Questions tagged [signal-energy]
The signal-energy tag has no usage guidance.
100
questions
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Can the total energy of a signal diverge while its average power converges to zero?
If the integral used to calculate the total energy for a continuous time real signal converges, its average power is equal to zero. But could the average power still equal zero if the total energy ...
2
votes
1
answer
63
views
In the RMS bandwidth equation, why do we have the energy of the signal in the denominator?
In the following equation:
$$B_{\rm rms}^2 = \frac{\displaystyle\int_{-\infty}^\infty f^2\lvert G(f)\rvert^2df}{\displaystyle\int_{-\infty}^\infty \lvert G(f)\rvert^2df}.$$
It is not clear why do we ...
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How to calculate energy of a signal whose frequency is varying with time (like chirp signal or any audio signal) using Fourier coefficients
If I have two audio signals, say $A_{1}$ (music) and $A_{2}$ (Speech), I want to calculate the energy of the two signals for their relative comparisons. One method I can use is by adding the square of ...
0
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3
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195
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Power / energy of complex signals - physical interpretation
I am wondering about physical interpretation of energy / power for complex signals. E.g. for signal energy definition:
\begin{equation}
E=\int\limits_{-\infty}^{\infty}|x(t)|^2 \, \mathrm{d}t
\end{...
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2
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What is the exact difference between Parseval's theorem and Plancherel Theorem?
This question also discusses what I am asking but the answer states that Parseval's theorem is for periodic functions as per wikipedia's notation here.
However, Parseval's relationship also holds for ...
user64710
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1
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184
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Autocorrelation of a random process
I have some doubt about the following exercise.
Let's consider the signal $X(t)= \operatorname{rect}\left(\frac{t}{2A}\right) $ , where $A$ is a
discrete random variable which can assume one value ...
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-3
votes
1
answer
114
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Parseval's theorem, Energy
I was wondering, how can Parsevals theorem (energy in time domain is equal to the energy in frequency domain) hold for sampling. I take three sampels from a sinc-function. This reduces the energy in ...
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Why am I not getting proper values of power(Px) and energy(Ex) signal as per book?
I am considering an energy signal in MATLAB as I am going through the book Signals and Systems Laboratory with MATLAB by Alex Palamides.
My Matlab code is below:
...
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1
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2
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297
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Is there instantaneous energy for signals? Why is $\big|x(t)\big|^2$ instantaneous power?
Today I learned, instantaneous power is
$$
p_x(t) = |x(t)|^2
$$
and I've known, energy is
$$
E_x = \int_{-\infty}^{\infty} |x(t)|^2 dt
$$
What I also thought was, $|x(t)|^2$ is instantaneous energy, ...
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2
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173
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Complex Envelope
Two signals have arrived with different phases. The sum signal is given by
$$x(t) = A\cos(2\pi f_ct) + B\cos(2\pi f_ct + \theta)$$
What is the complex envelope of $x(t)$? Need advice on how to get ...
-2
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1
answer
110
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Energy ratio of signal
What is the energy ratio of signal at frequency domain?
What is its mathematical formula at frequency domain and what can stand for?
I found it in this paper
https://www.researchgate.net/publication/...
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0
votes
1
answer
32
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Description of Rectified Linear Unit with energy?
I am working through the book Geometric Deep Learning (https://arxiv.org/abs/2104.13478) and have hit the following descrition of Rectified Linear Unit (Chapter 5.1, page 70).
Perhaps the most ...
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3
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198
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energy or power of exponential summation signal
Determine below signal is power or energy and derive its power or
energy accordingly. $$x(t)=\sum_{n=-\infty }^\infty e^{-\lvert
t-n\rvert } \tag 1$$
we have :
$$E_x=\int_{-\infty}^{\infty}(\sum_{n=...
1
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2
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82
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What is the intuitive interpretation of the transfer function of this system?
If I have the system that could be observed in the next Image:
I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
1
vote
1
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441
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Energy in frequency and time domain
I know from Parseval's Theorem that, given a signal $x(t)$, with $t$ a variable in the time domain,
$$
\int_{-\infty}^{+\infty} |x(t)|^2 dt = \int_{-\infty}^{+\infty}|X(f)|^2 df,
$$
where $|X(f)|$ is ...
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Strided unpadding energy relationship?
If x1 = x0[::2] is unaliased subsampling, then $E(x_1) = E(x_0)/2$, which can be proven via Parseval's theorem.
For same $x_0, x_1$, however, ...
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1
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617
views
Calculate the energy of x[n]
I'm trying to calculate the energy of this signal:
x[n] = $(\frac{1}{2})^n\sin(\frac{\pi}{2}n).u[n] $
$$E = \sum_{n=-\infty}^{+\infty}\left|\left(\frac{1}{2}\right)^n \sin\left(\frac{\pi}{2}n\right) u[...
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votes
3
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389
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Is there a relationship between the energies of the inputs to a convolution and the energy of its output?
I want to convolve discrete signals A and B. I can compute their energies beforehand by squaring the samples and summing the squares, but I'm curious if I can compute the energy of the signal I will ...
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2
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700
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Confusion regarding energy and power signals?
I know that when a signal has finite energy,it is energy signal and when its power is finite, it is power signal
But what is exactly meaning of finite here? Zero also included?
For example if a signal ...
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2
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High frequency and received signal power? Why using massive MiMo?
