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1answer
99 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}} + ...
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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 ...
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1answer
35 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 ...
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1answer
36 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 ...
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1answer
54 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 ...
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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 = ...
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2answers
105 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. ...
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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 ...
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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 ...
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0answers
35 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 ...
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1answer
102 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 ...
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22 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 ...
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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 ...
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0answers
13 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 ...
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0answers
34 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 ...
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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 ...
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3answers
67 views

Is $y[n]=x[n]-x[n-1]$ invertible system?

Well, the title says everything. I know I can find a z-transform, find $H(z)$ and then find a appropriate invert system and comment on that. How do I explain it to a person who does not know ...
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0answers
16 views

Sampling Theorem for Lattices

I am looking for a reference for an analogue of the Shannon sampling Theorem for more general lattices (in any dimension). Something along the lines of the theorem in this wikipedia article: ...
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17 views

Inverse z-transform of $z^4+1.827z^3+2.338z^2+1.827z+1$

I need to transform the following $H(z)$ back to time domain: $$ H(z)=(z-e^{j\frac{8}{15}\pi})(z-e^{-j\frac{8}{15}\pi})(z-e^{j\frac{12}{15}\pi})(z-e^{-j\frac{12}{15}\pi}) $$ I did the following steps ...
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1answer
146 views

How to determine the states of ideal diodes in simple circuits with only DC sources and resistors [closed]

How can the states of ideal diodes be determined in simple circuits with only DC sources and resistors without a trial and error approach? I posted this question on Electronics SE and found out ...
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0answers
20 views

Is a signal summable when given a z-transform?

The output of a system is given as z-transform: $$ Y(z)=\frac{1+z^{-2}}{(1+\frac{1}{4}z^{-1})(1-\frac{1}{2}z^{-1})} $$ I want to know if the signal in the time domain is summable, meaning that the ...
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0answers
62 views

fourier series of unknown functions

I am confused in understanding use of fourier expansions of functions. This answer, for example says that we can write voice as a sum of sines and cosines of different frequencies and amplitudes, but ...
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1answer
98 views

Is the power of a complex exponential signal always zero?

Is the power of a complex exponential signal always zero? For example say I have the function $ f(t) = Ae^{i\omega t}$ Then, I think power is defined as: $P=\int_{-T/2}^{T/2} f^2(t) dt$ So is it ...
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0answers
23 views

Do combined waves with non-rational frequencies have a common period?

I am facing a problem where I have two waves combined: \begin{equation} y = A\sin(b_1x)+B\cos(b_2x) \end{equation} Where $ b_1 $ and $ b_2 $ are non-rationals. i.e. \begin{align} & b_1 = ...
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15 views

How do I compute the output of this LTI system?

2.11. Consider an LTI system with frequency response $$H(e^{j\omega})=\frac{1-e^{-j2\omega}}{1+\frac12e^{-j4\omega}},\quad-\pi<\omega\le\pi.$$ Determine the output $y[n]$ for all $n$ if the ...
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0answers
68 views

Convolution between a discrete stochastic signal and a continuous function

I'm trying to find the convolution between a discrete, stochastic signal (for which I have data at each t) and an exponential decay function (which is continuous in t). Now I know that one can ...
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1answer
48 views

Expressing a function in terms of sinc(t)

Given the function: $S(t) = sin(t/\Delta)/t$ How can one express this function in terms of: $S(t) = sin(t)/t$ Thanks!
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1answer
53 views

Why do high-frequency dynamics quickly go away in a step response?

As we know, a step input hits all the frequencies of a dynamical system. However, my professor told me today that the high-frequency response is only present for a short time at the very start, and ...
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1answer
28 views

How does hard clipping change the frequency of a pure sinusoidal signal?

Suppose that we decide to limit the magnitude of a real-valued signal $f(t)$ by maximum cutoff $V_s$. Thus, if $|f(t)| > V_s$, a transformed signal $g(t) = V_s$ or $g(t) = -V_s$ depending on the ...
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0answers
9 views

Help with solving for difference equation coefficient terms

I am having trouble remembering how to solve for the $a_k$ and $b_k$ terms for a difference equation. (it has been some time since taking a signal processing course, where I first learned) I am trying ...
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2answers
60 views

Using DTFT to find the sum of $\sum_{n=-\infty }^{\infty }\text{sinc}(n\alpha_1)\text{sinc}(n\alpha_2)$

I am trying to use DTFT (as asked in a problem) to find the following sum $$\sum_{n=-\infty }^{\infty }\text{sinc}(n\alpha_1)\text{sinc}(n\alpha_2)$$ for real $\alpha_1>0$ and $\alpha_2<1$. I ...
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0answers
21 views

Express covariance function of a sampled process as a fourier transform (help with proof)

I'm wrestling with this theorem in my 'stationary stochastic processes' course.It's about sampling of a continous process and a way of rewriting the covariance function of the sample(I'm not entirely ...
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1answer
42 views

