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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
71 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 z-...
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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: https://...
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0answers
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
154 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 that ...
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22 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
79 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
105 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 = \sqrt{3+\...
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17 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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88 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
55 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
34 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
61 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
22 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
45 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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0answers
26 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}) &= \sum\limits_{n=-\infty}^\...
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1answer
98 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
92 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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0answers
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 $a_1$, $r[n]$...
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1answer
31 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})+ z^...
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1answer
57 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 \pi k}...
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0answers
56 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
37 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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0answers
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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0answers
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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0answers
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
115 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
95 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
51 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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0answers
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
94 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 ...
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0answers
47 views

averaging of multiple curves for signal processing

I have response (vibration amplitude over frequency steps) measured over various point on my structure. In simpler way: i have 5 response curves(amplitude vs frequency plot) from same structure is ...
2
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1answer
72 views

Find $a$, given $y(n)=x(n)+ax(n-d)$, interesting question

Me and two friends of mine are working on a project (scholarly purposes only). The goal of this project is to clean an audio signal (speech, a song, anything audio) of echo. Generally speaking, if $x(...
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0answers
25 views

Express the sum of squares as a percentage of how well two signals match?

So I am using matlab to compare two signals using the sum of squares. So the best possible match will be zero. eg $\sum(y_2 - y_1)$ where $y_2 = y_1$ would be $0$. The larger the sum of squared value ...
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1answer
41 views

How to calculate the partition function of a given distribution?

As noted in A FULL BAYESIAN APPROACH FOR INVERSE PROBLEMS, let $ y = Ax + n$, where $y$ is a $m$ dimensional signal and $n$ is white Gaussian noise with precision $\beta$, so we have: $$ y|x, \beta \...
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0answers
116 views

Is there a closed-form approximation to a band-limited sawtooth?

A partial Fourier Series with no coefficients is equal to the closed form expression: $${A \over n} \sum_{k=1}^n \cos(k\theta) = {A \over 2n} \left\{{\sin([2n + 1]\theta/2) \over \sin(\theta/2)} - 1\...
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1answer
28 views

Can an arbitrary real function be written in terms of quadratures of an arbitrary frequency with time dependent coefficients?

Given a real function $f$, and a frequency $\Omega$, is it the case that there exist two other real functions $I$ and $Q$ such that $f$ can be written as $$f(t) = I(t) \cos(\Omega t) - Q(t) \sin(\...
2
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0answers
70 views

Sampling a Chebyshev polynomial with the discrete cosine transform

I have a Chebyshev polynomial $f$ of degree $n$ in point-value form \begin{align} f&=:S = \left( \left( x_i, y_i \right) \right)_{i=0}^n, \tag{1} \\ x_i &= \cos\left( \frac{i \pi}{n} \right), ...
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2answers
72 views

Help needed with the integral of an infinite series

Can you please help me with the integral of this series? I came across it in a signal processing paper and haven't been able to figure out the solution myself. $$ \int\limits_{(n-1)T}^{nT}\left[\...
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1answer
61 views

Help needed with the integral of an infinite series

Can you please help me with the integral of this series? I came across it in a signal processing paper and haven't been able to figure out the solution myself. $$ \int\limits_{(n-1)T}^{nT}\left[\...
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0answers
25 views

DFT of subdomain of periodic domain

$f(t_i,x_j)$ is a solution of stochastic differential equation on grid. $j=[0,N+1]$, $i=[0,\infty]$ and boundary conditions are periodic: $f(t_i,x_0) = f(t_i,x_N)$ and $f(t_i,x_{N+1}) = f(t_i,x_1)$ ...
2
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1answer
46 views

Inverse-Fourier transform of a function after non-linear frequency modulation

Suppose $g\in L^1(\mathbb{R})$ such that $\hat{g}\in L^1(\mathbb{R})$ too. So $\tilde{g}(x) = \int_{-\infty}^{\infty}e^{i\pi \xi^2}\hat{g}(\xi)e^{2\pi i \xi x}\,d\xi$ is well-defined. Question is: Is ...
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0answers
18 views

How to apply a time shift to a pulse-shape, spanned with spline functions?

I have a sampled pulse shape: $ h = [1, 0.5]$ and I do not know what is its real underlying continuous-time pulse. I want to compute the samples of $h(t-\Delta t)$. If I write the continuous pulse ...
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0answers
68 views

How to decorrelate/Whiten a non-white additive random variable?

I have a signal processing problem where I have the Additive Noise Model (assume Gaussian noise). $$ y = x + w $$ where, $y$ is corrupted signal, $x$ is original signal & $w$ is a non-white ...
3
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0answers
51 views

Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
2
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0answers
72 views

Generating cross-correlated stochastic processes

I am looking for a robust way to represent and generate multiple stochastic processes that contain time and cross-correlations i.e. I am looking at stochastic processes $X_t^{1}$, $X_t^{2}$, $\ldots$, ...