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use wavelet transform to analyze signal

let us suppose that we have following signal ...
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1answer
63 views

Continuous time signal and Discrete time signal

I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time? Also, can all periodic signals be ...
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2answers
383 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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57 views

Harmonic F statistic

i am interested what does mean Harmonic F statistic in mathematical language?i have search about $F$ statistic and found a lot of explanation,for example like this "**F Statistic The F statistic ...
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16 views

Maximizing orthonormal subspace, Signal Processing

Let A any matrix. If we eigen-decompose $A^TA=HDH^T$, where $H$ is unitary and $D$ diagonal, then the columns $H_i$ of $H$ satisfy $$\|AH_1\|^2=\max \frac{\|Ax\|^2}{\|x\|^2}$$ ...
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How do I estimate the derivative of the current position, when I have only values from past to present?

If I have a discrete real-time signal $x[n]$, with its latest value $x[i]$ and all its past values $x[i-t]$, how can I estimate the derivative at $x[i]$?
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1answer
52 views

How does this phase shift in x-space affect the position of a spectrum in k-space?

I'm working on a new form of signal detection with which I hope to recover both the amplitude and phase of a very small signal. However, doing this requires the use of some Fourier maths that I don't ...
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1answer
50 views

Kronecker delta

$D=C\cdot V$ ; C and V are both matrices and C is a square by square matrix $C_{ij}=1$ if i=j and $C_{ij}=0$ for $i\neq j$ (Kronecker delta). $\mathcal{F}^{-1} D = \mathcal{F}^{-1} C$ $ * ...
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1answer
60 views

Can any piecewise function be represented as a traditional equation?

In "Fundamentals of Electrical Engineering" we learned about piecewise functions for the "unit-step" and "ramp" which are represented by $f(x)= \begin{cases}0, & \text{if }x< 0 \\ 1, & ...
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39 views

Asymptotic result on quadratic variation of a semi-martingale linear functional estimator

In the same context of this previous question. Consider $$ \mathcal E^{(n)}_t := \sqrt{n}(\widehat\Lambda_n(\phi)_t - \Lambda(\phi)_t )$$ I desire to prove that $$ \left \langle \mathcal ...
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1answer
38 views

Find if the system $(x(t-1))^2 + x(t) +(x(t+1))^2 = y(t)$ is invertible

If there wasn't the $x(t)$ term, I could use $x(t) = x$ and $x(t) = -x$ to disprove invertibility, but I can't think of two functions that give the same $y(t)$ in this case. When I tried proving ...
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Symbolic math engines barf on this ostensibly tractable integral.

$$\frac14 \int_{-M\pi}^{N\pi - s} \cos(tu/M) \cos((t+s)u/M)(1-\cos(t/M))(1-\cos((t+s)/N))\space \mathrm d t$$ with integer $u$. Alpha runs out of time. Maxima gives a tremendous result that can ...
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1answer
40 views

Arcsine for a value

I want to exactly determine the arcsine (sine inverse) for a value. Say I take $\sin$ for $60000$, which is approximately $-0.866$. I want to get back $60000$ from this. Taking a sine inverse will not ...
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2answers
47 views

Very short theory question signals?

My teacher asked us this question yesterday in the lecture but it didn't make any sense to me. He asked: What do the coefficients of the exponential Fourier series represent? Also, what's the ...
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2answers
47 views

What calculation remains constant for discretely sampled points of a sinusoid on a window of 1/4th its period?

I have a univariate time series that consists of discretely sampled (equally spaced) points of a sinusoid. If you have a window that slides over these points (like this animation) with a length of ...
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1answer
56 views

2-D Fourier Transform of complex exponential with 2-D quadratic phase

I've been looking around to see if there is either an exact transform pair or an approximation to either of the following but have not been able to find anything: $$ \mathcal{F}_{xy}\left( ...
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58 views

Detecting the respiratory rate of a breating lung.

