Questions tagged [integration]

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How to prove that the integral of Hilbert transform is not equal to the Hilbert transform of the integral?

To prove that $\int_{-\infty} ^\infty \mathcal{H}(g(t))(t)\text{d}t\neq\mathcal{H}(\int_{-\infty} ^\infty g(t) \text{d}t)$, where $\mathcal{H}(\cdot)$ is the Hilbert transform operator My approach to ...
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1answer
82 views

Fast computation of a convolution integral with Gaussian kernel

Given a convolution integral with gaussian kernel $$ g(y) =\int_a^b\varphi(y-x)f(x)dx=\int_{-\infty}^{+\infty}\varphi(y-x)f(x)\mathbb{I}_{[a,b]}(x)dx $$ where $\varphi(x)= \frac{1}{\sqrt{2\pi}}\exp{\...
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1answer
65 views

Integral of Kaiser window

I want to sample (evaluate at regular intervals) the integral of the Kaiser window. Is there a nice closed-form solution to this, so I don't have to do it numerically?
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32 views

How to make a definite integral in python?

Helo! I have this exercise to do but I don't understand how to define the integral. $$ v(t) = \int_{-\infty}^{t} y( \lambda) d \lambda $$ considering $$y(t) = 10 \Lambda \left( {t-1 \over 1} \right)$$ ...
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1answer
95 views

Digital integrator

I have been implementing a control software where I need to calculate a magnetic flux based on the measurement of the phase voltages of a three phase grid (basically three sinewaves) according to the ...
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37 views

Finding the integral of a signal

I'm trying to find the integral of the following signal: $x(t)=A, 0 \le t \le T$ $x(t)=0, otherwise$ The integral is defined as $y(t)=\int_0^t{x(\tau)d\tau}$ For $y(t)$, I'm getting $AT$ when $t \gt T$...
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1answer
96 views

Phase locked loop for three phase grid

I have been implementing a control software where one of its core functionalities is the ability to synchronize with the three phase grid. Basically I need to implement some form of the phase locked ...
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56 views

Eliminating drift generated from double integration of acceleration signal using Envelope Method

I'm trying to remove the drift generated upon the double integration of a noisy acceleration signal. But this question discusses only removing the drift upon single integration to generate velocity ...
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107 views

Integration of FTIR Absorbance Spectrum in Python

Hello I have a FTIR (fourier transform infrared) absorbance spectrum of a sample, Integrating the single lines is correlated to the quantity of substance present in the sample. The spectrum part I'm ...
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2answers
584 views

Fourier series of cycloid

What is the Fourier series representation of a cycloid? The parametric representation of the curve is as follows. $$ t=\dfrac{\theta-\sin\theta}{\pi}\\ x=\dfrac{1-\cos\theta}{\pi} $$ The period is $2$...
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49 views

How to find Integration of sinc function and then it's infinite summation?

I was doing this problem,i got answers of (a) and (b) by going following way, first i computed F.T. of x(t) as follows which in turn will be used to estimate it's bandwidth which will come as 2Hz and ...
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1answer
55 views

How can I get the function of a curve from a dataset without using a curve fitting tool?

previous relevant question here. I have a dataset of a signal captured from real hardware that produces a curve. Depending on the curve characteristics I can determine whether metal is present or not ...
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1answer
29 views

How to solve this Laplace integral for an averaging function in an iterative numerical (finite difference) model?

I am trying to implement a mathematical model for vibrational damping described in this article. They provide an equation for damping force ($F$) as a function of: a spring constant ($k$) a damping ...
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1answer
44 views

confusion related to finding inverse Z-Transform using Complex Integral Method

I am facing problems related to evaluation of inverse Z-Transform using Complex Integral Method; Consider $X(z)=\frac{z}{z-2} $ and $ROC: |z|>2$ then, $$x(n)= \frac{1}{2\pi j}\oint_c X(z) z^{n-1} \...
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1answer
145 views

Variance of Integral of a real white Gaussian Noise Process

In this question, is the answer not equal to infinity ? Answer is mentioned as 6. But my doubt is cant we think of it like a linear combination of many independent random variables each having ...
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2answers
85 views

Why this system is linear?

