Questions tagged [signal-energy]

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Analytically determine a PSD from a transient function

This question is related to a series of questions I have asked about the units of PSD and ESDs. I include it as a separate question as it may have worth in isolation. As I understand it to compute ...
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0answers
10 views

Effect of filtering on Energy of a Digital Signal

I am trying to detect (not remove) noise from the digital signal to get meaningful information out of it. The signal I need is in the frequency range of 0.1 Hz to 10 Hz. Anything beyond this is just ...
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0answers
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How to compute the energy of a NON-STATIONARY (transient) random discrete-time signal

When computing the energy of a NON-STATIONARY (transient) random discrete-time signal $x(n)$, does it make more sense to compute the energy as $ E=\sum_1^N{x^2(n)}$ over all the $N$ samples or does ...
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1answer
95 views

Energy definition for Autocorrelation lag 0 and lag 1 for complex signals

I am studying the role of an auto-correlation matrix for random signals and the difference of energy between a lag 0 and lag 1 matrix. Consider a complex input signal $x(k)=[x1,x2]^T$ and $x(k-1)=[x0,...
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1answer
133 views

Is there an equivalent of Parseval's theorem for wavelets?

Parseval's theorem can be interpreted as: ... the total energy of a signal can be calculated by summing power-per-sample across time or spectral power across frequency. For the case of a signal $x(...
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1answer
23 views

Is it possible to have high energy compaction in audio signal? [closed]

We all know that the energy compactness in image can be achieved in high scale.But in case of audio signal is it possible to have such high energy compactness?
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2answers
93 views

Unit of Energy Spectral Density

The continuous-time Fourier Transform (CTFT) of a signal $x(t)$ (with unit $unit$) is: $$X(\omega)=\int_{-\infty}^{\infty} x(t)e^{-i\omega t}dt$$ which should be in $unit\cdot sec$ or $\frac{unit}{...
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1answer
54 views

SNR contains $\log N$ term where $N$ stands for number of samples

Sampling the signal$ $N times increases the signal energy by a factor of $N^2$ and the noise energy by a factor of $N$. Why? This explanation is written for SNR(dB) = signal peak(dB) – ...
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1answer
120 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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3answers
192 views

What is energy in image processing?

There are several web articles on the topic, but, after having read them, I still don't know what "energy" is, in the context of computer vision (CV) and image processing (IP). It is related to ...
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1answer
280 views

Error analysis for uniform quantization of uniform input

I was told that error energy $$\delta^2_e=\Delta^2/12,\quad \Delta=(B-A)/2^R$$ signal energy $$\delta^2_x = (B-A)^2/12$$ Here signal bounded:$A\le x[n]\le B.$ $[A,B]$ is split into $2^R$ ...
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1answer
48 views

Nyquist Rate (Sampling Frequency) for $ {f}^{2} \left( x, y \right) $

We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$ Would it be correct to say that ...
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1answer
55 views

Is there a relationship between Average energy of transmission and power saving

As mentioned in many books, the average energy of transmitted symbol is given by: $E_s = (2/3)(M - 1) $ where $M$ indicated the modulation order. Suppose that we are using in the first scenario $...
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1answer
34 views

What's the maximum energy for a finite signal?

I'm trying to calculate the spectral density of a signal. What I'm expecting is a scale in dbFS where 0 dbFS would be the maximal theorical energy if all my signal is concentrated in a single ...
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1answer
752 views

Average Energy of modified QAM Constellation

How to compute the average energy for the modified 16-QAM constellation below? I know that for regular/rectangular 16-QAM we can utilize the 4-PAM along each axes but I'm not sure how can we find $E_{...
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1answer
50 views

Wireless Body Area Networks with Minimum Energy Consumption [closed]

For adaptive compressive sensing(cs),the sensing matrix is related to the input signal. For example, in rakeness-based(cs), the sensing matrix is obtained by solving an optimization problem which ...
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1answer
72 views

