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56 views

Source estimation for identification of anomalous events

I’m stuck on the following problem. There are two sources $S_A$ and $S_B$ at the ends of a channel. Both are made up of a white noise component $W_i$ plus an impulsive component $I_i$: $S_A = W_A + ...
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1answer
14 views

How to find period of a sum of periodic functions

I got this function: $$ x[n]=\sin(2*\pi*4/3*n) + \cos(2*\pi*5/2*n) $$ It is easy to see that period of the sin is 3/4 and the ...
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0answers
30 views

Deriving difference equation from a rational system function $H(z)$

If I have the system function $H(z)$ of a linear time-invariant system, how do I derive the difference equation relating its input $x(n)$ and output $y(n)$? The system function is given by $$H(z) = ...
2
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0answers
303 views

Intuition behind the DTFT vs Fourier transform of ideally sampled signal

So I am taking a signal processing course in EE and my professor is an Engineer who reallly likes math however his book which we use for the class falls in the dreadfull purgatory of math books in my ...
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0answers
26 views

Magnitude and Angle of Discrete Fourier Transform

I can't figure out how to get the magnitudes for periodic discrete Fourier transforms. For example if $x[n] = cos(\frac{\pi}{4}n + \frac{\pi}{2})$, I need to find and plot the magnitude ...
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17 views

Which is the total energy of the product of two discrete energy signals

Assume that I have two signals with finite energy. The first, $x_s$ \begin{equation} E_s= \sum_{i=0}^{N} |x_s(i)|^2 \end{equation} The second, $w$ \begin{equation} E_w= \sum_{i=0}^{N} |w(i)|^2 ...
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0answers
36 views

Why is the cross-correlation an integral?

The cross-correlation of continuous $f,g$ is: $$(f \star g)(\tau)=\int_{-\infty}^{\infty}f^*(t)g(t+\tau)dt$$ Why is it an integral? Why doesn't The cross-correlation of continuous $f,g$ is: $$(f ...
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12 views

Why does cross-correlation involve the complex conjugate?

The cross-correlation of continuous $f,g$ is: $(f \star g)(\tau)=\int_{-\infty}^{\infty}f^*(t)g(t+\tau)dt$ where * is the complex conjugate. Why is there the complex conjugate?
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0answers
12 views

Complex filter factorizations with invariant points

Based on this question, using the same $z_0$: $$z_0 = e^{2\pi i / 8}$$ if we modify the sequence from previous question to look like this ($*$ denotes discrete convolution): $$\left(z_0^{[-2k,3k]} * ...
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0answers
17 views

Complex filter factorizations - continued

Continuing from this rather silly trivial question factoring real valued filters into shorter complex ones, hoping this won't be as trivial. If we modify it a bit: $$z_0 = e^{2\pi i / 8}$$ and ...
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0answers
21 views

Complex filter factorizations

There is a famous low pass filter $[1,2,1]$ in signal processing which can be factored in the sense of a convolution product over the real numbers : $[1,1] * [1,1]$. This is the only way to do it over ...
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1answer
44 views

Signal processing : future values prediction

Let $f : \mathbb{R}^+ \rightarrow \mathbb{R} $ be a continuous function. Do you have some references (books or online resource) about techniques that allow to predict $f(x_{n+1})$, knowing $f(x_0), ...
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1answer
17 views

Second Order Damped System (Harmonic Oscillator)

I'm currently working on an electrical engineering problem involving an ideal operational amplifier. The system itself is governed by the transfer function, which relates output to input: ...
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0answers
35 views

Extracting a Cosine Function from a Linear Combination of Cosines

I have a frequency modulated signal which must contain only $ g(t)=B.\cos(\omega(t).t+\phi)$, but it gets the form as below $$ ...
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1answer
28 views

Inverse $Z$ transform of $\frac{1}{z-a}$

I don't really get what's happening here and I haven't been able to find a single example on how to get the inverse $Z$-transform of $\frac{1}{z-a}$. Can anyone show the way?
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1answer
35 views

is a “non-causal” system “memory”?

Is their a relationship between non-causality and memory? for example: is the system $Y(t) = X(t+1)$ memory or memory-less. I got confused because the memory system is defined to depend only on the ...
2
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1answer
74 views

Calculating convolution integral analytically

How can i compute convolution integral analytically, without using graphs. I hate using graphs, shiftings which are error prone. If this is possible can you explain what way i must follow? For ...
2
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1answer
38 views

How to mathematically model noise?