Hi guys i'm studying signals and systems, and my professor told us that $$y(t) = \int\limits_{ t+T }^{t-T/2} {x(a+T/2)}\mathrm{d} a$$ is a linear system. But a primitive of $x$ isn't $ x^2$ ? How it'...
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1answer
78 views

two dimensional integration of a trigonometric function

I am working on a detection problem which finally, I have to solve the following 2-D integral: $$\int\limits_{a}^{b} \int\limits_{c}^{d}e^{A\sin(x)\cos(y-B)}\, \mathrm{d}x \, \mathrm{d}y \ ,$$ where $...
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26 views

Energy or power signal for continuous signal

I have solved $w(t) = 1dt$ and determined it as power but when $w(t) =\Pi\left(\frac{t}{T_0}\right)$ it is energy.
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86 views

Inverse DTFT of phase shifted complex exponential

I have been working on this problem for a few days now and I think this is the closest I have gotten. I am getting an Answer of zero and I would like to know if that is correct and if someone could ...
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1answer
38 views

Twisted convolution - simplifying multiple integral via substitution

I need help with understanding a proof from a paper. Following is the description: Let $$r_{1}(t) = \int \int h_{1}\left(\tau, \nu\right) e^{j 2\pi \nu (t - \tau)} s\left(t - \tau\right) d\tau d\nu$$ ...
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123 views

Why Cramér spectral representation and not DTFT for stochastic process

In a lot of time-series analysis references I find (written by mathematicians or statisticians rather than engineers), I find the following signal decomposition for a stochastic process, termed the &...
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1answer
62 views

Behaviour of integrator at steady state

I wanted to calculate response of integrator of sinusoidal input at steady state via these two methods as mention in image but these two methods give two different answers at steady state, so where ...
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34 views

Resampling with factor linearly moving from one value to another: calculate expected target length

I am resampling an audio (1D) signal, using a resampling factor that moves linearly from startFactor to endFactor; say the input ...
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1answer
363 views

Complex Data type not accepted in Simulink

I am having an issue with the interaction of the Matlab function block in the Simulink with my model block. Below you can also find the picture. I have created a Matlab function with three inputs and ...
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1answer
24 views

integral with vectoric varying coeficient

i have a basic function exp(-x.^2).*log(x).^2 which i integrate in a certain interval. i want to multiply my basic function with a vectoric coefficient called coef_vec that varies with the interval. ...
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1answer
24 views

representing simple definite integral as convolution in matlab using CONV

A definite integral is a convolution with idial all '1' filter(by the theory) so i tried to test this issue with MATLAB. i have taken a function called fun made an integral over it in 1e-6 - 20*e-6 ...
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2answers
265 views

Running Integral of sine and cosine functions

In typical signal processing course we were taught that the integral of signal $x(t)$ is given by $$y(t) = \int_{-\infty}^{t}x(\tau) d\tau$$ How can we use this definition to evaluate the integrals of ...
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2answers
127 views

Coherent detection in radar and radio signals

Coherent demodulation\detection is usually done via matched filtering in RF signal processing. In radar signals, coherent integration can be done if the phases of the returns are known. In terms of ...
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2answers
353 views

Help with finishing this integral, to obtain the power spectral density of a pure cosine wave

I am trying to evaluate the power spectral density $S_{xx}(f)$ of a cosine signal $x(t) = A\cos(2\pi f_0t)$, by starting from its definition for deterministic power signals $$S_{xx}(f) = \lim_{T\...
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1answer
134 views

why does my integrator perform noise shaping?

I am designing (in matlab) a simple system with a DC signal at 0 Hz and some added noise. I am performing a differentiation of the signal (by simply subtracting the last values from each other), next ...
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1answer
154 views

CIC SINC3 Filter with unsigned Integrators

I want to use the AD7401 Sigma delta modulator connected to my FPGA. The Datasheet pg.15 has some demo verilog code which I understand alright except one thing: They use unsigned integers for all of ...
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1answer
86 views

y(t) a of an integrator circuit

I have a signal $$ x(t)= \frac{1}{T} e^{-\frac{t}{T}} u(t) - \frac{1}{T} e^{\frac{t}{T}} u(-t) $$ and I know that it transits in a integrator circuit and I have to find y(t) in time and frequency ...
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1answer
41 views

How to get discrete values from a nosiy data set that have a trend?