Energy of compressed signals

I have tried a code to compress a signal using Compressed Sensing(CS). The input signal is $x$ and the compressed signal $y$ is given by : $y=Φ*x$ where $Φ$ is the sensing matrix. I have used ...
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1answer
509 views

Negative exponential signal's energy and power

Earlier I have dealt with exponential functions multiplied with unit step function. But, energy and power of exponential function alone comes out to be infinite when I put limits of the integrals to ...
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1answer
129 views

Calculating the energy of trapezoid wave

Here is the trapezoid wave,although i know we can use $\int^{4}_0 |x(t)|^2dt$ to calculate its power,but i want to divide this trapezoid to right triangle$(t=0$~$2)$,and a square ($(t=2$~$4)$). I ...
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3answers
319 views

Is $\arctan(t)$ an energy or power signal?

Is the function $\arctan(t)$ an energy or power signal? I've tried working out the integrals for energy and power but I get stuck on both.
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1answer
200 views

Band energy and Parseval theorem

In Python, I consider a dummy signal as follows: fs = 512 sig = np.random.standard_normal((fs,)) sig corresponds to 1s of ...
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1answer
41 views

Need help deriving the energy of a signal

I am solving old exam problems in preparation of my exam in signals, and I'm having trouble with a question. For a continuous aperiodic signal with the spectrum $X(\omega)=\exp(-\omega^2)$ I am to ...
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1answer
84 views

What is signal-energy?

What is energy in terms of signal processing? You can read here, that energy is I just need a simple everyday-example for that energy. And yes, bringing an example like $x(t)$ representing the ...
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1answer
110 views

Total Variation of a Signal - Is It Proportional to Signal Energy?

In an audio application, I found it very useful to measure the total variation of a signal $y[n]$ $$\sum_{n=n_0}^{n_0+N} |y[n]-y[n-1]|$$ over a window of time length $N$ (discrete analogous to total ...
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2answers
4k views

Energy of Sinc function

How to find energy of sinc function $x(t) = \frac{\sin \pi t}{\pi t}$ with out the help of Fourier transform or Parseval's theorem?
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1answer
56 views

Recommended literature to learn essential aspects of signals and its propagation [closed]

Where can I learn about signal's features. For instance mean, power, amplitude, frequency, energy, how they propagate in space or any other medium?. What power means its amplitude increases and ...
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2answers
3k views

Even and odd signal energy property

In Signals and Systems by A. V. Oppenheim, A. S. Willsky, S. Hamid Nawab, 2nd Edition, and Signals and Systems, Simon Haykins, Barry Van Veen, 2nd Edition there is a problem related to energy of real-...
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0answers
136 views

Parseval's Theorm and Effective Bandwidth

This question says that RMS bandwidth (effective bandwidth) is defined based on the carrier frequency of a signal. This makes intuitive sense to me that the carrier frequency shouldn't determine the ...
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1answer
42 views

How is the energy conservation principle preserved in the case mentioned below?

Suppose there are 2 sinusoidal signals $\cos(\omega t)$ and $\cos(\omega t)$, which implies that their individual power is $1/2$ unit and total power is $1$ unit. When added, the signal $2\cos(\omega ...
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5answers
945 views

Does windowing affect Parseval's theorem?

I have computed Fourier transform from ecg data.It does obey Parseval's theorem, relation $$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2 = \frac{1}{N} \sum_{k=0}^{N-1} \Big| X[k] \Big|^2$$ is fulfiled. ...
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1answer
105 views

How to compute the energy of two signals?

Say I have two signals, one being $g_1(t)$ and the other one being $g_2(t)$, and say that I am being asked to compute the energy of $g_3(t)$, where $$g_3(t) = g_1(t) + g_2(t)$$ Is it correct to ...
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1answer
504 views

Probability of False Alarm versus SNR

I'm currently testing the performance of an energy detector using two tests. One test involves finding the optimal threshold to achieve a probability of detection(Pd) of 0.9 and a probability of false ...
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2answers
335 views

why total energy of a finite duration continuous signal becomes infinite after sampling

If I have a continuous-time energy signal and multiply it with an impulse train, the frequency domain representation has infinite replicas. The total energy if we sum them up becomes infinite. What ...
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1answer
70 views

Integral of the Fourier spectrum?