In my project I have to perform analysis of noise effect in certain signal. I am just wondering how is noise formally described? Up to now I always simulate a noisy signal using MATLAB in an additive ...
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0answers
28 views

Relation between Covariance and Energy of a random signal

Let's say I have the below random signal: $Y[n]=[y(n)y(n−1)y(n−2)....y(1)]$ I have two random variables now: The first one $X_1$ which express the maximum eigenvalue of the covariance matrix of $Y$. ...
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0answers
14 views

Does inverse of all Fouriers transforms have a corresponding function in time domain?

I am trying to cancel out the following transfer function of a system: $$\frac{( 1 - e^{(i*k*T)} ) }{ (i*k)}$$ I thought it would work if I find the inverse Fourier transform of $$\frac{ (i*k)}{( 1 ...
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2answers
61 views

Why is $\int e^{-t}u(t) dt = (1-e^{-t})u(t) + Constant$?

How do you solve $\int e^{-t}u(t) dt $? In which u(t) is the unit step function. $\int e^{-t}u(t) dt = (1-e^{-t})u(t) + Constant$ But what are the intermediate steps? Unit step u(t) = ...
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17 views

explanation of correlation of stationary stochastic processes

I have some questions about correlation in stationary stochastic processes. I know that the expectation of a random variable is $E(x)=\int_{-\infty}^{+\infty} a ...
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3answers
43 views

Why is the convolution output in terms of 't' not $\tau$?

The convolution integral is defined as: $$y(t) = (h * x)(t) = \int^{+\infty}_{-\infty} h(\tau). x(t-\tau)\ d\tau$$ where $h(t)$ and $x(t)$ are functions in terms of time. Why is $y$ in terms of ...
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2answers
35 views

Do decaying exponential signals have finite energy?

"A signal that decays exponentially has finite energy, so, it is also an energy signal." http://www.songho.ca/dsp/signal/signals.html I don't quite get how that can be true. Energy of a ...
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17 views

How to generate random noise with given parameters?

I'm studying optical fibers and trying to analyze how the core radius fluctuations along the fiber length affect the performance of optical fibers. How can I generate random noise dr which satisfies ...
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0answers
20 views

Is there a name for this “simplified” Volterra series?

Consider a nonlinear, time-invariant system of the following form: $g(t) = \left[h_1(t) \ast f(t)^1\right] + \left[h_2(t) \ast f(t)^2\right] + \left[h_3(t) \ast f(t)^3\right] + ...$ where $\ast$ ...
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1answer
36 views

Transforming a sawtooth into a sinus with one parameter

Can you help me in finding the analytical expression of a function $f_\alpha(\theta)$, with one parameter $\alpha=(0,1)$ by which one can continously transform a sawtooth curve into a sinus? With ...
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0answers
9 views

Estimate function given PDF and covariance

Let's say $h(x)$, random variable, represents the height of a surface, with x being the usual x-axis. The probability distribution function is: $P(h) = Ke^{-\frac{h^2}{2s^2}}$ is Gaussian, where $K$ ...
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0answers
18 views

Math required to solve Fourier Transform for periodic functions?

In my Signals & Systems course my professor said that although it's possible to solve the standard Fourier transform for periodic signals, it requires advanced math beyond what we've learned, so ...
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1answer
20 views

Assist on finding the impulse response fom a simple LTI graph

Could you please advise on the impulse response from this $LTI$ graph? I need to plot it and find if it is stable and causal... LTI system with response to unitary step ($t$):
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1answer
29 views

How do you solve $\int_{-3}^{2} ( e^{-t+1} + sin (\frac{2\pi}{3}t) ) \delta(t- \frac{3}{2}) dt$?

How do you sovle the equation: $\int_{-3}^{2} ( e^{-t+1} + sin (\frac{2\pi}{3}t) ) \delta(t- \frac{3}{2}) dt$ Because of the $\delta(t- \frac{3}{2})$ this is only non-zero at $t=\frac{3}{2}$ But I ...
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2answers
31 views

How do I find the poles of this difference equation?

I have an equation: $$y(n) = 0.634x(n) - 0.634x(n-2) + 0.268y(n-2)$$ I completed a $z$ transform and got: $$ H(z) = \frac{1-0.268z^{-2}}{0.634 - 0.634z^{-2}}$$ What is the next step to find the ...
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0answers
36 views

Why does inputting complex exponentials into a system give its frequency response?

