Questions tagged [integration]
The integration tag has no usage guidance.
58
questions
1
vote
1answer
34 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 ...
0
votes
0answers
39 views
I need to proof this equality [closed]
Let it be $\beta, f$ and $g$ real numbers, such that $\beta > 1$. Then
$$f\vert f \vert^{\beta} - g \vert g \vert^{\beta} = \beta \cdot (f-g
) \int_0^1 \vert x(f-g) +g \vert^{\beta-1} dx$$
0
votes
0answers
16 views
Zero delay cut of LFM complex chirp
I am computing the zero delay cut of the ambiguity function a LFM chirp:
$\chi(\tau = 0, \nu) = \int_{-\infty}^{\infty} u(t) u^{*}(t)e^{j 2 \pi \nu t} dt = \int_{-\infty}^{\infty} A e^{j(2 \pi f_0 t + ...
1
vote
1answer
131 views
Verlet integration first step
I'm trying to implement color-to-grayscale method from this paper. And they use Verlet's integration as:
$$L^*(t+\Delta t)=\frac{F(t)}{m}\Delta t^2+2L^*(t)-L^*(t-\Delta t),$$
for computing new ...
1
vote
3answers
235 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 ...
0
votes
2answers
28 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 ...
0
votes
1answer
98 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 ...
4
votes
2answers
4k views
Removing drift from integration of accelerometer data
I am trying to get a positional data from the accelerometer data using the following steps:
Re-zero the accelerometer value
Removing mean from accelerometer value
First integration of accelerometer ...
0
votes
1answer
45 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 ...
0
votes
2answers
101 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, ...
0
votes
2answers
416 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 ...
0
votes
1answer
404 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 ...
1
vote
2answers
1k views
How to calculate the displacement from the measured acceleration data?
I have an acceleration data which is collected from a vehicle. I do also have a displacement measurement.
I would like to calcuate the displacement vector from the measured acceleration data, but no ...
0
votes
1answer
395 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 ...
1
vote
0answers
42 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 ...
0
votes
1answer
38 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^...
1
vote
0answers
26 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:
$$...
0
votes
3answers
135 views
Causality as applied to capacitors
This question stems from a point of confusion that I still have about the causality, linearity, and time-invariance in LCCDEs. I wanted to use the capacitor as an example.
Consider a capacitor with ...
1
vote
2answers
792 views
Why is the Fourier transform valid only for absolutely integrable signals?
Why is the Fourier transform valid only for absolutely integrable signals?
For example, why can't we do the Fourier transform of exponential order functions?
0
votes
1answer
59 views
Finding the output of a system where the input is a sum of complex exponentials
So, I have to find $H\{ x(t)\})$ (which is an LTI system), where $$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)-\...
1
vote
1answer
56 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 ...
4
votes
2answers
221 views
Deriving the integration property of the Fourier Transform
I want to derive the property of the Fourier Transform that states that if $X(j\omega) = \mathcal{F} (x(t))$ then $$\mathcal{F} \left( \int_{-\infty}^{t} x(\tau) \mathrm{d} \tau \right) = \frac{1}{j\...
1
vote
1answer
84 views
How to differentiate a time domain signal in the complex transfer function?
I have an input-output data set where the input is current and the output velocity. I am interested in the transfer function from current to acceleration though. So suppose:
$H(s) = \frac{I(s)}{V(s)}$
...
2
votes
1answer
87 views
Dimensional analysis of integrated white noise process
This question is somewhat related to this post.
Let us consider we have a white noise current source $i_n(t)$, with a variance $\sigma_i^2$, and mean, $\mu_n=0$.
Assume that this current is passed ...
1
vote
1answer
182 views
How to convolve an arbitrary signal with a causal decaying exponential?
I need to simplify the following convolution
$$x(t)\star [e^{-2t} u(t)]$$
where $u(t)$ is the unit step function. I'm very confused with this. Using the definition of convolution of continuous-time ...
2
votes
3answers
88 views
Derivative of delta function
I've come across the below. Can you please help me understand the proof for this?
$$\int_{-\infty}^{\infty}x(t)\delta'(t-2.5)dt=-\frac{dx(t)}{dt}{\Big |}_{t=2.5}$$
1
vote
2answers
189 views
What does the $n$ do in $1/(j \omega)^n$
I'm currently working through a research paper on beam forming. In this paper a magnitude compensation is introduced to compensate for frequency dependency. Due to other calculations low frequencies ...
1
vote
1answer
491 views
Differential Equation and Transfer Function of Multiple Summer Integrator Block Diagram
I've been working on this more than 5 hour,
I know how to solve feedback, summer, but was not able to solve this one,
I've tried to simplify it by choose A(i) to be the first output of first summer ...
0
votes
2answers
620 views
BIBO stability of $y(t)=\int_{-\infty}^{t}{x(\tau)d\tau}$
How can I prove that the LTI system with (output $y(t)$, input $x(t)$)
$$y(t)=\int_{-\infty}^{t}{x(\tau)d\tau}$$
is BIBO (bounded-input/bounded output) stable?
0
votes
1answer
136 views
Amplitude value after a Discrete-Time integration calculation?
I am using Matlab block Discrete-Time
Integrator on Simulink and I would like to know in advance, what output of that block regarding to its amplitude and the current sampling frequency would be.
...
