# 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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### Mathematical backing for observations seen in adding independent random variables together

I have a function $Y = F(N)$ that takes as an argument an integer number $N$ and returns a summation of $N$ sine-waves of different random parameters. I have plotted the results of two function calls ...
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### Signal processing linear invariant causal systems

What is the frequency response of the linear invariant causal systems? I know that the response of linear invariant causal systems is g(k)=0 for k<0 but how about the frequency response?
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### Fourier series for a Sinusoid in a conventional way?

So my TA in class introduced this amazing way of finding fourier series coefficients for a sin wave, by writing $sin( \omega t ) = (e^{i\omega t}-e^{-i\omega t}) / 2i$ ----(1) Hence getting the ...
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### How should I calculate a rolling autocorrelation?

I have an array of data $\mathbf{y} \in \mathbb{R}^n$, and I need to calculate the lag-1 autocorrelation between sections of this array 7 elements long. For all intents and purposes, we can imagine ...
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### confused with the FFT output

I am taking some sensor output and doing fft on it. how to get the exact frequencies from the complex output? my understanding is that bin frequencies and the input frequencies are different. Please ...
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### averaging of multiple curves for signal processing

I have response (vibration amplitude over frequency steps) measured over various point on my structure. In simpler way: i have 5 response curves(amplitude vs frequency plot) from same structure is ...
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### Find $a$, given $y(n)=x(n)+ax(n-d)$, interesting question

Me and two friends of mine are working on a project (scholarly purposes only). The goal of this project is to clean an audio signal (speech, a song, anything audio) of echo. Generally speaking, if ...
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### Express the sum of squares as a percentage of how well two signals match?

So I am using matlab to compare two signals using the sum of squares. So the best possible match will be zero. eg $\sum(y_2 - y_1)$ where $y_2 = y_1$ would be $0$. The larger the sum of squared value ...
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### deconvolution of exp($x^2$)

I would like to know whether we can get the function of type exp($x^2$) by convoluting any functions. That is which function convolution gives exp($x^2$). Thanks in advance
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### Kolmogorov-Zurbenko filter - Calculation of coefficients

I'm currently researching the Kolmogorov-Zurbenko filter and trying to implement it myself as a way to smooth one-dimensional signal strength values. The basic filter per se is pretty easy to ...
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### Compressive sensing for complex matrix

I'm fairly new to compressive sensing, and I have been looking for a MATLAB implementation of the problem $$A x = b$$ where $A$ is non square, $x$ is kind of sparse and all the numbers involved are ...
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### How to analyse data samples scattered in time?

I want to analyse data corresponding to events happening at arbitrary moments in time, and conveying quantitative information. My goal is to study the relationship between the sum of these quantities ...
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### How to derive FWHM of sinc function

So this is probably a simple question, but I am unable to get my head around it. If we have $\operatorname{sinc}(2 \pi v L)$, what is the width of that $\operatorname{sinc}$ in terms of $v$ at half ...
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### Rate of convergence of a Weyl-Heisenberg (Gabor) frame expansion

If $\{g_{m,n}\}$ is a Gabor frame for $L^2(R)$, with window function $g$, and $f \in L^2(R)$, is there a bound on the approximation error of $f$ using a finite subset of the frame? That is, is ...
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### Why exponential is ignored in particular solution for impulse response ??

For a system govern by the equation: $$2y'(t) +4y(t) =3x(t)$$ To calculate it's impulse response we replace $y(t)$ with $h(t)$ and $x(t)$ with $\delta(t)$ and get $2h'(t)+4h(t)=3\delta(t)$ which's ...
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### Nonparametric changepoint detection for point process

This is a replication of a question I've recently asked on Cross Validated. It hasn't received an answer or much attention, so I've posted it here. I have a family of point processes representing ...
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### Convolution of various functions

There is asked in an example to do convolution $h_1(t)*h_2(t) + h_3(t)*h_4(t)$ where $h_1(t) = e^{-2t}u(t)$ $h_2(t) = 2e^{-t}u(t)$ $h_3(t) = e^{-3t}u(t)$ $h_4(t) = 4\delta(t)$ and then the ...