Let's say I have an FIR filter with the equation: $$ y[n] = \sum_{i=0}^{N-1} h[i] x[n-i] $$ I know that to find the frequency response of this filter, I need to input a complex exponential in place ...
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0answers
7 views

Systems properties assistance 2

I am a little confused about the properties (is it Linear, Causal, Time-Invariant, Stable?) of this T system. Would you tip me on this? enter image description here
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0answers
20 views

Calculating SNR

I am having trouble calculating SNR. We are given a wave file that we have to filter and then calculate the SNR before and after each filter and compare. I calculated the SNR using: ...
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1answer
40 views

Does the Discrete Fourier Transform assume a periodic signal, or one that dies off?

I keep hearing that the DFT assumes a periodic signal. E.g. the first answer in this MATLAB Q&A site. This doesn't make any sense to me. According to the derivations I've seen of the DFT one ...
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0answers
9 views

Does perlin noise have a constant-valued grid

As far as I understand, perlin noise is made by creating a grid, picking gradient vector over the vertices of the grid and computing the dot product of the distance vector from an end point to ...
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0answers
30 views

Can someone explain negative frequencies when doing the Fourier transform?

I apologize if this question has been asked before. I have looked and have not found a clear explanation. When doing the discrete Fourier transform (e.g. fft in MATLAB) for a vector of discrete time ...
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0answers
53 views

What is the inverse DTFT of a triangle in the frequency domain?

If I have a triangle in the frequency domain, what is the inverse DTFT? So $X(e^{jw})= 1-\frac{2*|w|}{\pi}$, what is x[n]?
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0answers
15 views

differentiating complex signal: dy/dx=d/dx(a+ib)= ???

1. Problem Outline I have a signal (array from 1:n) which has both real and imaginary parts. I require to take the derivative of the complex magnitude of that signal. The signal Y is a function of a ...
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0answers
12 views

Compute frequencies present in a sampled signal

I have a signal $$ X(t) = \sum^3_{k=1} A_k \cos (2\pi f_k t + \phi_k), -\infty < t < \infty $$ where $E[A_1^2] = 1, E[A_2^2] = 4, E[A_3^2] = 1$ and the phase functions are uniformly ...
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0answers
13 views

Minimizing function of overlapping volumes

I am implementing a method that performs alignment of slightly overlapping 3D volumes. To be more specific, I have a dataset of m x n volumes of size 1024 x 1024 x 100, and each volume overlaps for ...
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1answer
17 views

Systems properties assistance

I am a little confused about the properties (is it Linear, Causal, Time-Invariant, Stable?) of this T system. $$T[x(t)]=\sum_{k=t_0}^{t}{x(k)}$$ Some are obvious (it is linear), but can’t come up ...
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1answer
47 views

Why is the Discrete Fourier Transform exact for periodic signals?

I have in my course notes: $$ \sum_{k=0}^{N-1}y(k)e^{-j\omega_nk}\approx\sum_{k=-\infty}^{\infty}y(k)e^{-j\omega_nk} $$ Where the $\approx$ for some reason becomes $=$ when $y(k)$ is periodic. Could ...
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0answers
42 views

What is the Fourier transform of $x(t) =\frac{t\sin(t)}{(\pi t)^2}$?

I'm not quite sure how to tackle this Fourier transform. I'm lead to believe that the unit triangle function will be involved, but I'm not 100% sure. Could someone please explain the process of ...
0
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1answer
14 views

energy of a convolution

I have to find the energy of $y(t)$ $$h(t)=ho\;sinc^3(t/T)\\ x(t)=V_0+V_1\;sin(3\pi\; t/T)\\ y(t)=x*h\;(t) $$ Where "$*$" is the convolution and $sinc(t)=\frac {sin(\pi t)}{\pi t}$ I think that the ...
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1answer
24 views

$x(t)\rightarrow x(-t)$ and $x(t)\rightarrow x^\ast(-t)$ transforms

I have to determine if these transforms are linear and the core of the transforms: $x(t)\rightarrow x(-t), \quad t\in \mathbb{R}$ $x(t)\rightarrow x^\ast(-t), \quad t\in \mathbb{R}$ With "the ...
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0answers
15 views

Energy functions for CRF/MRF

I am currently working in image segmentation. I have read several papers and books where Markov or Conditional Random Fields are used in order to segment images. Most of them also mention an energy ...
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0answers
4 views

Independent components anaylsis with prior knowledge about the sources

I was wondering which algorithm performs the best if we already know something about the sources' distribution? Say all the sources(except the noise) are Bernoulli distributions. Which ...
0
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1answer
75 views

Expanding Fourier Series of $f(x)=\pi-x$ where $0<x<\pi$ (even and odd)

Please help me solve this Fourier series and correct my solution if it is wrong. it's a non-periodic function which we need to write its Fourier series (even and odd) : $ f(x)=\pi - x $ ; $ ...