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

learn more… | top users | synonyms (1)

4
votes
0answers
40 views

When is a mapping the proximity operator of some convex function?

Sorry for cross-posting from MO. It's been a few days and the question hasn't received any attention there. So, is there a characterization of mappings $p : \mathbb R^n \rightarrow \mathbb R^n$ which ...
0
votes
0answers
47 views

Why is the fundamental period $T_0$ of the complex exponential $e^{i\omega_0t}$, $T_0 = \frac{2 \pi}{|\omega_0|}$?

Assuming that $\omega_0 \in \mathbb{R}, t \in \mathbb{R}, T \in \mathbb{R}$. I realize that in order for $e^{i\omega_0t}$ to be perioric, it must be true that $e^{i\omega_0(t + T)} = e^{i\omega_0t}$ ...
-1
votes
0answers
6 views

How would I draw (sketch) the result of DT convolution sum

This picture shows the result of a convolution sum. PICTURE IS HERE! The question is how can I draw $y[n]$. I would appreciate any hints to start
0
votes
0answers
15 views

“Regressing out” nuissance covariates in fMRI data. [on hold]

How can I use the general linear model to remove a noisy signal from another signal of which it is part? In fMRI data, time series representing physiological noise can be included as regressors ...
-1
votes
1answer
27 views

Fourier Transform of u(-2-t)

I'm trying to find the Fourier Transform of x(t) = u(-2-t) Here's what I've tried: Can anyone tell me what I'm doing wrong? Thanks in advance. EDIT: Forgot to mention that u(t) is the unit step ...
1
vote
1answer
32 views

Summation of $A\cos (\omega n+\phi)$ [on hold]

I'm trying to evaluate the following summation: My original problem is $$\lim_{N \to \infty} \frac{1}{2N+1} \sum_{n=-N}^N \left|A \cos(\omega n+\phi)\right|^2$$ Now I'm stuck at calculating the ...
2
votes
1answer
1k views

How can I use the time-frequency uncertainty principle?

I have a signal composed of the summation of a set of sine waves of different frequencies. The amplitude of these sub-signals can change so many times a second. I have been told that, if I want to ...
3
votes
3answers
494 views

Any good introductory book/tutorial on Fourier Transform (up to FFT) with plenty of exercises and solutions?

I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I ...
0
votes
1answer
19 views

Simultaneous Diagonalization of A and B via $\Sigma = A^{-1}B$

I am reading the paper "A Generalized Subspace Approach for Enhancing Speech Corrupted by Colored Noise" by Yi Hu and Philipos C. Loizou. In the paper, they claim that given two matrices $R_{n}$ and ...
0
votes
0answers
16 views

Implementation of blind deconvolution for signal r(n) = h(n) * s(n) + a(n) in Matlab [closed]

r(n) is the recorded speech h(n) is impulse response of room acoustics s(n) is desired speech signal a(n) is noise from microphone I understand in order to find the desired speech signal, s(n), ...
0
votes
0answers
22 views

Cross-correlation, Fourier transform and Laplace transform: measure of how much signal are alike?

I'm studying electrical engineering and use correlation, Fourier transform and Laplace transform a lot. I know how and when to use them, however, the interpretation I've seen in the lectures still ...
0
votes
0answers
13 views

Continuous time fourier transform existance proof explanation

The continuous time fourier transform,$$X(jw) = \int_{-\infty}^{\infty}x(t)e^{-jwt}\mathrm{d}t$$ During a lecture a few months ago in my signals and systems class, the professor showed when the CTFT ...
1
vote
0answers
707 views

How to calculate wavelet energy?

Part of my assignment about signal processing says the following: Compute the Discrete Wavelet Transform for the input signals Group the wavelet coefficients in trees growing across scales ...
1
vote
0answers
88 views

Sampling a sinusoidal signal

Consider the signal $g(t)=\cos(2\pi \lambda t+\phi)$ that is sampled with a frequency $\tau$. Let $g_k$ denote the values of $g$ at the times $t_k=\frac{k}{\tau}$, $k \in \mathbb{N}$. (a) Show that ...
1
vote
1answer
58 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, ...
0
votes
0answers
20 views

Some questions about Hilbert transform

I have some questions about Hilbert transform when I read Real Analysis: In Stein "Real Analysis" p.220, the Hilbert transform is defined by $P=\frac{I+iH}{2}$, where $P$ is an orthogonal projection ...
1
vote
1answer
464 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 ...
2
votes
0answers
20 views

Estimating pseudo-periodicity of signals

I have pressure data which are measured at a given point in a standing wave. These data(signals) are 'almost' sinusoidal in nature. Each cycle may slightly vary from the original signal i.e the ...
0
votes
1answer
26 views

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: ...
1
vote
0answers
24 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 ...
1
vote
2answers
35 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 ...
3
votes
1answer
1k 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 ...
2
votes
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 ...
4
votes
1answer
105 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 ...
1
vote
1answer
268 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, ...
1
vote
0answers
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 $r_n=e_n-e_{n-1}$ ...
2
votes
0answers
85 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} ...
1
vote
1answer
423 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 ...
2
votes
0answers
185 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 ...
0
votes
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 ...
0
votes
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: ...
2
votes
0answers
211 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 ...
2
votes
3answers
811 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
votes
1answer
455 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 ...
0
votes
1answer
145 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 ...
0
votes
0answers
12 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 ...
0
votes
0answers
19 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 ...
-1
votes
1answer
14 views

Converting from complex to sinusoidal form and vise versa [closed]

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 ...
0
votes
0answers
26 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 ...
0
votes
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 ...
0
votes
2answers
27 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 ...
1
vote
1answer
18 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: ...
3
votes
1answer
838 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; ...
0
votes
0answers
25 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, ...
0
votes
0answers
7 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 ...
0
votes
2answers
21 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 ...
1
vote
1answer
20 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 ...
0
votes
0answers
19 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))?
0
votes
2answers
2k views

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 ...
0
votes
1answer
26 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 ...