I am currently working with some data-sets that represents the movements of a beating heart and breathing lungs. The data-sets are represented as a collection of floats that range from 47 to 51. We ...
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1answer
25 views

Prove that the function in the domain of Z is a high pass filter

I need prove that the function \begin{equation} L(z) = 1-z^{-1} \end{equation} is a high pass filter, but I have not much understanding of the $z$ transform and what really the $z$ domain is. So how ...
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45 views

How does SVD work?

Trying to find information, and, no-one seems to know the answers. I have a time-series, represented by $T = [0, 1, 1, 0, \ldots, n]$ the time series is then transformed into the Spectral results: ...
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2answers
64 views

Reducing a two term signal to one term

I am trying to solve a phasor addition problem, reducing from its original form to $$X(t) = A \cos(\omega_0 * t + \phi)$$ The original equation is : $$X(t) = 2 \sin(\omega_0 * t + 45) + ...
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1answer
121 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
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51 views

how to calculate inverse Fourier transform of given absolute function?

how to calculate inverse Fourier transform of abs(omega)? i have tried by it's standard formula and its properties but didn't get the answer please help... I used duality property also but its not ...
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1answer
213 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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67 views

Fourier Transform of a Gaussian Signal?

As far as I know this is the formula for FT : On this question on part b) I fint on the answer the part with e^-jwt is changed with cos(wt) I have no idea how cos(wt) came in ... would you please ...
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1answer
48 views

Frequency response of Continous-time system

Not sure where to start on this one: $$H(s)={(s-j\omega_0)(s+j\omega_0)\over(s+\omega_0\cos\theta+j\omega_0\sin\theta)\left(s+\omega_0\cos\theta-j\omega_0\sin\theta\right)}$$ Sketch the frequency ...
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93 views

Artifacts and low frequencies FFT.

I am working on analyzing a time signal and want to preform a FFT. However I run in to some artifacts at low frequencies. I have managed to reproduce the behavior in a test signal. Given by $S(t) = ...
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1answer
54 views

what is the period of this sinusoidal function funtion

How can we find the fundamental period of this sinusoidal discrete function $x(n) = 10\cos{(\frac{4n\pi}{31}+\frac{\pi}{5}})$ I tried using the formulae $\frac{2π}{\omega}$ and got the answer 31/2, ...
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2answers
145 views

Z-Transform, Transfer Function, Poles & Zeros

I've been working on a question that I'm now stuck on. I need to: Determine the transfer function and poles-zeros of: $y[n]=0.5y[n-1]-0.25y[n-2]+x[n]$ So far I've carried out a z-transform in ...
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1answer
485 views

Bandpass filter with Fourier and inverse.

My understanding of signals is limited. I did a signal processing subject in engineering, but I can't say I got much from it. For me, the subject wasn't taught with enough 'real world' explanation - ...
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1answer
52 views

Z-transform: Convolution <=> Multiplication giving strange results

I try two slightly different routes to an answer, and get two different answers. (This is from a past exam paper.) Find h[n] if $ H(z) = \frac{1}{(1-az^{-1})^2} $ First try: $ H(z) = H_1(z)\cdot ...
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Error bounds in representing a vector using a truncated Moore-Penrose biorthogonal basis

I was reading and trying to reproduce the results in the arXiv preprint of Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression by Asaf ...
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1answer
100 views

Given a Poisson-noisy signal, what is the noise distribution of its Fourier transform?

Disclaimer: I'm not a mathematician, but here's my attempt at a mathy version of my question Start with a noiseless, discretely sampled expected signal $I(x_n)$. Construct a Poisson-noisy measurement ...
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1answer
55 views

Fourier analysis of an exponential function review

I am working through and reviewing some of the examples presented on Fourier analysis from a Modern Digital and Analog Communication Systems book. In one of the examples, the author goes through the ...
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1answer
115 views

calculating an incoherence property

With respect to Matrix Completion and Compressive Sampling (CS) I'm trying to understand how to calculate an incoherence property μ between two bases Φ and Ψ. Getting this incoherence is important ...
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65 views

