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2
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1answer
39 views

$X \sim Rice(\nu,\sigma)$, what is the distirbution of $X^2$?

Let $X = |\nu e^{j\theta}+W|$, where $W \sim \mathcal{CN}(0,2\sigma^2)$, i.e. $X\sim Rice(\nu,\sigma)$, what is the distirbution of $X^2$? Note that X also can be writen in terms of real and imaginary ...
0
votes
1answer
49 views

Evaluate two dimensional frequency domain for single point

I need to compute one specific value in the original domain from the 2D frequency domain data I have. I can't just use IFFT for a whole set for performance reasons. I know how to do this in 1D by ...
1
vote
1answer
83 views

Have some queries about Fourier Transform

I have some queries about the Fourier transform In most of the cases, the Fourier transform of a signal is symmetric with respect to positive and negative frequency. I think the computational ...
0
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2answers
88 views

Whether the job of Fourier Transform is just to convert signals from time domain to frequency domain only or more than it?

I am a beginner . We convert a signal in time domain to frequency domain by applying Fourier transform on the signal to obtain frequency and phase spectrum. So,whether the job of Fourier transform ...
0
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0answers
19 views

Dsitribution of $|Ae^{j\phi} + W(t)|$, where $\phi \sim unif[-\pi,\pi]$

Let $Y(t) = Ae^{j\phi} + W(t)$, where $\phi \sim unif[-\pi,\pi]$ and $W \sim \mathcal{N}(0,\sigma^2)$. What is the probability distribution of $|Y(t)|$ ? If $\phi$ was deterministic, i.e. a constant ...
1
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2answers
47 views

Using Fourier transform to compute Fourier series.

I have found an exercise on a signal processing book that asks to compute the Fourier series of a function by using its Fourier Transform, let: $$ x(t) = \sum_{n=-\infty}^{\infty} \Lambda \left( ...
0
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1answer
100 views

Chirp with linearly changing frequency and amplitude?

A linear chirp or linearly swept sine is a signal in which the frequency changes linearly with time: the starting frequency changes into the ending frequency over time at a rate of: and ...
7
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2answers
581 views

What are the limitations /shortcomings of Fourier Transform and Fourier Series?

I am fond of Fourier series & Fourier transform. But every approach has some outcomes and some shortcomings. It's limitations lead to innovation of new approach. So, can anybody explain about ...
1
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0answers
36 views

PDF of $|X(t)| =| e^{j\omega_c t}+W(t)|$

let $X(t) = Ae^{j\omega_c t}+W(t)$, where $W(t)$ is a gaussian process that follows the statistics $W \sim \mathcal{CN}(0,\sigma^2)$ and $\omega_c$ denotes the carrier pulse frequency and $A$ is a ...
1
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0answers
22 views

Explain the formula of energy in signal processing [duplicate]

Please, give me intuitive understanding of this formula (http://en.wikipedia.org/wiki/Energy_%28signal_processing%29): So t is time, x(t) - signal function, integral is sum of this function on ...
0
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0answers
31 views

Laplace transform and “imaginary infinity”

I was recently studying Laplace transform for the first time, and I'd like to ask the following thing: there was an integral with limit of integration, something like that: a+j×infinity, j the ...
0
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2answers
56 views

Given the probability distribution of X, whats the PDF of X²?

Let's say we have a random variable $X$ with a certain probability density function $f_x(x)$. 1) How should I find out the PDF of the random variable $X^2$? Problem background: $X_1 = s_1 + W$, ...
0
votes
1answer
22 views

Probability function of Acos(x)

Let's say I have a signal $y(t) = Acos(2\pi f_c t)$, where $f_c$ is the carrier frequency and $t$ is the independent variable. Since I work with discrete signals i sample this signal with a sampling ...
0
votes
1answer
36 views

How to find out transient response of z-transform (discrete)

Given z-transform transfer function $H(z) = \frac{Y(z)}{X(z)}$, with the corresponding linear ODE, how does one find out transient response of such a transfer function given a certain input?
0
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0answers
16 views

is this possible to put condition on time series

I have a time series $y$ of $N$ data points. I want to apply ARX model with least squares estimation to this time series. Is this possible that I can apply a condition on the time series that if ...
4
votes
3answers
84 views

What the terms “basis functions” and “orthogonal” denote in the case of signals?

