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Modal Identification, e.g. frequencies or mode shapes, … [on hold]

I want to extract modal data from a non-stationary signal. which method does work better? How good are Blind Source Separation (BSS) methods, for example ICA or SOBI for this purpose?
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24 views

l1 regularization mathematical explanation [on hold]

I somewhat understand what l1 regularization is, however, the mathematical formula and how to use it are confusing me. I'm not really sure what a regularization term is and how I could apply it to a ...
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0answers
23 views

Explicit solution to a summation of fractions equation.

I am struggling the following problems. It is not ensured to solve completely because these problems are generated by myself. Particularly, I guess the second problem is very hard if we try to solve ...
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0answers
11 views

psd of two signals

I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the PSD $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $S_{w_1,w_2}(\omega),S_{w_1,...
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0answers
9 views

What different between huffman and EBCOT?

I have a question about entropy coding and Image compression. Huffman coding and EBCOT coding are entropy coding. correct or not? I knew about huffman coding but I don't know EBCOT, How it working?...
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9 views

How to crop a matrix/array based on a condition [on hold]

I have a matrix consisting of 10 columns/arrays. First 9 are my data. The 10th column/array is a "trigger channel" which has sharp spikes from baseline 0V to 5V and back down to 0V. I need to crop all ...
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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 ...
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0answers
9 views

Phase correlation vs. normalized cross-correlation

In 2-dimensional discrete signal analysis (specifically image processing), a definition I found for the normalized cross-correlation between two images, both of size MxN $g_1(x, y)$ and $g_2(x, y)$ is:...
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35 views

Delaying signals in Matlab

I'm new to MATLAB and have a question that I need help on: The problem I have is to plot the simple signals: a 1Hz Sine wave, a standard rectangle function and a standard triangle function Here is ...
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0answers
16 views

How can I show that any integrable Passband or Baseband signal is also a finite energy signal?

I have supposed that, as the definition of a baseband/passband signal says, the function x(t) is integrable, continuous and bounded due to the fact that it forms a Fourier Transform pair with x'(f) (...
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25 views

Has the theoretical explanation of Compressed Sensing been simplified since 2005/2006?

Is the theoretical explanation of compressed sensing given in the Candes, Romberg, and Tao papers from 2005 / 2006 still the simplest and most clear explanation available? Are these original papers ...
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2answers
75 views

Using Parseval's theorem to solve an integral

The question at hand is to use Parseval's theorem to solve the following integral: $$\int_{-\infty}^{\infty} sinc^4 (kt) dt$$ I understand Parseval's theorem to be: $$E_g = \int_{-\infty}^{\infty} ...
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1answer
492 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 ...
4
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1answer
34 views

Equation for a sinusoidal wave with changing frequency

I would like to find a sinusoidal wave whose period or frequency change to half (or double) with every step, someting like this But I cant find the precise coefficients for the period to decrease (...
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1answer
905 views

What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...
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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 ...
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1answer
460 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
864 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
17 views

Inital condition for 1st order derivative

I have a PT2 system filter, Y'' = (a0)*Y'+(a1)*Y+(b)*u. I want to apply this filter to my signal, i have a problem in deriving ...
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0answers
118 views

How to keep up when converting between bases?

Here is a schematized binary channel that neatly conveys a decimal number. $ \require{begingroup}\begingroup \def\T {{ \cal T }} \def \Ti {{ \T \raise5mu{ \text- \scriptsize 1 } }} \def\Bx #1{{ ~ ...
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1answer
31 views

why analytic signal can separate into odd and even part

According to the following video at 3:50,the man said that by the reason of Fourier series,the f(t) can divided into odd and even part. I understand the function of fourier series,but I still can't ...
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1answer
14 views

Negative autocorrelation values

Autocorrelation is informally defined (Wikipedia article) as "the similarity between observations as a function of the time lag between them". I create the following time series in MATLAB: ...
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0answers
31 views

Estimate original matrix from matrix multiplication result

Let $A$ be $m \times n$ real matrix. Let $B$ be $n \times k$ real matrix. Let $C= A \times B$ ($m \times k$ matrix). Now, the question is: given $C$ and $A$, give an estimate for $B$. Possible ...
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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 ...
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1answer
457 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
16 views

Calculation of an FIR filter in Matlab.

I have been researching FIR filter design with regard to my signal processing assignment and am having a lot of difficulty trying to understand how the frequency response and ultimately the magnitude ...
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1answer
35 views

Conceptual Question : Relationship between entropy and a technique for source coding

I want to encode the messages to a sequence of 1s and 0s (subsequently called "bits"). This is called "source coding". Shannon's source coding theory states that the entropy of a source that emits a ...
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0answers
31 views

Convert floating point number to short int [closed]

This is the transfer function of a FIR filter $$H(z) = -0.125 + 0.25z - 0.125z^2$$ How to convert the coefficients to short int? Is it correct if I just multiply ...
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0answers
10 views

Gaussian filter. Formula for filtering sample

I need to apply gaussian filter to the sample of signal. Can you tell me the formula which I should use and say what is the purpose of gaussian filter?
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0answers
30 views

What is computational complexity of a coding technique

In my previous Question Help in understanding a coding technique based on inverse mapping of a dynamical system I learnt how to apply chaotic map in coding theory in communications. Steps: (1) The ...
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1answer
1k views

Wiener filter: A good tutorial

I am interested in image analysis and am looking for an approachable tutorial to the Wiener filter. At some point I am interested in implementing such a filter but I would like to have a deeper ...
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0answers
45 views

Formula of phase correlation

If I have two 2D signals, and one is the shift of another. I can propose such schema for define offset via continious Fourier Transform: $$f_2(x,y)=f_1(x-x_0,y-y_0)$$ Then $$Ff_2(s_1,s_2)=e^{-2\pi j(...
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0answers
45 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 ...
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0answers
54 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 $e^{i\omega_0(t + T)} = e^{i\omega_0t}$ ...
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1answer
30 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 ...
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1answer
35 views

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

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 ...
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3answers
496 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 ...
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1answer
23 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 $...
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0answers
26 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 ...
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0answers
14 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 ...
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0answers
728 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 ...
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0answers
91 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 ...
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1answer
60 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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0answers
21 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 ...
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0answers
22 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 ...
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1answer
30 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: $...
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27 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
39 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 ...
2
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2answers
374 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
107 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 ...