Calculate Inverse Discrete Time Fourier Transform

Calculate Inverse Discrete Time Fourier Transform of the following where $|a| < 1$: $$ X(e^{j\omega}) = \frac{1-a^2}{(1-ae^{-j\omega})(1-ae^{j\omega})} $$ Plugging this directly into the IDTFT ...
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23 views

Derive Symmetry Properties of Discrete Fourier Transform

Using the standard definitions of IDFT and DFT: \begin{align*} x[n] &= \frac{1}{2\pi} \int_\pi^\pi X(e^{j\omega}) e^{j \omega n} d\omega \\ X(e^{j\omega}) &= ...
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1answer
80 views

Simple Discrete Convolution Question

With the discrete step function $$ u[n] = \begin{cases} 1, & n \ge 0 \\ 0, & n < 0 \\ \end{cases} $$ And the output $y[n]$ defined as a discrete convolution of the input $x[n]$ ...
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1answer
85 views

Series of $\csc(x)$ or $(\sin(x))^{-1}$

In some cases I found that $$\csc(x)= \lim\limits_{k\rightarrow \infty}\sum_{n=-k}^{k}(-1)^{n}\frac{1}{x-n\pi}$$ Is anything to prove or disprove that?
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21 views

Variance of estimating coefficients by correlating a sequence

I have a sequence $$ r[n] = a_1.t_1[n] + a_2.t_2[n] + a_3.t_3[n] + ... $$ where $t_1, t_2, t_3,...$ are uncorrelated, two-level (+A/-A), zero mean, pseudo-random sequences. To estimate $a_1$, ...
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1answer
30 views

Signal processing very short question?

We have $Y(k)=x(k-1)+ kx(k-5)+x(k)^4$ .I have to find the impulse response for the function So I know that $G(z) = \frac{Y(z)}{X(z)}$ but how do I relate that to this? $Y(z)=(z^{-1}) + k(z^{-5})+ ...
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1answer
54 views

Expected value of product of sinusoids

In the book Adaptive Signal Processing by Widrow, an equation (2.20) on page 23 is presented without proof as: $$E \left[ x_k x_{k-n} \right] = \frac{1}{N} \sum_{k=1} ^{N} \sin\left(\frac{2 ...
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0answers
49 views

Fourier kernels relations to windowing in signal processing.

In engineering a common practice is to "window" a signal (by multiplying a function which decays smoothly at each end) before applying a Fourier transform. Windowing is done to avoid false frequency ...
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0answers
36 views

What are the name of these signals

It might be funny but there are two signals which confuse me about how to call them. Signal1: http://s3.postimg.org/ffefhwqyr/Capture1.png Signal2: http://s3.postimg.org/samf4o683/Capture2.png I am ...
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29 views

Decompose summation of signals

Imagine a summation of three distinct signals such as in the following graphic. Is it possible to estimate the original signals? Below is a matlab-code to generate the image: I have found similar ...
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2answers
41 views

Mathematical backing for observations seen in adding independent random variables together

I have a function $Y = F(N)$ that takes as an argument an integer number $N$ and returns a summation of $N$ sine-waves of different random parameters. I have plotted the results of two function calls ...
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14 views

Signal processing linear invariant causal systems

What is the frequency response of the linear invariant causal systems? I know that the response of linear invariant causal systems is g(k)=0 for k<0 but how about the frequency response?
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36 views

Fourier series for a Sinusoid in a conventional way?

So my TA in class introduced this amazing way of finding fourier series coefficients for a sin wave, by writing $ sin( \omega t ) = (e^{i\omega t}-e^{-i\omega t}) / 2i $ ----(1) Hence getting the ...
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1answer
82 views

How should I calculate a rolling autocorrelation?

I have an array of data $ \mathbf{y} \in \mathbb{R}^n $, and I need to calculate the lag-1 autocorrelation between sections of this array 7 elements long. For all intents and purposes, we can imagine ...
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4answers
94 views

Integrating unit impulse function

Given that, $$ \delta(t) = \begin{cases} \infty & \text{if } t = 0 \\ 0 & \text{if } t \ne 0\\ \end{cases}$$ How is it that, (A) $$ \int_{-\infty}^\infty \delta(t) dt = 1 $$ (B) $$ ...
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1answer
48 views

Rewrite sinc function

I am working on an exercise in binary transmission systems. The pulses are modeled using a special sinc-function in the time-domain, $f_0$ is the bitrate but just a constant in time domain: $s(t) = ...
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18 views

Change of Variable for Time Invariance Check

I've been studying for a signals and systems class coming this fall and can't figure out how the following change of variable is being applied according to standard definition: $$T[x(t-\sigma)] = ...
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1answer
90 views

confused with the FFT output

I am taking some sensor output and doing fft on it. how to get the exact frequencies from the complex output? my understanding is that bin frequencies and the input frequencies are different. Please ...