4
votes
1answer
124 views
Numericaly computing an integral in MATLAB [closed]
I have the following integral
$$\int_{-\infty}^{\infty} g(t-\tau) \, \mathrm d\tau$$
where $g(\cdot)$ is a known function, e.g., $g(t) = \sin(t)$, and I want to evaluate its value with MATLAB. How ...
1
vote
0answers
198 views
How use FIR filter for simulating an integral implemented using the trapezoidal integration?
Suppose I have this equation
$$
\phi = \frac{60}{T^5} \int_0^T \left( T^2 - 6T \tau + 6\tau^2\right) y(t-\tau) d\tau - \frac{30 \alpha}{T^5} \int(T-\tau)^2\tau^2 u(t-\tau) d\tau
$$
and I want to use ...
1
vote
1answer
666 views
The essential bandwidth of a rectangular pulse
The problem is to estimate the essential bandwidth of a rectangular pulse
\begin{equation}
g(t) = \Pi(t/T),
\end{equation}
Where the essential bandwidth must contain at least $90\%$ of the pulse ...
0
votes
1answer
113 views
How does one “count” filter order?
This is primarily a question about how to name my filter. Suppose that I have a photon detector, and that I want to measure the rate at which photons arrive, with a simple gated counter (because this ...
1
vote
1answer
661 views
Eigenfilters in Matalb [closed]
I have to implement an eigenfilter for an arbitrary frequency response in MATLAB. I have this algorithm:
$N$ - order of the filter
$M = N/2$
$c(\omega) ...
2
votes
1answer
147 views
Orthogonal signal generator using integer arithmetic
I have a problem with implementing an orthogonal signal generator (OSG) algorithm on a microcontroller using integer arithmetic. I use this algorithm for a single-phase phase-locked loop (PLL) ...
1
vote
1answer
124 views
Graph of $[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$
I'm trying to visualize what would the following signal be like
$$[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$$
Consider that $\tau$ is the independent variable here, $t$ is the shift variable.
...
0
votes
2answers
433 views
Determining time variance of integrator
Say we have an integrator $y(t)= \int_{- \infty}^{t} x(t) dt$
It is incorrect to use the following method to determine if it is time variant/invariant?
First, when we have input signal $x(t),$
$...
2
votes
1answer
224 views
Mutual information of $ \infty $-PAM
I'm trying to compute using matlab the mutual information for an $ \infty $-PAM input (the limit of a very dense PAM constellation) for a range of snr and I got stuck.
I'm working with a real-valued ...
1
vote
1answer
80 views
Integrating over an image?
I am currently trying to implement the method described in this paper. In short we have a system of the form $a=B\times c$. Where
$$a_i = \int d^3r \space w(r)f_i(r)t(r)\quad\text{and}\quad B_{ij} = ...
0
votes
1answer
2k views
Cancel Drift after numerical integration
I am trying to integrate angular acceleration obtained from a set of accelerometers positioned specifically at opposite corners of a cube, based on the paper
EcoIMU: A Dual Triaxial-Accelerometer ...
2
votes
2answers
189 views
Why is $\int^\infty _{0^-}\delta(t-nT)e^{-st}dt = e^{-nsT}$?
I'm currently in the process of going over the $\mathcal Z$-transform and more specifically its derivation. I understand and I am able to follow it up until the final step whereby involving the ...
1
vote
1answer
113 views
Evaluating the inverse $\mathcal Z$-transform on the unit circle
I am trying to understand the math. The inverse $\mathcal Z$-transform is given by:
$$x[n] = \displaystyle\frac{1}{j2\pi} \int_cX(z)z^{n-1}dz$$
where $\displaystyle \int_c$ is a contour integral. ...
0
votes
1answer
378 views
Double Integrating Gaussian Noise
My question has to do with integrating gaussian noise.
Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. These noise samples are passed ...
-1
votes
1answer
105 views
Change of discrete summation to definite integral
The Exponential Fourier Series for a signal is written as,
$$x(t) = \sum_{n=-\infty}^{\infty} X_n e^{jnw_0t}\tag{1}$$
and, Fourier Coefficient, $X_n$, is written as,
$$X_n = \frac{1}{T} \int_{t_0}^{...
2
votes
2answers
950 views
Integration of square wave
trying to program an integrator. My input is a square wave and my expected output should be a triangle wave. However, whenever I pass it through my low pass filter algorithm (just a 2nd order ...
1
vote
1answer
431 views
Filter wrap-around to avoid dealing with settling time? Using a Butterworth
I've been using a Butterworth high pass filter to correct the low frequency distortion of an acceleration waveform integrated to a velocity waveform. I throw out a small number of the first data ...
1
vote
1answer
167 views
Integral of an upsampled signal, without actually resampling it
Given a signal X which is sampled at a certain frequency. The value we currently compute is given as the integral of the upsampled signal. Thus: Y = X but 100 times upsampled, by means of sinc ...
1
vote
1answer
1k views
Inverse z transform - contour integration
Here is my task:
Find inverse z transform of $X(z)=\frac{1}{2-3z}$, if $|z|>\frac{2}{3}$
I need to find it using definition formula, $x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$. How can I ...
2
votes
0answers
195 views
Designing a practical integrator
One way to describe a practical integrator ("leaky integrator") is
$$
H(s) = \frac{g R}{1 + sRC}
$$
I am trying to understand how to choose the values $g$, $R$ and $C$ because in practice, I will ...
