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LTI system with sinc input and unit impulse output?

I have a few "conceptual" questions given to me in preparation for a signals and systems exam, and I can't seem to grasp this one. Does there exist a linear time-invariant (LTI) system S such that: ...
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17 views

Computing Hilbert transform and envelope of a function

The following is a function with $\alpha$ being a real constant $$f(t) = \frac{\sin(\alpha t)}{\alpha t}.$$ Determine the analytic signal $f_a (t),$ Hilbert transform $\hat{f}(t),$ and the envelope ...
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2answers
28 views

Understanding Fourier Transforms

I'm trying to understand Fourier Transforms, so I thought I'd try to explain the following in an english sentence, but I can't. If I bury myself in equations, I can trick myself into understanding ...
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0answers
32 views

Geometric explanation of a methodology in the article about Image Denoising

In article Ghimpeteanu G., et al. - A Decomposition Framework for Image Denoising Algorithms, I found as below: Let $\displaystyle I : \Omega \subset R^2\mapsto R$ be a gray-level image, and $(x, ...
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1answer
988 views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
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2answers
372 views

Encoding a Discrete Signal to an Artificial Neural Network?

What might be some potential methods to encode a 100-point signal (curve) for input to a Artificial Neural Network? Example: we have a large number of 100-pt 'curves' ranging from flat-line to ...
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1answer
104 views

Estimating the input to a system from a system state

[ Cross-posted to: http://dsp.stackexchange.com/questions/3098/estimating-the-input-to-a-system-from-a-system-state-using-ekf ] I have a system for which I have obtained a non-linear time-varying ...
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1answer
243 views

How to derive the process noise co-variance matrix Q in this Kalman Filter example?

How to understand the process co-variance matrix Q in the example below ( I extracted it from Wikipedia http://en.wikipedia.org/wiki/Kalman_filter ) Consider a truck on perfectly frictionless, ...
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26 views

Is there a standard way for modeling a Kalman filter where the measurements are obtained from differences?

Consider for simplicity a Kalman filter applied to the one-dimensional state space model $x_{n}=f_{n}x_{n-1}+q_{n}$ $y_{n}=h_{n}x_{n}+r_{n}$ with white noise errors. Assume that $r_n=e_n-e_{n-1}$ ...
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0answers
81 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} ...
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1answer
394 views

Convolution: $ f (-)*g = g(-)* f$ does this mean both $f$ and $g$ have to be even functions?

Assuming $f$ and $g$ are different functions, does $ f (-)*g = g(-)* f$ mean both $f$ and $g$ have to be even functions? In fact, this is equivalent to $f\star g = g \star f$ (i.e., cross-correlation ...
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0answers
184 views

What is the Difference between Various Kalman Filters?

What is the difference between additive and multiplicative kalman filters, as well as some other kinds? I'm also looking for reference texts and articles that describe the algorithms, so ...
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2answers
228 views

Applying a Kalman filter to a WiFi power signal

I have created an app that uses the power of a WiFi signal to determine distance to the WiFi access point. Problem with that power reading is that it is not very stable. I have been looking into ...
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1answer
56 views

Differences of distributions inside Kalman filter.

I am studying the Kalman filter algorithm but i can't understand one point. The k factor has to be chosen in order to minimize the variance of the signal. This lead to following equation: ...
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0answers
210 views

How to solve the recursive relation in Kalman filter?

I was wondering how to solve the Kalman filter's recursive equation (also see the appendix at the end of this post) for the estimated state $\hat{\textbf{x}}_{n|n}$ at time $n$, over discrete times ...
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3answers
800 views

Sensor fusioning in Kalman filter

I'm interested, how is the dual input in a sensor fusioning setup in a Kalman filter modeled? Say for instance that you have an accelerometer and a gyro and want to present the "horizon level", like ...
3
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1answer
445 views

Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car. In a Kalman filter the matrix ...
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1answer
136 views

Continuous Hidden Markov Modeling

I am writing a speaker recognition program in Matlab using Mel Frequency Cepstral Coefficients, and although I have gotten the problem to work using discrete time wrapping, I was interested in try to ...
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0answers
10 views

Learning point spread function image processing

Given a set of images, that are blurred by Gaussian point spread function, how can I learn the parameters of the PSF, i.e. standard deviation of the Gaussian kernel. One way that I can think of is to ...
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0answers
17 views

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 ...
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1answer
12 views

Converting from complex to sinusoidal form and vise versa [on hold]

I'm having some trouble understanding this type of transformation. The materials provided by my professor doesn't even mention the method that is being used to switch from complex to sinusoidal and ...
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0answers
25 views

Hilbert transform analytic signal frequency range

For the real signal $f(t),$ show that if it is band-limited to the range $$\nu_0 - \frac{1}{2} \alpha \leq \nu \leq \nu_0 + \frac{1}{2} \alpha$$ (where $\nu_0 >\frac{1}{2} \alpha >0$), then the ...
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0answers
15 views

Significance of the complex conjugation symmetry of the DFT for real-valued input

For real-valued input $\mathbf{x} = (x_0, ..., x_{N-1})$ and its discrete Fourier transform (DFT) $\mathbf{X} = \mathcal{F}(\mathbf{x})$ we have that $$X_{N-k} = X_k^*$$ where * denotes complex ...
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2answers
25 views

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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1answer
17 views

How can I analyse signal with discrete wavelet transform?

