Questions tagged [integration]

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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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2answers
47 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
23 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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1answer
90 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
39 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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0answers
25 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
30 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
17 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
135 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
50 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
106 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
59 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
80 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
81 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
37 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
306 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
180 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
701 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
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 ...
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1answer
395 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
165 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
2k 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
1k 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
1k 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
61 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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0answers
27 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
41 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
1k 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
67 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
198 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
62 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 ...
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2answers
2k 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\...
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1answer
94 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: $H(s) = \frac{I(s)}{V(s)}$ ...
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1answer
103 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 ...
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2answers
2k 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 ...
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1answer
241 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 ...
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3answers
111 views

Derivative of delta function

I've come across the below. Can you please help me understand the proof for this? $$\int_{-\infty}^{\infty}x(t)\delta'(t-2.5)dt=-\frac{dx(t)}{dt}{\Big |}_{t=2.5}$$
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1answer
830 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 ...
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2answers
919 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?
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1answer
213 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. ...
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1answer
136 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 ...
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0answers
255 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 ...
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1answer
874 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) ...
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1answer
186 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) ...
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2answers
811 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 $x(t),$ $...
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1answer
146 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 ...
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2answers
193 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 ...
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1answer
93 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} = ...