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3
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0answers
30 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 $\ast$ ...
0
votes
1answer
40 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 $\...
0
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0answers
10 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 $K$ ...
1
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0answers
20 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 ...
1
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1answer
22 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 ($t$):
0
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1answer
30 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 ...
1
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2answers
37 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 ...
1
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0answers
37 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 ...
0
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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
0
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0answers
24 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: ...
2
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1answer
56 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 ...
1
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0answers
10 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 ...
1
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0answers
34 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 ...
0
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0answers
67 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]?
0
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0answers
27 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 ...
0
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0answers
13 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 ...
0
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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 ...
0
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1answer
18 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 ...
1
vote
1answer
50 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 ...
0
votes
1answer
16 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 ...
0
votes
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 ...
0
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0answers
27 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 ...
0
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0answers
7 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 algorithm(...
0
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1answer
102 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 $ ; $ 0<x&...
1
vote
2answers
55 views

Time period of Sinusoidal Signal

I have confusion in calculating the Time period of different signals. 1) $x(t) =3cos(4t + \pi/3)$ solution: 2$\pi$/4 = $\pi$/2 (It is periodic) 3) $x(t) =cos(t-\pi/9) +9sin(2\pi t + \pi/12)$ Solution: ...
0
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0answers
22 views

How to calculate the cross-correlation of a halfwave?

I'm trying working on a vehicle modle and testing it with steering maneuvres standardised by the ISO. When it comes to data analysis the ISO standard says the following: 6.4 Time lag and Sine Time ...
1
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0answers
73 views

Sampling theorem - signal reconstruction

Hi and thank you for your help. I got stuck for the last days with this chapter in this book https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html. What I do not understand is http://www....
0
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0answers
26 views

Can someone explain the steps to the solution in detail please

I've got this question here. I already have the solution but I have no idea how the solution came up. Can someone share any steps in detail for dummies to understand the logic behind it. Any video any ...
1
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1answer
16 views

How to know for sure this is a low-pass filter

Given the transfer function $$H(z) = \frac{1}{4}(1+z^{-1}+z^{-2}+z^{-3})$$ I understand I have to switch $z$ to $e^{j\Omega}$, $0\le\Omega\le\pi$, in order to find out how it interacts with ...
0
votes
1answer
19 views

Constructing a 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: $\mbox{dct(eye($n,n$))}$ where dct is the ...
4
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0answers
74 views

Best sources on complete transforms (classic orthonormal transforms) and overcomplete transforms in signal processing

In the introduction section of a thesis I read a little about classic orthonormal transforms such as Fourier, discrete cosine and wavelet transforms and their application in signal processing. Then ...
1
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0answers
34 views

Isomorphisms of normed vector spaces

I'm having difficulty with the following question: Show that, for $\mathbb{F} \in \{\mathbb{R}, \mathbb{C}\}$ and for an infinite discrete time-domain $\mathbb{T}$, $\exists$ an isomorphism of normed ...
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0answers
21 views

Is the sum of all cross-correlation samples representative of target existence likelihood?

Answers to this question take the peak in the cross correlation as the measure to the likelihood of the trigger signal exist in the received signal - this is pretty much text book. My question is ...
0
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0answers
20 views

2D convolution with one-dimensional function

I am somewhat stumped on what may be a very basic question. I have a 2D input function $F(x,y)$ and an impulse response $H(x)$ that is independent of $y$. The output function is a convolution $G(x,y)...
1
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1answer
121 views

Subderivative of $ ||Au||_{L^{\infty}} $ to compute proximal operator

I am looking for ways to compute the subderivative of $ ||Au||_{L^{\infty}} $, as I want to solve the minimization problem of \begin{equation} \min\limits_u \quad \lambda ||Au||_{L^{\infty}} + \frac{...
0
votes
0answers
18 views

Orthogonalization of two N dimensional signals as a similarity check

I'm trying to find how 'similar' or 'different' two vectors are, in relation to a third vector. Say A and B are features in my data set, with C being the output. I have N data points for each of them ...
0
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1answer
37 views

Find Fourier transform of triangular function based on a Fourier results of rectangular

I have a triangular pulse given by $$x\left(\frac{t}T\right) = \begin{cases} 1-\frac {|t|}T, & \text{if $T\ge t$} \\ 0, & \text{otherwise} \end{cases}$$ Given that $F\left(\operatorname{rect}...
0
votes
1answer
44 views

Effect of sampling frequency on Discrete Fourier Transform?

I don't get it. I have the following form of the DFT: $$ Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1 $$ But this assumes that the sampling ...
1
vote
1answer
58 views

Minimum number of zeros of this Laplace transform

I've come across this question in my Signals and Systems class but I can't seem to understand what the answer might be. Here is the entire question: Consider a signal x(t) which has its Laplace ...
0
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0answers
12 views

Result of sampling of function with too small fs and reconstruction with square function

everybody I have an exam in signal processing tomorrow and doing past exams to prepare myself however I'm on stuck on a particular problem. It is stated as: Considering an ideal sampling with f_s = ...
3
votes
2answers
110 views

secret formula for the “sin” wave with variable rising/falling edge

My math is pretty much forgotten. I was wondering if someone can take a look at this and share what's the formula for creating something like this. https://drive.google.com/file/d/...
1
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1answer
41 views

Find Discrete Time Fourier coefficients of $(-1)^n x[n]$

Given that $x[n]$ is an N-periodic sequence with Fourier coefficients $a_k$, I want to find the Fourier coefficients of $$(-1)^n x[n]$$ for the situation in which $N$ is odd. I'm also interested in ...
0
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0answers
25 views

Lost power with apodizing mask

I previously asked a similar question on the signal processing community, but I think may be more easily solved from a mathematical perspective. I start out with an image, $I$. To be able to process ...
0
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0answers
36 views

Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
0
votes
1answer
122 views

Derivative of unit step function

The ramp function is given by r(t)=tu(t) If we differentiate ramp ,we get unit step function. That is, u(t)=1 So the derivative of unit step function is definitely 0 since u(t) is constant over the ...
0
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0answers
23 views

Amplitude vs. Amplitude Spectrum?

I feel like I keep getting confused about amplitudes when talking about signal processing. Maybe someone can help clear my confusion. Lets say I have a simple sinusoid $f(t)=Asin(\omega_0 t)$ The ...
1
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2answers
36 views

Confusion with a function transformation

I got a HW problem wrong in my Signals and Systems class and am hoping someone can help me understand why. There's a discrete-time signal ...
0
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0answers
15 views

Limits to Discrete Fourier Transforms for Spectral Analysis

I am trying to leverage DFT and IDFT for some noise filtering on some data I am collecting. I am trying to do this in a user friendly/cheap manner by coding this in excel (I know this is not the best ...
1
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0answers
35 views

ICA obsession with gaussianity

There are two reasons to focus on "gaussianity". (1) Orthogonal transformations of gaussian distributions are again gaussian. (2) Mixing of signals tends to a gaussian distribution via Central Limit ...
0
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0answers
15 views

Error analysis for a non-optimal nonuniform quantizer

I'm new to the theory on the subject of quantization. I'm wondering if there are any references that I can look at on error analysis for a non-optimal nonuniform quantizer. More specifically, I ...