With CWT it's clear enough. We have function of two variables which are scale and translation. But what about DWT? Here is Matlab code: ...
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1answer
824 views

Plotting discrete time signals involving sumations in matlab.

Many of the examples I've encountered while looking for an answer are simple functions that do not involve summations. Suppose I have the following function; ...
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0answers
24 views

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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0answers
6 views

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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2answers
18 views

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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1answer
18 views

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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0answers
18 views

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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Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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1answer
23 views

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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2answers
31 views

Find an function that oscillates between a given upper and lower envelope

Suppose I'm given two real, continuous functions $f(x)$ and $g(x)$ such that $f(x)\ge g(x)$ for all real $x$. I'd like to determine an oscillating function $h(x)$ that has $f(x)$ as its upper-envelope ...
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0answers
22 views

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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0answers
32 views

Estimating a sparse vector: Mean squared error when support known

I was reading this paper ("How well can we estimate a sparse vector?" by Candès and Davenport, link: http://arxiv.org/pdf/1104.5246v5.pdf). They consider the problem of estimating a $k$-sparse vector ...
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1answer
391 views

Find convolution of u[n]-u[n-2] and u[n]-u[n-2]

Question: Find convolution of $u[n]-u[n-2]$ and $u[n]-u[n-2]$ I have found that $u[n]\cdot u[n]=n$, $u[n]\cdot u[n-2]=n-2$, $u[n-2]\cdot u[n-2]=n-4$ Use linear property, my answer is: ...
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1answer
23 views

Help in understanding a coding technique based on inverse mapping of a dynamical system

Based on paper titled : Simultaneous Arithmetic Coding and Encryption Using Chaotic Maps by Kwok-Wo Wong et. al The Authors use a non-linear dynamical system for generating keys to be used in ...
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1answer
29 views

CTFS: What happened in this integral?

Specifically, what happened in the last line to obtain the answer? It seems like they ignored the exponential term $e^{-jw_{o}kt}$?
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2answers
3k views

Finding the period of complex exponential function

I am having some trouble finding the period of the following discrete signal: $x[n]=e^{jn2\pi/3}+e^{jn3\pi/4}$
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1answer
24 views

Signal whose Laplace transform contains derived Dirac-deltas: How do I find the inverse transform?

I must reconstruct the input signal to a system, knowing the output signal and the system transfer function. At the end, I found that the Laplace-Transform of the input signal is something like: $$ ...
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2answers
37 views

$\cos(2\pi f nT +2\pi N_n) =\ cos(2\pi f nT)$ and more, why?

I am studying signals and systems and this came up? Could someone explain why is $\cos(2\pi f nT +2\pi N_n)$ equal to $\ cos(2\pi f nT)$? The book says: "because $N_n$ is an integer" I am ...
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0answers
134 views

Scale invariance and $1/f^2$ power spectrum

In the paper Occlusion Models for Natural Images : A Statistical Study of a Scale-Invariant Dead Leaves Model; Lee, A. B. Mumford, D. B. Huang, J.; International Journal of Computer Vision I read ...
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1answer
446 views

Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
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2answers
36 views

Prove Differentiator is Linear and Time-Invariant

The differentiator gives an output equal to the derivative of its input. Show that the differentiator is a linear time invariant system. Consider the input $f(t)=\sin(t^2).$ Attempt For ...
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1answer
19 views

Quick Fourier Series help?

I was given a graph (shown above) and was asked to represent this as a Fourier Series. I was able to solve $a_0$ with no problem. However, when I was integrating for $a_n$ and $b_n$, I was having a ...
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0answers
13 views

What is the absolute phase and the relative phase, of a signal? [closed]

I need to know what is the absolute phase and the relative phase, of a signal? and why these phases are important in the signal processing?
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1answer
43 views

Shape of Impulse Responses of $ARMA(p,q)$ Processes

Suppose that $x_t$ is an $ARMA(p,q)$ stochastic process, $$ \phi(L)x_t = \theta(L)\varepsilon_t ,$$ where $\varepsilon_t \sim N(0,\sigma^2)$, and $\phi(L)$ and $\theta(L)$ are lag-polynomials given ...
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0answers
23 views

Find the inverse z transform of $H(z)=\frac{0.2685}{1-0.146z^{-1}}-\frac{0.2685}{1-6.8493z^{-1}}$

I need to find the inverse z transform of: $H(z)=\frac{0.2685}{1-0.146z^{-1}}-\frac{0.2685}{1-6.8493z^{-1}}$ My initial attempt gave: $h(n)=0.2685(0.146)^nu(n)+0.2685(6.8493)^nu(-n-1)$ by using the ...
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2answers
46 views

How to show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$

I am trying to solve the following exercise: Show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ (i.e. $x_n = w_1 x_{n-1} + w_2 x_{n-2}$). ...