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How to determine the step response using convolution of the signal's impulse response?

The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system. ...
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2answers
21 views

Mathematical Backing for Observations seen in Adding Independent Random Variables Together

So 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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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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32 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
527 views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
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307 views

Matlab: Impulse response of linear time invariable (LTI) sine-signal

I'm preparing for a lab in a Signals and Systems course in my university, 5th semester. I've found old exercise material from the class and since I know some Matlab and have dealt with LTI systems ...
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1answer
57 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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11 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
70 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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Integration of sawtooth, square and triangle wave functions

Context After a discussion about how to plot the results of a frequency modulation between two signals on Stack Overflow, I understood that I need to find the time-integral of the following wave ...
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1answer
33 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
17 views

estimate the effective size of a gaussian?

How can I estimate the effective size of a gaussian? How bad is think that the size of the gaussian is twice its FWHM? Exist a better way of estimate this effective size?
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12 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
375 views

Plotting discrete time signals involving sumations in matlab.

Many of the examples I've encountered while looking for an answer are simple functions that do not involve summations. Suppose I have the following function; ...
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1answer
46 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 ...
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1answer
358 views

What is a moving average system?

Can someone elaborate on what a moving average system is? I know that the system is defined as: $$y[n] = \frac{x[n] + x[n-1] + x[n-2]}{3}$$ How would we draw $y[n]$ given that we have a graph with ...
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18 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 ...
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1answer
50 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. $$ ...
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0answers
22 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 ...
2
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1answer
376 views

Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car. In a Kalman filter the matrix ...
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1answer
35 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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90 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)} - ...
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1answer
16 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) ...
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0answers
33 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
721 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
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2answers
69 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. $$ ...
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0answers
18 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 $f(t_i,x_{N+1}) = f(t_i,x_1)$ ...
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53 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 ...
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1answer
826 views

Calculate phase and amplitude of a sampled sine wave

I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two ...
2
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1answer
31 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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1answer
42 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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12 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 ...
2
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0answers
30 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 $X_t^{1}$, $X_t^{2}$, $\ldots$, ...
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1answer
53 views

Using Product rule to take derivative

I'm trying to take the derivative of: $$\frac{-1}{6}(e^{-3t}-1) u(t)$$ The $u(t)$ is the step response. So the answer I get is by just doing product rule: ...
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Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
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1answer
150 views

Artifacts and low frequencies FFT.

I am working on analyzing a time signal and want to preform a FFT. However I run in to some artifacts at low frequencies. I have managed to reproduce the behavior in a test signal. Given by $S(t) = ...
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24 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 ...
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35 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 ...
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2answers
60 views

How does one verify if a vector is really recovered?

In compressed sensing, how to verify if a vector is really recovered or how does one plot the figures on recovery rate? Since in numerical experiments, there is always a difference between the ...
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2answers
42 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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2answers
231 views

Can the measurement matrix used for compressive sensing be a sparse matrix?

I am interested in analyzing Compressive Mechanism: Utilizing Sparse Representation in Differential Privacy. In my research, the measurement matrix $A\mathbb \in R^{m \times n}$ needs to be sparse. ...
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3answers
42 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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2answers
443 views

Plot recursive signal in Matlab

I need to create and plot this signal in matlab with 2000 points: x(n) = 0.6530 x(n-1) - 0.7001 x(n-2) + v(n) Where $x(-1)=x(-2)=0$ and $v(n) =$ white noise I ...
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1answer
25 views

What is the impulse response of the system

Given this input-output system what is the impulse response 𝑑𝑦(𝑑)/dt + 𝑦(𝑑) = 𝑑π‘₯(𝑑), 𝑑 β‰₯ 0, 𝑦(0) = 0 I used an integrating factor to find y(t) y(t) = ${\int t*x(t) *e^tdt\over e^t }$ ...
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84 views

What could be the mathematical equation of the given signal?

We know that Fourier series for periodic signal $y(t)$ is given by $$ y(t) = \sum\limits_{m=0}^{+\infty} a_m \cos(w_m t) + \sum\limits_{m=0}^{+\infty}b_m \sin(w_m t). \quad (2)$$ Now,I want to find ...
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1answer
52 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 ...
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2answers
55 views

How can I calculate the frequency when my samples don't span a whole period?

I am taking samples at 30Hz of a signal which is a slowly-varying sinewave. The period of the sinewave is expected to drift slowly, but will always be somewhere between 0.5s and 2s. I would like ...
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0answers
23 views

Haar wavelet transformation of a binary vector data over $GF(2)$

I am trying to perform Haar wavelet transformation on the following vector which is defined over $GF(2)$. $[1, 0, 1, 0, 1, 0, 1, 0]$ I am doing it as follows. $[1, 0, 1, 0, 1, 0, 1, 0]$ $\implies ...
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2answers
28 views

particular solution of a difference equation

I am unable to find a particular solution of the following difference equation $$ y[k-1]-5y[k]+6y[k+1]=-u[k-1]+4u[k] $$ with $u[k]=\big(\frac{1}{2}\big)^k$. This is what I tried so far. Because ...
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2answers
54 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 ...