I have a sensor that produces values over time (appr. 50/sec). I visualized these values (X axis is the time), this can be seen on the picture, measurement A and B - these are two independent ...
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1answer
1k views

Integral over power spectral density

The wikipedia entry on PSD has one confusing line: Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process) But ...
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1answer
545 views

Convolution Integral of Harmonic Signal (Cosine) with the Sinc Function

I was asked to show that this convolution integral results in the answers also given in the image. Not quite sure how to approach this integral, everything seems to be coupled together. Does anyone ...
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3answers
1k views

integration property of fourier series

Please help me sort this issue out. The integration property in Fourier series is as follows: So, for proving the above property, i took this approach: This is where my doubt is. Some books and ...
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2answers
29 views

I am trying to convert a signal into another unit, but the error keeps increasing during each iteration

I have a signal, A, and I want to convert it into another unit by using a formula: $$s_i = \frac{(1+x_i)}{(1-x_i)}\cdot s_{i-1}$$ where $x_i$ is each sample of ...
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1answer
917 views

Absolute and Square Summability & Integration of sinc function

Is the sinc function both absolutely summable (L1 norm for Continuous time signals and l1 norm for Discrete time signals) and square summable (L2 norm for Continuous time signals and l2 norm for ...
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1answer
46 views

Area under waveform in t-domain including 2 delta functions

question: my attempt: $(a)$ $\displaystyle\int_{-\infty}^{\infty} f(t) dt=2 u (t)+r(t)-r(t-T)+Ku(t-T)$ then we draw it's diagram and found it was unbounded so,we doubt how area can be zero for any ...
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2answers
222 views

Reconstructing band-limited signal's integral from discrete samples [closed]

I'm thinking about building an e-bike consumed power meter. I'm planning on sampling a low-pass filtered current sensing and voltage analog signals on the battery to e-bike controller connection, ...
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2answers
3k views

z-Transform Methods: Definition vs. Integration Rule

The definition of the z-transform is defined as $z = e^{sT}$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
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1answer
2k views

How to model state space for complex valued system correctly in SIMULINK (MATLAB)?

When trying to use the default state-space model block, if there is a complex number valued in the matrices, there will be an error To resolve that, firstly I need to look at pseudo reference model ...
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1answer
2k views

Difference between these two integrators

I am an electrical engineering student but new to digital signal processing. However while searching references for my senior project I came across following two different discrete integrator blocks ...
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0answers
95 views

Rocketry : Combine two accelerometers to reduce noise?

I am designing an IMU for an experimental rocket. I'll be using the BN055 9DOF that has sensor fusion - orientation quaternion - and gravity compensation. My main goal is speed computation, and I was ...
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31 views

Estimating a discrete summer with constrained input bandwidth

I have a discrete-time system which can be described as: $$ Y_m = \sum_{r=-N_g}^{R-1+N_g} c_r x[R(m-1) + r] $$ The unknowns are $c_k$ but I know that they have the following approximate behavior: $$...
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1answer
42 views

The computation procedure problem of calculating the BER

Here is the processing of calculating the BER average \begin{align} P_e &=\int^\infty_0Q(\sqrt{2uSNR})e^{-u}du \\ & =\frac{1}{\sqrt{2\pi}}\int^{\infty}_0\int^\infty_{\sqrt{2uSNR}}e^{-\frac{t^...
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2answers
2k views

Why is the Fourier transform valid only for absolutely integrable signals?

Why is the Fourier transform valid only for absolutely integrable signals? For example, why can't we do the Fourier transform of exponential order functions?
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1answer
100 views

Finding the output of a system where the input is a sum of complex exponentials

So, I have to find $H\{ x(t)\})$ (which is an LTI system), where $$x(t) = \sum_{k=0}^{\infty} a_ke^{ \ jw_kt}$$ and where the impulse response of the system is given by: $$h(t) = \frac{\delta(t+\tau)-\...
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3answers
326 views

Causality as applied to capacitors

This question stems from a point of confusion that I still have about the causality, linearity, and time-invariance in LCCDEs. I wanted to use the capacitor as an example. Consider a capacitor with ...
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1answer
64 views

How to model a generic low frequency signal?

I'm trying to apply Fourier analysis to a specific problem I have. I have essentially an integral like the following $$ \int_{\Omega} f(t) g(t) dt $$ And I'm trying to assume that $g$ is a narrow ...