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2answers
64 views

MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
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2answers
129 views

MLE parameter estimation — confusion regarding some terms in the pdf of complex normal r.v (Part 2)

This question is based on the application of the pdf which was an earlier question of mine asked here Confusion regarding pdf of circularly symmetric complex gaussian rv If $v \sim CN(0,2\sigma^2_v)$ ...
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2answers
128 views

Differential Equations applications in Signal Processing [closed]

Does differential and partial differential equations subject has applications in Signal Processing? I have basic DSP background and know Matrix algebra and Fourier transforms very well, but I am not ...
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1answer
46 views

how to set Equalizer's coefficient using generalized eigenvector.

In that paper https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2012-72 .. Equation 3, $J(w) = w^HBw/w^HCw$ .. $B$ and $C$ are matrices, $w$ the filter coefficients vector ...
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1answer
27 views

Equation Derivation: Help with intermediate steps

As per the attached image above, I don't know how the equation in the first line transformed to the form in second line. I tried solving it by multiplication but the result was different.
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2answers
748 views

Convolution by IIR filter, a case where circular convolution is allowed?

The question is, how to attain the frequency domain representation of any signal (which is finite, non-unit length) convolved with an IIR filter. The correct answer in my opinion is that there is in ...
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1answer
86 views

Advantages of Splines in Compressed sensing

I am working in compressed sensing, basically in ECG reconstruction Normally we were using biorthogonal wavelets for reconstruction. Someone advised me to use exponential spline basis instead of ...
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1answer
355 views

Hidden Markov Model

I am trying to construct a Hidden Markov Model to predict the next state to go to. I am doing an example system, or, a test system that contains the following: Ok so the training I have used is: ...
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1answer
20 views

Why is the anisotropic diffusion equivalent to the heat equation when using a constant diffusion coefficient?

The anisotropic diffusion is defined as $$\frac{\partial I}{\partial t} = \mathrm{div} \left( c(x,y,t) \nabla I \right)= \nabla c \cdot \nabla I + c(x,y,t) \Delta I$$ where $\operatorname{div}$ is ...
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1answer
192 views

What is stochastic differential equation and its need?

A white noise process can be simulated using the Matlab command randn(). The numbers will be drawn from a Normal distribution of zero mean and variance 1. Is the ...
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1answer
35 views

Help with Determinants [closed]

Okay so i understand the first det, which is why i got the correct solution. However for the second det, im not sure how to solve it since because of the different coefficents (0,2,4) and i tried of ...
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1answer
74 views

Hi, If I really want to focus on the mathematics of signal procesing, Should I do a Masters in EE or Math? [closed]

I'm an undergraduate electrical engineering student who has an interest in mathematics of signal processing. I want to be able to go to a graduate school where I can focus on more the mathematics and ...
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1answer
215 views

Shape of Kaiser windowing function FFT response

I'm trying to determine the shape of the FFT response of a signal which had a kaiser windowing function applied to it. What I mean by this is if the shape is a normal bell curve or a Lorentzian ...
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2answers
93 views

Resolution of Discrete Fourier Transform is 1/T - Mathematical proof?

In many articles I see that the frequency resolution of the Discrete Fourier Transform (DFT) equals Fs/N where Fs is the sampling rate and N is the total number of samples. Fs/N is equivalent to 1/T ...
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1answer
94 views

How to find the impulse response of filter that outputs the autocorrelation of the input?

I am trying to solve question 9.61 in the attached image. I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
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1answer
55 views

Explicit a succession using z inverse transform

Is it possible to explicit $y(n)$ of this mathematical succession in recursive form using z inverse transform?: $ y(0) = 1 \\ y(n+1) = 2y(n) + 3 $ I can't write ...
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1answer
62 views

How is this was derived? DTFT for symmetric pulse

do not understand how the middle expression was derived from above expression, after all summation\multiplication i get: $$\frac{e^{-jwN} + e^{jwN} - e^{-jw(N+1)} + e^{jw(N+1)}}{2 - e^{-jw} - e^{jw}...
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2answers
104 views

Help in proper notations and mathematical formulation

For a given series, $S = \{-1,0,-2,1,etc\}$. The number of elements in $S$ is $N = 100$. Each $s_i$ belongs to a alphabet from a finite alphabet set $\mathcal{A} = (a_1=0, a_2=1, a_3=2, a_4=3, a_5=-1,...
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1answer
142 views

Laplace transform of averaging operator

I am studying dc-dc converter now. I got a problem with Laplace transform of the averaging operator as in the image below. Can anyone help me derive the Laplace transform result $G_{av}(s)$ as in the ...
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1answer
82 views

Unable to understand how the paper simplifies the covariance matrix - Kalman filter

The paper Convergence Analysis of the Unscented Kalman Filter for Filtering Noisy Chaotic Signals presents the convergence analysis of Unscented Kalman Filter download http://www.eie.polyu.edu.hk/~...
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2answers
322 views

Polar form of the Fourier transform of $\sin(t)$

I came across the Fourier transform of sin(t). It ends up being a purely imaginary (dirac delta) impulse pair. But when considering the frequency domain representation of a signal, we consider the ...
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1answer
43 views

Capacity computation in Costa sheme

I can not understand the following sentences, could you please anyone guide me ? "Comparing with the embedding in audio signals, the usable bandwidth is greatly reduced, from 22.05 kHz to 4 kHz. ...
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1answer
79 views

A 3x3 image kernel takes 9 multiplications and 8 or 9 additions for each pixel?

