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17 views

integration for the this function

I would like to integrate a function in the range $[0,1]$. I tried a lot of ways including Mathlab. All solutions come in terms of some error function. I would like the answer in terms of $a$. ...
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0answers
22 views

Unknown variable in formula - binomial coefficient? [duplicate]

I'm currently researching a filter and don't quite understand one of the equations used there, since it contains a variable I don't know how to calculate: $$(1)\,\,a^{m, k}_s = \frac{c^{k, ...
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0answers
28 views

deconvolution of exp($x^2$)

I would like to know whether we can get the function of type exp($x^2$) by convoluting any functions. That is which function convolution gives exp($x^2$). Thanks in advance
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1answer
28 views

Kolmogorov-Zurbenko filter - Calculation of coefficients

I'm currently researching the Kolmogorov-Zurbenko filter and trying to implement it myself as a way to smooth one-dimensional signal strength values. The basic filter per se is pretty easy to ...
2
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0answers
20 views

Fast Way to Compute DFT with index summation subject to a constraint

I really appreciate if anyone can help me with this problem. Problem: Let $W_n=e^{\frac{2\pi i}{N}}$ which is the $N$th root of unity. The backward Discrete Fourier Transform of a complex vector ...
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0answers
27 views

Compressive sensing for complex matrix

I'm fairly new to compressive sensing, and I have been looking for a MATLAB implementation of the problem $$ A x = b $$ where $A$ is non square, $x$ is kind of sparse and all the numbers involved are ...
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0answers
18 views

How to analyse data samples scattered in time?

I want to analyse data corresponding to events happening at arbitrary moments in time, and conveying quantitative information. My goal is to study the relationship between the sum of these quantities ...
1
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2answers
60 views

How to derive FWHM of sinc function

So this is probably a simple question, but I am unable to get my head around it. If we have $\operatorname{sinc}(2 \pi v L)$, what is the width of that $\operatorname{sinc}$ in terms of $v$ at half ...
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1answer
21 views

Show that a sinusoid having a frequency larger than one corresponds to a sinusoid having a frequency less than one.

I am studying electrical engineering for fun online. There is this one solution to a question on an online textbook that does not make any sense to me. The question is: Show that $\cos(2\pi ...
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1answer
47 views

What if the Fourier series of a periodic function also has periodic coefficients $a_k$

If given that $x(t)$ is a periodic continuous time signal, with periodic $T$. It can be expressed by the Fourier series, i.e. $x(t)=\sum\limits_{k=-\infty}^{+\infty}\,a_k\cdot e^{j k \frac{2 ...
2
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0answers
15 views

Rate of convergence of a Weyl-Heisenberg (Gabor) frame expansion

If $\{g_{m,n}\}$ is a Gabor frame for $L^2(R)$, with window function $g$, and $f \in L^2(R)$, is there a bound on the approximation error of $f$ using a finite subset of the frame? That is, is ...
1
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2answers
30 views

Why exponential is ignored in particular solution for impulse response ??

For a system govern by the equation: $$ 2y'(t) +4y(t) =3x(t) $$ To calculate it's impulse response we replace $y(t)$ with $h(t)$ and $x(t)$ with $\delta(t)$ and get $2h'(t)+4h(t)=3\delta(t)$ which's ...
1
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0answers
13 views

Nonparametric changepoint detection for point process

This is a replication of a question I've recently asked on Cross Validated. It hasn't received an answer or much attention, so I've posted it here. I have a family of point processes representing ...
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0answers
36 views

How windowing is done in Short time Fourier transform?

From Fourier transform we can get features localised in Frequency domain but we neglect all time domain features. So we use Short time Fourier transform (STFT) in which we do some windowing to ...
2
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1answer
34 views

Convolution of various functions

There is asked in an example to do convolution $ h_1(t)*h_2(t) + h_3(t)*h_4(t) $ where $h_1(t) = e^{-2t}u(t)$ $h_2(t) = 2e^{-t}u(t) $ $h_3(t) = e^{-3t}u(t) $ $h_4(t) = 4\delta(t) $ and then the ...
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1answer
45 views

First Order differential equation … How did they do it ?

I was studying "continuous and discrete signals and systems" by Samir S. Soliman where I encountered with this first order differential equation: $$ \frac{dy(t)}{dt} + \frac{R_1R_2}{L(R_1+R_2)}y(t) = ...
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0answers
35 views

How to proceed with this simple proof?

If $$\alpha_k = \sum_l a_l \ \ g((k-l)T-l\Delta T)$$ $$s_k = \sum_l \alpha_l \ \ q((k-l)T+k\Delta T)$$ where $a_l \in \pm1$ and $g(t) = \frac {\sin(\pi t/T)}{\pi t/T}$ and $q(t) = \frac {\sin(\pi ...
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1answer
50 views

Condition for existence of Fourier transform?

We can convert signal into frequency domain using Fourier transform. But I think we can't compute Fourier transform of any signal . Fourier transform also should have some limits. So I want to ask ...
0
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1answer
21 views

Find a difference equation for $h_r[n]$

I'm having a signal \begin{align} h_r[n] &= r^n \sin\Big( \frac{\pi}{2} n \Big) u[n] \end{align} where \begin{align} u[n] &= \begin{cases} 1 & \mbox{if } n \geq 0 \\ 0 & ...
1
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1answer
18 views

How does this transform algebraically

I have two lines of working that I am trying to understand. First line: \begin{equation} \frac{(1+Z^{-1})\tan\frac{wc}{2}}{(1-Z^{-1})+(1+Z^{-1})\tan\frac{wc}{2}} \end{equation} Next line: ...
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0answers
34 views

Recovering Time Shift Using DFT of Translated Square Pulse?

