# Questions tagged [signal-processing]

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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### Change of variables on a double summation to yield a single sum

I'm going through a proof in Monson's Statistical Digital Signal Processing and Modelling on page 98. They used the substitution $k=n-m$ in order to change the double summation into a single summation....
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### Where is the sinc function zero? [closed]

Like in the question, where the $\text{sinc}(x)=0$? Thank you so much.
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### Why doesn't my expression for the fourier transform of a function match its numerical fourier transform?

I am seeing a frustrating discrepancy between my evaluation of $F(\omega) = \frac{1}{a + iw}$, and the fast fourier transform of $f(t) = e^{-at}u(t)$ (where $u(t)$ is the step function from 0 to 1) ...
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### Calculating convolution of two piecewise functions

Let $$x(t) =\begin{cases}2&-2\lt t \lt 0 \\ -2 &0\lt t \lt 1\\ 0& \text{otherwise}\end{cases}$$ and $$h(t) =\begin{cases}4(1-|t|)&|t|\le1 \\0& \text{otherwise}\end{cases}$$ ...
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### Property of real-valued Fourier transformation

When it is given that a signal $x(t)$ has a real-valued Fourier transformation $X(f)$ then is the signal necessarily real-valued? I have thought the following: We have that the real and imaginary ...
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### Meaning of “generalization”? in math

What is the meaning of word "generalization"? Please kindly explain in simple words For example in wikipedia article of interpolation, in sub heading "polynomial interpolation " a line is written ...
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### Filtering time series

I'm filtering the highest frequencies off of a time series signal, but something strange happens. What I am expecting is a trigonometric curve fitting the time series without taking into account all ...
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### Calculatee impulse response for given system

i am given an exercise in which i need to find the impulse response for this given system: y[n] + 2y[n-1] = x[n] + 2x[n-3] This is the only information i have. ...
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### Estimating a cost of a graph smoothness

For a given video scene, I have a task to evaluate a score for its stability. I have managed calculate their deltaX and deltaY ...
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### Going from a Discrete time signal to a continue time signal given a sampling rate.

I am given a DT signal x[n] = sin((pi/100)*n^1.5) for n is an integer [0,1499] and a sampling rate Fs = 1000Hz. How can I obtain the original continue time signal which was sampled @ 1000 Hz to obtain ...
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### Evaluating $\sum_{k=1}^{\infty}\left(\frac{\sin(tk)}{k}\right)^2$

Using Poisson Summation Formula, how do you evaluate the following infinite sum $\sum_{k=1}^{\infty}\left(\frac{\sin(tk)}{k}\right)^2$? The Poisson Summation Formula states that: \$\sum_{k=-\infty}^{\...
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### Can properties for (circular symmetric) complex random matrices automatically work for real random matrices?

I am dealing with a theorem which relates to circularly symmetric complex Gaussian random matrices (CSGRM). It seems quite tempting to assume that the theorem also extends to real-valued Gaussian ...
I have been presented with the following question: Perform the discrete-time Fourier transform (DTFT) on $$x[n] = 5\cdot\!0.25^n \cdot\cos \left(\frac{2\pi}{3}n \right)\cdot u[n]$$ My workings ...