Questions tagged [signal-energy]

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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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0 votes
1 answer
34 views

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, ...
0 votes
1 answer
192 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[...
4 votes
3 answers
248 views

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 ...
0 votes
0 answers
17 views

Computing Speech Signal Energy for the TMS5220

I am writing a C++ program that performs LPC analysis on speech data and then compresses it in a format acceptable to the TMS5220 Voice Synthesis Processor. During LPC analysis, I compute the energy ...
0 votes
0 answers
50 views

Confused about the Normalized Sinc function?

I apologize if this is a little pedantic. I am a little new to signal processing concepts. I always thought that a "normalized" function is one whose L2 norm (and hence energy) is 1 (just ...
2 votes
2 answers
185 views

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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0 votes
2 answers
38 views

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}{...
-2 votes
1 answer
56 views

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 vote
1 answer
52 views

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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4 votes
0 answers
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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 vote
1 answer
41 views

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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-1 votes
1 answer
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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.
1 vote
3 answers
77 views

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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4 votes
2 answers
201 views

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 ...
0 votes
2 answers
416 views

Units of a Fourier Transform (FFT) and Spectrogram [closed]

I am very interested in analyzing signals in the frequency domain. Units of a Fourier Transform (FFT) when doing Spectral Analysis of a Signal 1.In the previous question, answer the unit for the ...
1 vote
1 answer
43 views

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 ...
4 votes
1 answer
113 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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1 vote
1 answer
67 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}...
0 votes
1 answer
140 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 $x$ = $y$?
0 votes
1 answer
163 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 ...
0 votes
1 answer
107 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 ...
0 votes
1 answer
77 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 ...
0 votes
2 answers
61 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 $[t_{1},t_{2}]$ : $$...
0 votes
3 answers
50 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 ...
0 votes
1 answer
1k 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?
0 votes
1 answer
71 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 ...
1 vote
2 answers
580 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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3 votes
2 answers
151 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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0 votes
0 answers
31 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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1 vote
0 answers
147 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 $\int \limits _{-\infty}^{+\infty}$...
1 vote
2 answers
47 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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1 vote
2 answers
251 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 ...
1 vote
2 answers
65 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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1 vote
0 answers
94 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 ...
1 vote
2 answers
273 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 ...
0 votes
2 answers
58 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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5 votes
2 answers
578 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)|^...
11 votes
5 answers
1k 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 continuous signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\...
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0 votes
1 answer
31 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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2 votes
0 answers
138 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. ...
1 vote
1 answer
128 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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1 vote
0 answers
96 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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0 votes
0 answers
24 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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1 vote
1 answer
345 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,...
6 votes
2 answers
718 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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0 votes
1 answer
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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?
2 votes
2 answers
1k 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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0 votes
1 answer
63 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) – ...
1 vote
1 answer
1k 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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