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1answer
18 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
20 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
105 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
70 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 ...
1
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1answer
32 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
39 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
60 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
272 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
49 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
596 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
70 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 ...
2
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1answer
39 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
341 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. ...
4
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1answer
63 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 ...
0
votes
1answer
223 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 ...
5
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2answers
160 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 ...
0
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1answer
43 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? $$\...
0
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1answer
57 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 ...
6
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4answers
2k views

Is dirac delta (impulse) signal, a power or 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
62 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
124 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 ...
7
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3answers
878 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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0answers
83 views

How to evaluate the weight between DC component and AC component in one signal?

I have one signal with average value is above zero. Using PSD I can know the weight of each high frequency component. But how to compute the weight of DC component compared to AC component in the ...
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1answer
401 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 ...
0
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0answers
148 views

Power or Energy Signal doubt

I have to determine whether sin((n*π)/6) is a power or energy signal. This is the answer given in my textbook: How did they declare that ((-cos((n*π)/3))/2) is equal to 1? @Matt This is that ...
0
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1answer
2k 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\,\...
4
votes
1answer
73 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+\...
2
votes
2answers
169 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 ...
0
votes
1answer
63 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 ...
0
votes
1answer
119 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, ...
0
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1answer
122 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 ...
0
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1answer
106 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
41 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?