The power received by an isotrapic antenna is calculated by:
$P_0=\frac{P_T}{4 \pi d^2}\cdot \frac{\lambda^2}{4 \pi} = \frac{P_T}{4 \pi d^2}\cdot A_e$
or, by Friis transmission formula:
$\frac{P_r}{...
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104
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How to find energy of the signal $S_1(t) = \sqrt{t}$ where $t \in [-1,1]$
What is the energy of the signal $S_1\left( t\right) = \sqrt{t}$ for $ t \in{[-1,1]}$ and $S_1(t) = 0$ otherwise. As all of we of us know, the energy of this signal should be finite.
However this ...
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1
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150
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How can I show this equality for the inner product of two bandpass signals?
Given the real bandpass signals $x(t)$ and $y(t)$ with center frequency $f_0$ and lowpass equivalents $x_l(t)$ and $y_l(t)$ respectively, I want to show that
$$
\int_{-\infty}^\infty x(t)y(t) \ dt= \...
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0
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131
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Energy and Time Signals
In Signal Processing, we broadly categorize signals as either being "Energy Signals" or "Power Signals". If the total Energy for a signal is finite, we categorize it as a Energy ...
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1
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1
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180
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Find the unit-energy for $\mathrm{rect}(t/T)$?
My book says:
The width-1 NRZ pulse is
$$
\mathrm{rect} (t) =
\begin{cases}
1 , \qquad -1/2 \leq t \leq 1/2\\
0, \qquad \mathrm{otherwise} \tag 1
\end{cases}
$$
The unit-energy width-$T$ NRZ pulse ...
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Random Signal Energy
Why the energy of random signal(random process) is infinite? and why random signal can not be zero at infinity?
I know that there is a relation between the tow questions but I'am still confused.
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3
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Multiplying complex signal with its own complex conjugate transposed copy? [closed]
Let input be a real (audio) signal, and let X be its complex frequency domain representation.
What does the output represent when the frequency domain signal is ...
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2
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404
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How can I prove that convolution of two energy signals is an energy signal?
In other words, how can I show that if we feed an energy signal to a system whose impulse response is an energy signal, the output will also be an energy signal?
I've been trying using Rayleigh's ...
1
vote
1
answer
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What does not happen if we limit the duration of this sequences to 2014 samples?
I am confused with this multiple-choice question:
Assuming that $x(n) = e^{-2n}u(n)$, what does not happen if we limit the duration of this sequences to 2014 samples?
A. The signal power leaks out ...
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4
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1
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130
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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 ...
- 151
1
vote
1
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86
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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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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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1
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348
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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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1
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181
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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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1
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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 ...
0
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2
answers
94
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 $[t_{1},t_{2}]$ :
$$...
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3
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Energy of a signal with decreasing amplitude
I read that a infinite extension continuous time signal with decreasing amplitude will always be an energy signal. Though if you take the integral of, for example, f(t)=1/(t+1) we can see that is ...
0
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1
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How to find the energy of a rect signal?
Given a signal
$$
x(t)=-2\operatorname{rect}\left(\frac t4\right)
$$
What is the energy of signal $-x(t + 1)$?
What are the steps needed to find the energy?
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Spectral Property of Bandlimited Quantized Signal
recently I meet a problem.
I generate a random Gaussian signal $x$ with mean $0$ in MATLAB. And use a $4$th lowpass Butterworth filter to acquire $x'$. Then I use the binary rounding quantization ...
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2
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951
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Is this an energy or power signal?
Is the given input signal x[n] an energy or power signal?
The image shows what I did so far. Is it correct?
Thank you!
EDIT:
I solved it again, please tell me if I did it correctly this time.
$$E= \...
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votes
2
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225
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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 $$\int_{-\infty}^{+\infty}|h(t)|dt\lt\...
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0
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Energy or power signal for continuous signal
I have solved $w(t) = 1dt$ and determined it as power but when $w(t) =\Pi\left(\frac{t}{T_0}\right)$ it is energy.
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0
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187
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Finding the Energy & Power of a Composition of Odd and Even Signal
Given two CT signals $x_1(t)$ (even signal) and $x_2(t)$ (odd signal). If $x_1(t)+x_2(t)$ is an even signal then what is the energy and power of $x_2(t)$.
My Attempt
$\int \limits _{-\infty}^{+\infty}$...
1
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2
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Partitioning the energy of a signal between its components
In physics, the total energy of a system is the summed energy of its component subsystems, and energy must be conserved, ie, adding the energy of the components gives the total energy.
In signal ...
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2
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608
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How are the constellation point coordinates determined in digital modulation
I need to understand where the concept of the distance comes from. What I mean is, how do we know what coordinates are to assign to points in the constellation. For example here for QPSK the points ...
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Showing error energy goes to zero
Let
$$\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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0
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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 ...
- 143
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vote
2
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777
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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 ...
0
votes
2
answers
90
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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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2
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1k
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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:
$$\tag{1}\hspace{1cm} E_x = \int_{-\infty}^{+\infty}|x(t)|^...
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5
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Inconsistency between the units of power spectral density and the definition that people often give
Perhaps someone can help me resolve something - this is my understanding:
In deterministic signal analysis, for a continuous signal $x(t)$ the signal energy is defined by
$$E_{\textrm{s}} = \int^{+\...
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