I am a beginer. I have read that any given signal whether it is simple or complex one,can be represented as summation of orthogonal basis functions. Here, what the terms Orthogonal and Basis function ...
2
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0answers
13 views

Fourier coefficients for pattern analysis

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
0
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1answer
25 views

How to calculate power of a non-continuous signal

I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it. The equation for power in my textbook is $\overline{m^2(t)} = ...
1
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0answers
21 views

Parameterizing a linear compressor

I am hoping to build a function $f_{A,B,\alpha}(x \in \mathbf{R} ) \rightarrow y \in \mathbf{R}$ that serves as a positive signal compressor. The function acts on an input signal $x\left(t\right)$ one ...
2
votes
1answer
69 views

Is this solution correct? [Discrete-time signals and systems]

Consider this question taken from Oppenheim - Discrete-time Signal and Systems: Now consider its solution (from the Solutions manual) My question is: is the solution for itens (a) and (b) valid? ...
0
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0answers
29 views

A 2D smoothing convolution filter

I'm trying to find the right form of a 2D filter that will do the following to a matrix after linear convolution: Let A = [ ? ? ?] [ ? ? ?] [ ? ? ?] and B = ...
1
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0answers
19 views

Filter transfer function to state space

I'm trying to change this filter transfer function to state space representation $ y_t=\frac{1+b_1 z^{-1}}{1+a_1 z^{-1} +a_2 z^{-2}}u_t $ I tried writing it as time series $ y_t+a_1 ...
2
votes
2answers
112 views

Fourier Decompositon problem

have a look at this video of Fourier Decomposition of an image (otherwise you can also refer the image, which shows few plots of different extracted waves from an image). We also know that a Fourier ...
0
votes
1answer
52 views

Calculating Fourier Transform of $\sum_{n=1}^{3}\sin(2\pi \frac{n}{8}\frac{t}{T})$

This question deals with finding the Nyquist Frequency of a given signal. Suppose you have the signal $x(t)=\sum_{n=1}^{3}\sin(2\pi \frac{n}{8}\frac{t}{T})$ in the time domain where $T>0$ is some ...
2
votes
1answer
37 views

What is the sum over a shifted sinc function?

What is the sum of a shifted sinc function: $$g(y) \equiv \sum_{n=-\infty}^\infty \frac{\sin(\pi(n - y))}{\pi(n-y)} \, ?$$
0
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0answers
27 views

How to represent a periodic function as the sum of sinc functions in fourier transform

Suppose function $f(t)$ is 1-periodic. This means that in fourier transform, $F(\omega)$ is sum of impulse signals (dirac delta function and its shifts) at the multiples of $1$. Now we can form $g(t)$ ...
1
vote
1answer
52 views

What will happen if we try to reconstruct signal using phase only or magnitude only?

I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together My question is that What will happen if we try ...
1
vote
1answer
27 views

Meaning of co-ordinate system of Covariance matrix

Can we think that any matrix representation has an underlying co-ordinate system? Now consider a positive definite sample covariance matrix. If so what is the meaning of the co-ordinate system of the ...
1
vote
2answers
44 views

Discrete Fourier Transform of generalised Hamming Window

The generalised Hamming Window is defined as: $$ w(n) = \begin{cases} \alpha - (1 - \alpha)\cos(2 \pi n /N), & \text{if $ 0 \leq n \leq N$} \\ 0, & \text{otherwise} \end{cases} $$ with $ 0 ...
0
votes
0answers
31 views

Fourier transform of a 3sinc^2(100πt)

I'm currently studying for an exam, and I'm not sure the textbook's answer for the fourier transform of 3sinc^2(60πt) is correct. For this question, I incorporated the duality property. Below is my ...
1
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0answers
18 views

How to express a signal in terms of Riesz bases?

Fast discrete wavelet transform allows us to express any discrete signal in terms of wavelet bases by convolution with filter coefficients. How can one express a digital signal in terms of ...
1
vote
1answer
67 views

Proof of the discrete Fourier transform of a discrete convolution

Let the discrete Fourier transform be $$ \mathcal{F}_N\mathbf{a}=\hat{\mathbf{a}},\quad \hat{a}_m=\sum_{n=0}^{N-1}e^{-2\pi i m n/N}a_n $$ and let the discrete convolution be $$ ...
0
votes
0answers
14 views

Errors of approximating continuous Fourier transform by discrete Fourier transform

In http://planetmath.org/approximatingfourierintegralswithdiscretefouriertransforms some error analysis of using DFT to approximate continuous Fourier transform is indeed done, but there are things I ...
0
votes
1answer
32 views

Show if signal is time variant or not

I know that I have to show that \begin{align*} y[n-n_0] &= f \Big( \{x[n - n_0]\} \Big) \end{align*} in order to tell if a signal is time-varying of not. Having a signal $y[n] = ...
1
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0answers
44 views

Real and imaginary part of an Eigenvector.