Compressive Sensing - Incoherence Property

Compressive Sensing is built on 2 properties: 1) the sparsity of the representation basis relative to the sampling basis and 2) the incoherence between the singular vectors from each of the 2 bases in ...
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2answers
88 views

Applying a Kalman filter to a WiFi power signal

I have created an app that uses the power of a WiFi signal to determine distance to the WiFi access point. Problem with that power reading is that it is not very stable. I have been looking into ...
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64 views

Gradient of a complex quadratic form

I have to compute the gradient of the following expression: $$ \nabla_\overline{h} \left( h^H R h - h^H s\right) $$ where the overline means "conjugate of" and $^H$ means conjugate transpose (or ...
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1answer
72 views

fitting the content of an elliptical region in an image into the equivalent stretched circle

Assuming that I know the ellipse parameters (the major/minor axis, theta and the centre), and I could get the equivalent circle of this ellipse (I mean the equivalent x and y positions of the pixels ...
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1answer
550 views

Prove that Unit Impulse Function Integral is equal to one? [duplicate]

Unit impulse function is one of the special functions which is widely used in the field of signal processing. It has nice properties that helps in some situations specially its sifting property. But ...
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105 views

Continous wavelet transform and shannon Entropy.

Note: I have asked the same question on signal processing forum,but didn't get any answer. so it might be more like a math or physics question. Hope you don't consider it as cross-post. I am trying to ...
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1answer
99 views

circle affine transformation

I am trying to convert a region of pixels surrounded by an ellipse into an equivalent stretched circle.This basically means affine transformation. Assume I want to extract the region in light blue ...
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1answer
143 views

Convolution of indicator function with itself

A paragraph in Mallat's "A wavelet tour of signal processing" says: Spline Dyadic Wavelets A box spline of degree $m$ is a translation of $m+1$ convolutions of $\mathbf{1}_{[0,1]}$ with itself. ...
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1answer
122 views

Finding period of a periodic function

I am having some trouble finding the period of this function: $$W(\omega) = \frac{\sin[(2N +1)\omega \Delta t / 2]}{(2N + 1)\sin[\omega \Delta t /2]}$$ Here $N$ is an integer, $\omega$ is angular ...
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2answers
141 views

Why is the DTFT (Discrete Time Fourier Transform) unique to each input?

As the title implies. I know the DFT of a signal is unique due to the matrix, but can anyone give a solid explanation as to why the DTFT is unique for each signal input? Thanks for your time!
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41 views

Find the maximum of an integral function with respect to another function

I'm facing this statistical data analysis problem, where I have to maximize a certain statistic in order to find the optimal filtering function. I'm a little bit out of practice with the mathematics ...
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1answer
404 views

Calculate phase and amplitude of a sampled sine wave

I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two ...
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1answer
85 views

How to derive this frequency response?

Given this difference equation $y(k)$ ... $$y(k) = \frac{1}{K^2} \sum_{m = k-K+1}^k \; \sum_{n = m-K+1}^m x(n) - \frac{1}{L^2} \sum_{m = k-L+1}^k \; \sum_{n = m-L+1}^m x(n)$$ ... how does one derive ...
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1answer
84 views

Paley Wiener Theorem on sinc function

Use the Paley-Wiener theorem to argue that, although ${\rm sinc}\left(t\right)$ is bandlimited, ${\rm sinc}\left(t^{3}\right)$ is not. Explain how the above result allows reconstruction of some ...
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1answer
54 views

Complex Integration of DTFT

Question A discrete-time signal $u \in \mathcal{l}^2(\mathcal{Z})$ has DTFT \begin{equation} \hat{u}(\omega) = \frac{5+3\cos(\omega)}{17+8\cos(\omega)} \end{equation} Use complex integration to find ...
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36 views

Integration containing a complex number

Folks, Can I treat the complex number in the following integral: $$\frac1{2\pi}\int\frac1{(1+jw)^2}dw$$ as a constant and move it outside of the integral, like this: ...