As an exercise, I attempted to manually translate a pulse $n_0$ steps to the right and recover the translation using the time-shift property. The problem I'm encountering is that the phase unwrapping ...
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0answers
30 views

Properties of the sum of two sine waves with different frequencies.

When you have the functions $u_1 = A_1 \sin(\omega_1 t)$ $u_2 = A_2 \sin(\omega_2 t)$ $u_{\text{total}} = A_1 \sin(\omega_1 t) + A_2 \sin(\omega_2 t)$ How do you calculate the average amount of ...
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3answers
42 views

What does it mean that a sine wave is unchanged when added to another sine wave?

From the wikipedia article on sine waves: The sine wave is important in physics because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and ...
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0answers
35 views

Is there an exact solution for this resampling (synchronization) problem?

I want to know if there is an exact solution for the following problem and how to approach solving it: I have a discrete-time signal where the Nyquist theorem is satisfied: $$ r_k = \sum_i ...
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1answer
30 views

How can I remove correlated noise spikes from 2 signals?

I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I ...
0
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2answers
99 views

Why Fourier series has summation and Fourier transform has integration symbol in their respective formulae?

Fourier transform for aperiodic signal is given by $$ X(\omega) = \int\limits_{t=-\infty}^{+\infty} x(t) e^{-j \omega t} dt. \quad (1) $$ Fourier series for periodic signal is given by $$ y(t) = ...
3
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2answers
61 views

Calculation of the power of a signal

Suppose we want to calculate the power of the signal $y(t) = m(t)\cos(\omega_c t)$, where $m(t)$ has zero mean, and the power of $m(t)$ is P watts. It is easy to show that the power of $y(t)$ is ...
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0answers
47 views

Compare between Short Time Fourier Transform and Wavelets

Fourier transform is localised in only frequency domain but Short time Fourier transform(STFT) is localised both in time and frequency domain same as in wavelets. I want to know How are STFT and ...
0
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0answers
30 views

Signal processing and Z transform question?

I was reading a solved exercise and it said in a part that $u(k-1)* [z^{-1}]$ is equal to $z^{-1}$. Why is that so? Also, is $u(k-4)* [z^{-1}]$ equal to $z^{-1}$?
2
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0answers
28 views

Acceleration/Position signal correction

I have a set of data for a car position, velocity and acceleration. % my data time car_x car_velocity car_acc The problem is that these arrays have error and I ...
1
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1answer
42 views

Linear combination to recover particular data entry from denoised data?

Let $\mathbf{x} = [x_1, x_2, x_3]^t$ the 'data' where $x_1$ is considered to be 'noise', $M$ a $3\times 3$-matrix with full rank, and $\mathbf{y} = M\mathbf{x}$ the obserced mixture. Let $m^-_i$ ...
2
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0answers
29 views

Inversion of the Burrows Wheelers Transform

The "Burrows-Wheeler Transform" in signal processing is a transformation which is used in for instance data compression and pattern recognition. It can be described in mathematical terms as: Start ...
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0answers
21 views

What is the range on a fourier transform?

In particular, I want to know the range of the coefficients on the type-IV discrete cosine transform. Assuming no normalization factor or window is applied, what interval can I expect the coefficients ...
1
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2answers
83 views

Is Fourier series used always for periodic signals and Fourier transform for aperiodic signals only?

I want to ask basic question. In our mathematics classes ,while teaching the Fourier series and transform topic,the professor says that when the signal is periodic ,we should use Fourier series and ...
1
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1answer
26 views

Inversion of $z$-transform using partial fraction decomposition

I want to inverse a $z$-transform of this general form $$X(z) = \frac{b_0 + b_1z^{-1}+\cdots+b_Mz^{-M}}{a_0 + a_1z^{-1}+\cdots+a_Nz^{-N}}$$ where $M$ < $N$. In order to do this, I use partial ...
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1answer
42 views

Fourier synthesis of periodic signals

I was reading the Fourier synthesis of periodic signals But I didn't understand the sentence i.e. "Although the calculation of $a_0, a_1, b_1, a_2, b_2$, is a mathematically straightforward ...
0
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0answers
15 views

Wiener filtering for image denoising

To my knowledge, Wiener filter is a least mean squares filter, which minimizes the mean squared error between the filtered signal and the target signal. (http://en.wikipedia.org/wiki/Wiener_filter) ...
0
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0answers
22 views

Example of BIBO stable system that is not internally stable

In the theory of system, we know that a system can be BIBO stable but not internally stable (if there is a pole-zero cancellation in the transfer function for example). I find this concept quite ...
0
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0answers
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 ...
0
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2answers
36 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 ...
1
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1answer
79 views

What is the importance of phase spectrum in Fourier transform

For any given signal using Fourier transform, we can compute it's magnitude and phase spectrum. But I have found that while discussing Fourier transform ,only frequency spectrum or magnitude ...
1
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0answers
39 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 ...
0
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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 ...
1
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1answer
21 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
37 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 ...
0
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1answer
40 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 ...
0
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1answer
32 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 ...
0
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2answers
113 views

Features of phase and magnitude spectrum?

I have read in many books that whether the signal is 1D or multidimensional , The magnitude spectrum tells you how strong are the harmonics in the signal and The phase spectrum tells where this ...
3
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2answers
122 views

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

We know that a Fourier series for signal $x(t)$ is given as $$\frac {a_0} 2 + \sum \limits _{m=1} ^\infty (a_m \cos \frac {2 \pi m t} T + b_m \sin \frac {2 \pi m t} T)$$ So my question is what ...
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 ...