Apology if my question not clear or appropriate. Consider a complex positive definite sample covariance matrix (SCM) generated by a band limited signal on a set of sensors. Is there a relation ...
0
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0answers
53 views

Savitzky-Golay Coefficients for end points

I've been looking for solution to clean up SG Filter end points and I discovered a shifted set of coefficients in Numerical Recipes that might do the trick. Nr = 0; Nl = 4; 0.086, -0.143, -0.086, ...
1
vote
1answer
53 views

Is there a relation between half space and Eigenvectors?

I request earnestly apology if the question is not well defined. I think I understand half space and Eigenvectors to an extent, but could not connect both of them under the same geometry or ...
0
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0answers
38 views

Spectral Analysis: How to interpret a periodogram.

I'm reading a paper that has to do with financial volatility. The author uses a periodogram to estimate the power spectrum density of the volatility time-series. Evidently, the plot (below) is ...
0
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0answers
28 views

Condition Butterworth polynomial

My course states that a polynomial is a Butterworth polynomial when it satisfies the following condition: $|B(j\Omega)|=\sqrt {1+{\Omega}^{2\,n}}=\sqrt {1+{(\omega/\omega_p)}^{2\,n}}$ I'm really ...
2
votes
0answers
93 views

Properties of eigenvectors of a sample covariance matrix?

My apology if the question is not appropriate. For me Eigenvectors are quite a mystery. Does it have any property that we can relate to the matrix it came from? By property I mean something like the ...
0
votes
1answer
36 views

how can I plot the infinite sum in matlab [closed]

I'm lookin for a way to plot $$\hat x= \sum_{n=-\infty}^\infty 0.5cos(1.3\pi n)sinc(t-n)$$ in matlab, and I can't find out how
1
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0answers
31 views

A “Fourier Phase” for (stationary) random processes?

Let $X_t$ be a real w.s.s. random process. Its spectrum is given by $S(f)=\mathcal{F}R_X(\tau)(f)$ where $R_X$ is the process autocorrelation. As $X_t$ is real, the spectrum will be real and ...
1
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0answers
23 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal f(t) that is continuous and periodic. It is known that this f is T-periodic. (but it's not necessarily a single cosine f(t).( I'd like to make the mean of samples be ...
0
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1answer
26 views

Frequency scaling property for Fourier series

For Fourier transform, there is an equation connecting time-scaling with frequency-scaling. (By scaling, I mean multiplying by constant for time or frequency) Is there such a relation for Fourier ...
0
votes
1answer
34 views

Help in understanding step function calculation

Dear community I would appreciate if you can help me understand these equations. I mean how did he jump from line 1 to line 2? How do u[n] get cancel? Then in the last line where did the "8" come ...
1
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0answers
16 views

How to check periodicity of $f(t)$ using samples

Suppose that we know that signal $f(t)$ is $T_1$-periodic. Let $f_1 = 1/T_1$. But we want to know whether signal is $T_2$-periodic also. Let $f_2 = 1/T_2$, and $f_2$ is positive integer multiples of ...
0
votes
1answer
29 views

If $f(t)$ is periodic, is there any $t$ that would equal to DC components?

Suppose $f(t)$ is periodic with period $T$. Would there be $t$ that would necessarily equal to DC component (it can be scaled)? By DC component, I mean $F(0)$ where $F$ is fourier coefficient of $f$. ...
0
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0answers
23 views

Is there anything similar to DTFT for Fourier series?

So if sampling condition is met well, with aperiodic signals we have discrete-time Fourier transform (DTFT) that allows us to get frequency-domain data that resemble continuous-time fourier transform. ...
0
votes
1answer
24 views

Convergence property of DTFT toward DFT when function is periodic

from Wikipedia: When the input data sequence $x[n]$ is $N$-periodic, DTFT can be computationally reduced to a discrete Fourier transform (DFT), because: $ X_{1/T}(f)$ converges to zero ...
1
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1answer
24 views

Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies?

Is it possible for continuous fourier transform of a function to have values only on finite number of frequencies? Or do these values necessarily impulse values, not complex numbers?