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Analysing the modes of a signal with Laplace transform

If I have a linear dynamical system (assume continuous time for the time being) I can create the transfer function, let's say: $$\frac{1}{(s+a_1)(s+a_2)}$$ and the pole-zero map (this one is for e.g. ...
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21 views

Using 2D Parseval-Plancheler theorem to solve an equation

In the context of a digital communications problem I have to solve the following equation with respect to $\tilde{\tau}$: \begin{eqnarray*} &&Im\Big\{\Big(\int\limits_0^{T_0}r^{*}(t)g(t-\tilde{...
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15 views

Quality of a signal (cascaded)

This question extends my previous one Quality of a signal to the case of two cascaded signals. We have a signal x(t) that is transformed (T1) into v(t) that is transformed (T2) into y(t). We want to ...
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1answer
27 views

Quality of a signal

Let's consider a signal y(t) that is an output of a linear transformation with the addition of noise. $$y ( t ) = Ax ( t − \theta) + m ( t )$$ The hypothesis on the signals x(t), y(t) is that they ...
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1answer
24 views

Is it true that a rational transfer function without RHP pole must be square integratable?

I am stuck with a problem: For a rational transfer function without RHP pole, for example $$H(s)=\frac{(-z_0 + s)(-z_1+s)\cdots(-z_n+s)}{(-p_0+s)(-p_1+s)\cdots(-p_m+s)}$$ where $Re\{p_i\}<0$ and $...
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0answers
10 views

Direction of arrival and distance to source

Suppose we have $3$ receivers $a,b,c$ and one wave source which are all located on the same $XY$ plane and we do not know the position of only $c$ on the plane. Assume a plane wave is transmitted $s(...
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23 views

FFT butterfly diagram

I got confused in the FFT butterfly diagram. Can someone please help me understand it? If I have the vector $x = (-3, -2, -1, 0, 1, 2, 3, 4)$, and I want to apply FFT to it using the Butterfly ...
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0answers
22 views

DFT of a sequence while ignoring some of its elements

I sample a signal at a certain frequency for a finite amount of time to get a sequence $$(x_n)_{n=1}^N = (x_1, x_2, ... , x_N)$$ with the intention of analyzing its power spectral density by ...
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13 views

Unknown normalization

I am trying to do BPP imaging and have been trying to replicate the algorithm in "Photoplethysmographic imaging of high spatial resolution" however I've ran into a problem. They say they normalize ...
0
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0answers
9 views

Question about the process of inducement of “MAP, MLE, MDE, and MCE”

Question about "Maximum A Posteriori (MAP), Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE), Maximum Correlation Estimation (MCE)" Let the space of $\mathbf{x}_k$'s $$\...
3
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1answer
42 views

Get an approximate factorization for a number $n$

For a given number $n$, I am interested in the closest number that can be written as a product of a given set of prime factors. More precisely, I am interested in a solution of the following problem ...
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13 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,...
3
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1answer
53 views

l1 regularization mathematical explanation

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
12 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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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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0answers
39 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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0answers
9 views

need help with following butterworth filter unit sample response.

I have a problem for you. Can anyone help me to solve this. A system is represented by a0y(n)+a1y(n-1)+a2y(n-2)+a3y(n-3)=b0x(n)+b1x(n-1)+b2x(n-2)+b3x(n-3) B= [b0, b1 , b2 , b3 ]= [0.3151*10-3 0....
0
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1answer
35 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 ...
4
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1answer
35 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 (...
0
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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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126 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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2answers
78 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} ...
0
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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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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 ...
1
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1answer
36 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 ...
1
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0answers
32 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 ...
0
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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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0answers
46 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
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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
vote
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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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
29 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
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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
15 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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1answer
31 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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0answers
23 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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92 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 ...
2
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0answers
23 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
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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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2answers
40 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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1answer
61 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
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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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1answer
15 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 ...
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0answers
29 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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0answers
27 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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1answer
40 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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2answers
29 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 ...