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12 votes
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What are the units of the product of two signals?

If the multiplier takes two voltages as input and returns a voltage as output, then there is necessarily a constant involved, with units of [1/V]. Take for example, AD633 (which was the first search ...
Juancho's user avatar
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7 votes
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Is the Dirac delta (impulse) signal a power signal or an energy signal?

[Added a reference on Schwartz's impossibility theorem for products of distribution] The continuous Dirac delta $\delta$ is not considered a true function or signal, but a distribution. From its ...
Laurent Duval's user avatar
6 votes

How can I get the power of a specific frequency band after FFT?

To get the total power across bins, sum the power in each bin. Also you need to compensate for your window loss if you want an accurate result. For a rectangular window, the power in each DFT bin is ...
Dan Boschen's user avatar
  • 52.3k
6 votes

$\frac{\mathbb{E}[P]}{\mathbb{E}[N]}$ vs. $\mathbb{E}\left[\frac{P}{N}\right]$

Would the definition be equally intuitively valid? No. Using the expectation operator $\mathbb{E}$ implies that both $P$ and $N$ are functions of time. The problem with the second definition is that $...
Hilmar's user avatar
  • 45.6k
5 votes

Calculating the complex signal's average power

Solve the integral: $$ P = \lim_{T \to \infty} \frac{1}{T}\int_{-T/2}^{T/2} |x(t)|^2 dt $$ This is usually unwieldy to solve directly; it can be shown that if a signal is periodic, you only need to ...
Robert L.'s user avatar
  • 2,222
5 votes
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variance in the time domain versus variance in frequency domain

Variance is never defined as power. For a wide-sense stationary random process $X(t)$ with zero mean $$\mu_X=E\{X(t)\}=0\tag{1}$$ the variance of $X(t)$ equals its power. The autocorrelation of $X(...
Matt L.'s user avatar
  • 90.5k
5 votes

formula derivation for periodic signal power

I'd like to show you a more formal derivation. Note that the first formula for arbitrary (non-periodic) signals could be rewritten as $$P_x=\lim_{M\rightarrow\infty}\frac{1}{(2M+1)N}\sum_{n=-MN}^{(M+...
Matt L.'s user avatar
  • 90.5k
5 votes
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Random signals as power signals

Note that the condition $$\int_{-\infty}^{\infty}|f(t)|^2dt<\infty\tag{1}$$ (i.e., that the signal $f(t)$ has finite energy) is very restrictive when we try to model signals, even though ...
Matt L.'s user avatar
  • 90.5k
5 votes

How can I calculate the amplitude of a signal from its power in dBm?

The Decibel Miliwatts Scale $dBm$ is the power ratio in Decibels, considering a reference of $P_0=1mW$. $$P[dB]=10\text{log}_{10}(P/P_0)=10\text{log}_{10}(P[W]/0.001)$$ The general context is ...
Brethlosze's user avatar
  • 1,430
5 votes

Is there instantaneous energy for signals? Why is $\big|x(t)\big|^2$ instantaneous power?

Consider $$ \begin{align} E_x(t) &= \int\limits_{-\infty}^{t} p_x(u) \, \mathrm{d}u \\ \\ &= \int\limits_{-\infty}^{t} \big|x(u) \big|^2 \, \mathrm{d}u \\ \end{align} $$ For a capacitor ...
robert bristow-johnson's user avatar
5 votes
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Can the total energy of a signal diverge while its average power converges to zero?

That's indeed possible, at least in theory. Just come up with a signal which when squared and integrated diverges as $t\to\infty$, but slower than linearly. E.g., $$x(t)=\frac{1}{\sqrt[4]{|t|}}$$ $$\...
Matt L.'s user avatar
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4 votes
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Power of a periodic sequence

The basic trick is to bound the series above and below. Let us do it on one side, for positive indices. For any $N> 0$, you can write $N=kN_0+r_N$, with $0\le r_N< N_0$. Then if $a_n$ (here $...
Laurent Duval's user avatar
4 votes
Accepted

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

The typical inverse tangent function maps the input range of $ t \in (-\infty,\infty)$ into an output range of $(-\pi/2, \pi/2)$ as in the figure below: Based on this, its values are bounded for all $...
Fat32's user avatar
  • 28.3k
4 votes
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Why the "20" in calculating db ratio?

According to this source, the sound power received by an aperture is proportional to the pressure squared, i.e.: $$ P = \frac{A p^2}{\rho c} \cos \theta, $$ where: $P$ is the received power $A$ is ...
Robert L.'s user avatar
  • 2,222
4 votes

What are the units of the product of two signals?