The integral $$\int_{-\infty}^{\infty}|X(f)|^2df$$ of the absolute Fourier spectrum squared is the energy in the signal, but what about the integral of the 'simple' absolute Fourier spectrum? $$\...
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1answer
134 views

Product of power signal and energy signal

I tend to believe that if we multiply an energy signal with a power signal the product is an energy signal. My reasoning is that the energy signal will have finite bandwidth and consequenty the ...
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4answers
5k views

Is the Dirac delta (impulse) signal a power signal or an energy signal?

I'm a beginner so sorry if this question is very fundamental. Dirac impulse has finite area i.e = 1. But I've heard that $|\delta(t)|^2$ is undefined. So area under $|\delta(t)|^2$ is also undefined ...
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1answer
98 views

Energy detector based sensing

In the this paper, A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications, what is $L_f L_t$ in equations $(8)$ and $(9)$ as shown below? \begin{align} P_F&=1-\Gamma\left(...
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1answer
266 views

Definition of minimum-phase system

I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them. The first definition I saw was: An invertible system which ...
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3answers
1k views

Random signals as power signals

Why are random signals considered as power signals (i.e. signals with infinite energy and finite average power)? Does this make any sense? What does it mean for random signals to have infinite energy ...
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1answer
726 views

How to evaluate Spectral Density of DC component vs. AC component during computing PSD?

When computing the PSD, how to manipulate the DC component?  PSD integral is the total signal power, does it include the power of DC component? In other words, if there is one signal with DC value ...
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1answer
3k views

Sinc function's energy

Given this signal: $$4000\,\mbox{sinc}(4000t)+D1000\,\mbox{sinc}(1000t)$$ with $ D=6000$, find its energy. To find the energy of sinc I use this transform: $$A\,\mbox{sinc}(Bt) \rightarrow A\,\...
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1answer
87 views

Fourier transform exercise

I have this signal: $$ X(f)= 2\delta(f)+ \delta\left(f-\frac 1{T_0}\right)+\delta\left(f+\frac 1{T_0}\right)+\textrm{rect}\left(\frac{f-\frac 4{T_0}}{\frac 2{T_0}}\right)+\textrm{rect}\left(\frac{f+\...
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2answers
208 views

Is MATLAB documentation wrong on when to use discrete versus continuous wavelet transform?

I was reading some of the MATLAB documentation and I get confused when reading the part about When is Continuous Analysis More Appropriate than Discrete Analysis? My knowledge before reading the ...
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1answer
83 views

Normalizing Cepstrum by Energy

I have separately computed the cepstrum and the energy of a finite discrete-time signal. If the energy of the signal is high, we would expect (on average) larger cepstral values than if the energy of ...
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1answer
195 views

Pathloss effect MATLAB code

I want to implement the pathloss effect using MATLAB simulation. I use the D2D path loss model: $$148+40\log_{10}(d)$$ I did not find the right way to add the pathloss effect in the received signal, ...
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1answer
191 views

select local maxima in energy signal

I have the following plot which represents the RMS energy of a signal over time. The energy goes up and down with varying maximum amplitude. I want to keep the portions of the signal where the energy ...
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1answer
118 views

Power and Energy spectral densities of a linear system

Here is a schematic of my desired circuit. I want to calculate Power and Energy that the load dissipates during 0< t<8 You can see my attempts: Therefore How can find load's energy in ...
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1answer
58 views

Why does the given solution we dont have to integrate the rect function?

In the given solution energy is given as $$E=\dfrac{A^2}{2}\int_{-0.5T}^{0.5T}1+\cos\left(\dfrac{2\pi t}{T}\right)dt=\dfrac{1}{2}A^2T $$ Why does the rect function disappear?