y[-1]=y[-2]=0$ and the difference ...
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### The set of inputs x(n) to a system is described with a small superscript T - what is that?

I think it means TRANSPOSE, but I can't figure out the need to perform a transpose operation: Similarly, the set of weights that go with the inputs is written with a small T as well: There is ...
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### Graph of the Angle of a Fourier Transform

If I need to graph the magnitude and angle of a discrete Fourier transform which happens to be $X(e^{j\omega}) = 4\cos(4\omega)$, I know how to graph the magnitude, but how do you graph the angle? I ...
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### A signal on a noisy channel is input to a filter

Question: A Wide-sense stationary (weakly stationary, (WSS)) random signal {X(t)}t∈R with Power spectral density(PSD) S_X(ω) is transmitted on a noisy channel where it is disturbed by an additive ...
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### How to find period of a sum of periodic functions

I got this function: $$x[n]=\sin(2*\pi*4/3*n) + \cos(2*\pi*5/2*n)$$ It is easy to see that period of the sin is 3/4 and the ...
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### Why does cross-correlation involve the complex conjugate?

The cross-correlation of continuous $f,g$ is: $(f \star g)(\tau)=\int_{-\infty}^{\infty}f^*(t)g(t+\tau)dt$ where * is the complex conjugate. Why is there the complex conjugate?
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### Complex filter factorizations

There is a famous low pass filter $[1,2,1]$ in signal processing which can be factored in the sense of a convolution product over the real numbers : $[1,1] * [1,1]$. This is the only way to do it over ...
Let $f : \mathbb{R}^+ \rightarrow \mathbb{R}$ be a continuous function. Do you have some references (books or online resource) about techniques that allow to predict $f(x_{n+1})$, knowing \$f(x_0), .....