I doubt because you have 9 multiplications and you are adding 9 numbers together, when using a 3x3 convolution matrix. Adding 9 numbers: 1+2+3+4+5+6+7+8+9 We are performing 8 additions as we repeat ...
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1answer
477 views

Inverse Discrete Time Fourier Transform of a given Function using the definition

I would like to compute the Inverse Fourier Transform of a given function using the DTFT definition $$H(e^{jω})=\frac{1}{(2−e^{jω})(2−e^{−jω})}$$ But I have to use the definition of the DTFT $$H(e^{...
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0answers
41 views

Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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0answers
53 views

Power, energy and amplitude spectrum from fft in MATLAB - scaling

I've looked at previous answers and none of the answers seem to agree (perhaps I'm missing something obvious): I would like to know what the correct scaling to use is for amplitude, energy and power ...
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0answers
36 views

How to find the filter coefficient of matched filter to detect the pulse of a signal?

I would to understand how to find the coefficient of a matched filter. Let's consider we have a signal and the signal is buried in the following noise. we want to find the coefficient of a matched ...
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0answers
16 views

How to match resolution of two or more signals

I have received the following 4 time-series signals and wanted to do some data analytics using these. Although the sampling is the same for all of these signals, 2 samples per second, problem is that ...
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0answers
38 views

On $H_\infty$ norm for transfer function

For a given scenario in the context of control system, I'm trying to investigate how the $H_\infty$ norm can be calculated for a transfer function as follows: $$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
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1answer
68 views

How to measure the distance between two circle-like-lines over 360 degree

I am looking for a slim and with that quickly programmable image processing strategy to measure the distance between two circles over 360°. It is important to notice that the circles are not perfect, ...
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0answers
39 views

Relationships between $f(t)$ signal and $f(t) \times \sin(\omega t)$ signal

Let's assume that there is a signal $f(t)$, $0\le t \le T$. Then, is there any special meaning of the signal $g(t) =f(t) \times \sin(\omega t)$? Like AM transmission. What is shown/heard when we play ...
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0answers
65 views

What kind of math is introduced in this answer related to DSP?

What kind of math is introduced in this answer: https://dsp.stackexchange.com/a/40225/30897 It smells like standard linear algebra course (which I haven't studied, yet), but is it only that? Thanks!
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1answer
670 views

Z-transform of an impulse signal in discrete time

am trying to compute the Z-transform of the following signal \begin{equation*} x\left[n\right]\:=\:\sum_{k=-\infty \:}^{\infty \:}\:\delta \:\left[n-k\right] \end{equation*} so I thought it would be \...
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1answer
57 views

Getting a part of the invert of Si function

I'm working on an algorithmus that sould need the inverse of the SI function. since this last once isn't oviouse to calculate, I'm trying to get only the parobla part from the SI function, to be ...
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1answer
132 views

How to predict the cramped frequency of a digital filter based on an analogue frequency?

I have a second order analogue high pass transfer function (unity gain at infinity). It's magnitude response hits the -20 decibel line at a frequency of 5706 Hz (the corner frequency is 18000 and ...
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0answers
26 views

Why the formula below are critically-damped second-order linear systems?

This is part formula of command-response model (Fujisaki Model): ...
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0answers
294 views

Problem calculating the average power of a vector?

I am calculating the average power of a vector. I would like to compare the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. Thank ...
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3answers
103 views

How to interpret the notation of a transfer function

Probably a stupid question, but I'm slowly making my way through Julius Smiths' filter book. The maths is slightly defeating me at points. This function $H(e^{j\omega t})$, why is it a function of ...
-1
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1answer
108 views

BIBO Stability of a piecewise function

I have a function $y$ defined as $$ y(t) = \left\{\begin{array} ~t~ \mbox{ where} |t| \le 3\\ 0~ \mbox{ otherwise} \end{array} \right . $$ With a system defined as $$G(t) = ty(t), $$ is it BIBO ...
-1
votes
1answer
187 views

Accumulator with decay?

I am using an accumulator in the form of X + [Y-1], X plus the unit delay of the output. Is there an accumulator that follows this form, but will fall to 0 over time, similar to a differentiator?
-1
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1answer
33 views

Why GCD(1+D, 1+D^2) = 1+D?

I'm reading Digital Communications, Proakis, and in order to classify an encoder as catastrophic or noncatastrophic I need the GCD of the elements in the generator G(D). I don't really know what kind ...
-1
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1answer
78 views

Is it mathematically possible to compute Fourier transform without comparing the signal?

If I'm correct, Fourier transform lets me know the magnitude and phase of any given frequency in a signal. I have a sampled signal and I want to compute its Fourier transform (any frequency) without ...
-1
votes
1answer
39 views

What is a “functional”? [closed]

I have read the wiki page (https://en.wikipedia.org/wiki/Functional_(mathematics) but it is not helping. I understand what a regular function is input > do something to that input > output. but ...
-1
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1answer
284 views

FFT: Linear to Logarithmic (TM4C, CMSIS & NeoPixels/ws2812)

I'm trying to perform an FFT using the CMSIS libraries. My FFT_Output[] provides 1024 bins of data as expected. The issue is that it's linearly spaced and I want to change it to a logarithmic scale ...
-2
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0answers
42 views

Directional derivative [closed]

I know that D ⃗ v f = ∇ f ⋅ ⃗ v Dv→f=∇f⋅v→ is the directional derivative. My question is why must the vector ⃗ v v→ be a unit vector? I am sure there is an obvious answer, but my book doesn't really ...