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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Optimal estimation of the fusion of two measurements

Suppose I have a sensor measuring a quantity $\text R$. For example the sensor could be a radar estimating the range of a target. We can write: $$R(t)=r(t)+\nu_0(t)$$ where $r(t)$ is the real range ...
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How to solve a difference equation with an input?

How do you solve the difference equation (initial conditions are given) $$y(k)+ay(k-1)+by(k-2)=cx(k-1)+dx(k-2)$$ where the input $x(k)=\theta(k)$ (the unit step function). I know that the general ...
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Solving traveling wave usin the shooting method

The spatially-dependent Hodgkin-Huxley equation for a cylindrical dendrite or unmyelinated axon: where $\frac{a}{2\rho}\frac{\partial^2V}{\partial x^2}$ is a diffusion term $a$ is the fiber radius, ...
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Fourier series: can a function be odd and have a dc component?

Long story short: fourier series is taken in two subjects (for now). One doc says that the dc component is 0 if the function is odd. The other says that odd and even has no effect on the dc ...
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Using Linear Kalman Filters with a Nonlinear System?

Can you answer these questions I have about using linear Kalman filters and extended Kalman filters with a nonlinear system? 1. Does using a linear Kalman filter mean that I must have a time-...
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What is Z-tranform of signum function?

If Z-transform of x(k) is X(z), then what will be the Z-transform of sign(x(k))? Furthermore, what will be the Z transform of sign(x(k-1))?
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Autocorrelation of heaviside functions

I'm trying to find the expression that describes the auto-correlation $r_{xx}(\tau)$ of two heaviside functions $u(t)$. I was told that the result must be $1/2$, which makes total sense, as the power ...
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Instant frequency of sine sweep function?

Firstly, I'm not a mathematician, I'm an engineer, so you can freely make fun of the question. I have the following counter-intuitive behaviour in a sweep function. I have a sweep sine function (...
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Power of a signature (sum of squares divided by number of elements)

I need to find some literature to study the theory of an exercise I am working on (it is from a course in digital image processing and pattern recognition). I have an $n\times n$ matrix, I have to ...
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spectral density of Guassian random matrix

I am interested in the spectral properties of Gaussian random matrix. I can see the constant dominance (mostly by the two most extreme ones-largest and smallest-) of the extreme eigenvalues in the ...
Smooth sawtooth wave $y(x)=\cos(x-\cos(x-\cos(x-\dots)))$
Consider an infinite recursive function $$y(x)=\cos(x-\cos(x-\cos(x-\dots)))$$ $$y=\cos(x-y)$$ Plotting the function $y(x)$ implicitly we get a smooth sawtooth-like wave: Was this function ...