In addition to Juancho's answer for the general mixer, I would like to give an example for a more simpler frequency mixer most commonly used in communication systems to shift the frequency spectrum of ...
Fat32's user avatar
  • 28.3k
4 votes
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Does the RMS value of a signal yields its root-power?

Given that RMS means Root Mean Square the answer is rather obvious: it's a root power quantity. The RMS of a signal has the same units that the signal itself. Saying that "RMS is proportional to ...
Hilmar's user avatar
  • 45.6k
4 votes

Undestanding antenna gain applicability

The answer has to do with the definitions of antenna gain and space loss. Antenna "gain" is essentially defined relative to space loss, which is due to isotropic (uniform spherical) ...
Gillespie's user avatar
  • 1,906
4 votes
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Undestanding antenna gain applicability

Of course, the gain of an antenna is not like that of an op-amp. It is just a measure of how sharply it focuses the beam in a specific direction with regards to a reference antenna, e.g., an isotropic ...
Karakoncolos's user avatar
4 votes

Power of noise signal through a matched filter (Digital Receiver)

Can anyone explain why that is? Which is the starting thought, or formula that yields to different times $t_1$ and $t_2$? The noise power $P_N(t)$ at any given time $t$ at the output of any filter (...
Dilip Sarwate's user avatar
4 votes
Accepted

What's the meaning of negative frequencies after taking the FFT in practice?

negative frequencies don't exist in practice, and this is just a mathematical representation? I'd say it's exactly the the opposite. Signals with only positive frequencies do not exist in nature and ...
Hilmar's user avatar
  • 45.6k
3 votes

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

$\delta(x)$ doesn't really exist at all for any particular $x$. Like Laurent Duval said, Dirac is not an $\mathbb{R}\to\mathbb{R}$ function, rather the whole mapping $$\backslash f \mapsto f(a) \equiv ...
leftaroundabout's user avatar
3 votes

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

You're right that the square of a Dirac delta impulse is undefined, so energy and power cannot be defined in the usual way for signals containing Dirac impulses. However, in analogy with discrete-...
Matt L.'s user avatar
  • 90.5k
3 votes

Random signals as power signals

I think simple. We want to model a random physical phenomenon for analysis purpose. One way is to model it by a stochastic process $X(t)$, i.e. a time series of random variables $\left\lbrace X(t_k) =...
AlexTP's user avatar
  • 6,605
3 votes
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Limiting bandwidth by adjusting sample rate

Depends on your signal. Typically we try to sample at the Nyquist rate, which is equal to two times the maximum frequency of your signal. If you sample less often than this, you will lose information ...
goldrik's user avatar
  • 460
3 votes
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Definition of average power?

The first definition works for deterministic as well as for random signals. For random signals we define the autocorrelation by $$R_x(\tau)=E\{x^*(t)x(t+\tau)\}\tag{1}$$ where $E\{\cdot\}$ is the ...
Matt L.'s user avatar
  • 90.5k
3 votes
Accepted

Calculate the signal's average power

A signal either has finite energy, finite power or even infinite power. If it has finite energy, it will have zero average power, according to your definition $$P_x=\lim_{T_0\rightarrow\infty}\frac{1}{...
Maximilian Matthé's user avatar
3 votes

How to determine the power of a finite signal?

First of all, note that your formula for signal power is only valid for real-valued $x(t)$ that satisfy $x(t)=0$ for $t<0$. A more general formula is $$P_x=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{...
Matt L.'s user avatar
  • 90.5k
3 votes

PSD of modulated signal

If $x(t)$ is a finite-energy signal with Fourier transform $X(f)$, then $x(t)\cos(2\pi f_c t)$ is also a finite-energy signal with Fourier transform $\left.\left.\frac 12 \right[X(f-f_c) + X(f+f_c)\...
Dilip Sarwate's user avatar
3 votes

How to adjust receiver gains to avoid saturation and quantization noise to optimise post digital processing?

This is a great question and comes down to the AGC design and optimizing the available dynamic range on the ADC, given a receiver minimum SNR, sensitivity and interference rejection requirements. I ...
Dan Boschen's user avatar
  • 52.3k
3 votes
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Inconsistency between the units of power spectral density and the definition that people often give

The OP is correct in their dimensional analysis $|X(f)|^2$ is NOT the power spectral density, despite what other authors might claim. Other authors probably call this the power spectral density ...
Jagerber48's user avatar

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