Questions tagged [signal-energy]

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0answers
23 views

Output of a stable LTI system (discrete)

Consider an LTI (linear and time invariant) system that is BIBO (bounded input bounded output) stable and is such that x[n] = 0 for all n < 0 (note: this is sometimes referred to as a relaxed ...
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1answer
55 views

Different values when calculating signal's energy by hand vs MATLAB

Given the following signal: $$ x(n) = \left\{ \begin{array}{ll} u(0.01n-0.025)2.3704e^{(-0.287682n)}, & n\ge 0 \\ u(-(0.01n+0.025))2.3704e^{(0.287682n)}, & n< 0 \\ \end{array}...
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1answer
44 views

What does energy of the difference between two DFT's $X$ and $Y$ being 0 tell us about their corresponding signals $x$ and $y$?

I think that would mean that the energy of difference between the signals $x$ and $y$ should also be 0, but how can I prove this? Does this also mean $x$ = $y$?
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1answer
26 views

Calculating SNR & Es/No and placing noise onto a signal

I have a signal power of -12 dBW from a 16 QAM signal after the first RRC. I want to create a channel SNR of 30 dB I calculate my noise power from this, i.e. its -42 dBW and make the noise to add to ...
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1answer
47 views

Concept of energy threshold

I am analyzing some program responsible for detecting the correct signal in the channel on the receiver side. It seems to me that such an implementation allows for the detection of the correct packets ...
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1answer
35 views

How do I find the Energy Density Function of $g(t)$ if i am not given an input or impulse response?

$$g(t)=\frac{12a}{t^2+a^2}$$ I need to find the Energy Density Function of the signal, but everywhere I look has an input and an impulse response. Does anyone know how to solve this. Would I just take ...
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2answers
30 views

Looking for a Mathematical Derivation for the Energy Formula in Continuous-time Domain

I have just started my signal and system course and I would like to know how we derive the corresponding formula for the energy of a continuous-time signal $x(t)$ over an interval $[t_{1},t_{2}]$ : $$...
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3answers
34 views

Energy of a signal with decreasing amplitude

I read that a infinite extension continuous time signal with decreasing amplitude will always be an energy signal. Though if you take the integral of, for example, f(t)=1/(t+1) we can see that is ...
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1answer
51 views

How to find the energy of a rect signal?

Given a signal $$ x(t)=-2\operatorname{rect}\left(\frac t4\right) $$ What is the energy of signal $-x(t + 1)$? What are the steps needed to find the energy?
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1answer
53 views

Spectral Property of Bandlimited Quantized Signal

recently I meet a problem. I generate a random Gaussian signal $x$ with mean $0$ in MATLAB. And use a $4$th lowpass Butterworth filter to acquire $x'$. Then I use the binary rounding quantization ...
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2answers
72 views

Is this an energy or power signal?

Is the given input signal x[n] an energy or power signal? The image shows what I did so far. Is it correct? Thank you! EDIT: I solved it again, please tell me if I did it correctly this time. $$E= \...
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2answers
100 views

Output of a stable LTI system

Let $\mathcal{L}$ be a stable LTI system. Is it true that if input has finite energy then output also has finite energy? I'm not sure about that. We know that $$\int_{-\infty}^{+\infty}|h(t)|dt\lt\...
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0answers
21 views

Computing Energy of sparsly sampled spherical function

I'm trying to understand the following paper: http://www.cse.cuhk.edu.hk/~ttwong/papers/shfit/shfit.pdf On page 8, the energy of the function Ec is mentioned. How ...
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0answers
23 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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0answers
73 views

Finding the Energy & Power of a Composition of Odd and Even Signal

Given two CT signals $x_1(t)$ (even signal) and $x_2(t)$ (odd signal). If $x_1(t)+x_2(t)$ is an even signal then what is the energy and power of $x_2(t)$. My Attempt $\int \limits _{-\infty}^{+\infty}$...
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2answers
33 views

Partitioning the energy of a signal between its components

In physics, the total energy of a system is the summed energy of its component subsystems, and energy must be conserved, ie, adding the energy of the components gives the total energy. In signal ...
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2answers
70 views

How are the constellation point coordinates determined in digital modulation

I need to understand where the concept of the distance comes from. What I mean is, how do we know what coordinates are to assign to points in the constellation. For example here for QPSK the points ...
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2answers
63 views

Showing error energy goes to zero

Let $$\hat{x}[k] = \frac{1}{2\pi}\int_{-W}^{W}X(e^{j\omega})e^{j\omega k}d\omega,\label{ift}\tag1$$ where $$X(e^{j\omega}) = \sum_{n=-\infty}^{+\infty} x[n]e^{-j\omega n}\label{dft}\tag2$$ Also, $$d[k]...
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0answers
40 views

What is the “Energy” equivalent of the Magnitude Spectrum

I have a semantic issue regarding the discrete spectrum $X[k]$ of a time domain signal with limited length $x[n]$, so we're talking about the FFT. Now, when I what to compare the bandwidth and ...
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2answers
73 views

Energy of audio signal

From audio file [y,FS]=something.wav So the y is typically N cross 2 matrix I want calculate energy so i.e sum(abs(y.^2)) So when I apply these I end with two answer for each column. So I want ...
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2answers
35 views

Simultaneously minimize and maximize two cost functions

I want to solve the following optimization problem, in which I have two cost functions $J_1 = \mathbf{w}^T R_1 \mathbf{w}$ and $J_2 = \mathbf{w}^T R_2 \mathbf{w}$, where $R_1$ and $R_2$ are covariance ...
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2answers
226 views

Continuous vs discrete signal energy

I am looking to calculate the signal energy of real, sampled acoustic data. According to this source, the energy of a continuous signal is: $$\tag{1}\hspace{1cm} E_x = \int_{-\infty}^{+\infty}|x(t)|^...
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5answers
731 views

Inconsistency between the units of power spectral density and the definition that people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\infty}_{-\...
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1answer
28 views

Manipulating line level signals

I need to manage several line level signals (physically, not in software), and need to know what to expect. I was expecting AC signals, but am not quite sure. Are line level audio signals AC or DC? ...
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1answer
71 views

Bandwith of a energy signal

I'm studying for my finals , and I'm struggling with finding bandwidths. I have this energy spectral density : Ψ(f)=rect(f) , and I need to find the bandwith, 3 dB band and the band with 90 % power. ...
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1answer
72 views

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
22 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
22 views

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
203 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
443 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
25 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
609 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
58 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
672 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
1k 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
883 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
89 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
71 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
52 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
2k 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
52 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
94 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
2k 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
313 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
538 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
281 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
49 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
424 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
214 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
10k 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?