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A question in signals and systems [on hold]

How do I mathematically prove that $Y(t)=2X(t)$ is linear and memoryless?
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12 views

how fast should i output discrete data to recreate continuous frequency?

How do i recreate a continous sine wave from a discrete set of points? I have a dataset consisting of a discretized sine wave, but how fast should i send each value such that the receiver knows that ...
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2answers
25 views

Convert from complex exponentials to sinusoids

I'm working through some notes on signals and systems, and got stuck trying to fill in the missing steps in converting the left hand side to the right hand side of the following equality: $$ \alpha_i ...
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1answer
29 views

How Fourier decomposition is performed?

The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it. Suppose a sinusoidal periodic signal is ...
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1answer
35 views

What information is contained in the phase spectrum of a signal?

For any given signal using Fourier transform, we can compute it's magnitude and phase spectrum. In that I want to give focus on phase spectrum. But for phase spectrum, I don't have much data ...
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0answers
28 views

Can a DTFT have a period different of $2\pi$?

I think almost everything is in the title. In an exercise, a DTFT is given : $$X(e^{j\Omega}) = \sin(\Omega) + \cos(\Omega/2)$$ The period of this DTFT is $4\pi$. Is that possible? I mean, the ...
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1answer
21 views

Please explain the $*$-operator in $x^*[n]$

I have to calculate the $IDFT$ for a signal $y_2[n]$: \begin{align*} y_2[n] = DFT^{-1} \Big\{ \Im m \{ \tilde{X}[k] \} \Big\} \end{align*} and I am allowed to use some formulas from a collection ...
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1answer
18 views

Finding peaks and oscillations in a signal

I am working on a problem where I'm analysing a signal and trying to find a measure of whether a roughly Gaussian shape appears or oscillations - though the oscillations may not be periodic. For ...
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1answer
23 views

Please verify correctness of $H_2(e^{j\theta}) = \sum_{n=-\infty}^{\infty} h_2[n] \cdot e^{-j\theta}$

This frequency spectrum of a signal $h_2[n]$ is bugging me. I am not sure if what I've done here is correct. It's the sum \begin{align*} \sum_{n=-\infty}^{\infty}(-1)^{n-1} \end{align*} in ...
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1answer
39 views

Phase-spectrum: $arg(\cdot)$ function

I came to this frequency spectrum for a signal $h_1[n]$: \begin{align*} H_1(e^{j\theta}) &= \sum_{n=-\infty}^{\infty} h_1[n] \cdot e^{-j\theta} \\ &= \sum_{n=-\infty}^{\infty} (0.3 \cdot ...
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1answer
23 views

Dot product of a sinusoid with a complex tone in Octave

I am trying to figure out how to solve this problem; Now make a new sinusoid with amplitude 1 and frequency 1000Hz. Calculate the dot product of this sinusoid with your complex tone using ...
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1answer
73 views

Can anybody give justification about features of phase and magnitude spectrum in case of Fourier transform?

I have read that from Fourier transform we obtain magnitude and phase spectrum. The magnitude spectrum tells you how strong are the harmonics in a image and the phase spectrum tells where this ...
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2answers
94 views

What do $a_0$ ,$a_m$ and $b_m$ terms mean in the Fourier series formula?

Let us take an example, a white ray (which is composed of bunch of frequency components) is passed through a prism, the ray gets split (decomposed) into its elementary vibgyor colours (i.e.different ...
2
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1answer
35 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 ...
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1answer
45 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 ...
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1answer
71 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 ...
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2answers
70 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 ...
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0answers
17 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 ...
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2answers
44 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( ...
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1answer
61 views

Find the fourier series for following signal $x(t)$ [closed]

Find the fourier series for following signal $x(t)$ :
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1answer
65 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 ...
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2answers
416 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 ...
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0answers
34 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 ...
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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 ...
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0answers
26 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 ...
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2answers
52 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: $X_1 = s_1 + W$, ...
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1answer
19 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 ...
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1answer
15 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?
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15 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
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3answers
73 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 ...
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Band Periodicity

this is one of sounds features and it has been used in some AI voice app. "The periodicity property of each sub-band is represented by the maximum local peak of the normalized correlation function." ...
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12 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 ...
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1answer
24 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)} = ...
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0answers
16 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
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1answer
63 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? ...
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0answers
20 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 = ...
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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
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2answers
97 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 ...
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1answer
46 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 ...
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1answer
21 views

What is the sum over a shifted sinc function?

What is the sum of a shifted sinc function: $$g(y) \equiv \sum_{n=-\infty}^\infty \frac{\sin(\pi(n - y))}{\pi(n-y)} \, ?$$
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0answers
18 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 $g(t)$ ...
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1answer
40 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 ...
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1answer
26 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 ...
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2answers
41 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 ...
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0answers
30 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 ...
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0answers
16 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 ...
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1answer
50 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 $$ ...
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0answers
10 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 ...
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1answer
29 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] = ...
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0answers
32 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of ...