12
votes
Accepted
Significance of energy and power signals in real world
I mostly agree with @PeterK.'s answer; in practical terms, all signals are energy signals. However, a signal's energy does have important practical significance. Producing a signal of a given energy ...
- 14.9k
12
votes
Accepted
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 ...
- 4,986
10
votes
Significance of energy and power signals in real world
An energy signal is defined as one with a finite energy:
$$
E = \int_{-\infty}^{\infty} \left|s(t)\right|^2 dt \lt \infty
$$
A power signal is defined as one with a finite power or energy per unit ...
- 25.3k
7
votes
Accepted
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 ...
- 31.7k
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 ...
- 48.9k
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 $...
- 42.7k
5
votes
Accepted
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(...
- 89k
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
$$P_x=\lim_{M\rightarrow\infty}\frac{1}{(2M+1)N}\sum_{n=-MN}^{(M+...
- 89k
5
votes
Accepted
Random signals as power signals
Note that the condition
$$\int_{-\infty}^{\infty}|f(t)|^2dt<\infty\tag{1}$$
(i.e., that the signal $f(t)$ has finite energy) is very restrictive when we try to model signals, even though ...
- 89k
5
votes
How can I calculate the amplitude of a signal from its power in dBm?
The Decibel Miliwatts Scale $dBm$ is the power ratio in Decibels, considering a reference of $P_0=1mW$.
$$P[dB]=10\text{log}_{10}(P/P_0)=10\text{log}_{10}(P[W]/0.001)$$
The general context is ...
- 1,420
5
votes
Is there instantaneous energy for signals? Why is $\big|x(t)\big|^2$ instantaneous power?
Consider
$$ \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} $$
For a capacitor ...
- 20.1k
5
votes
Accepted
Can the total energy of a signal diverge while its average power converges to zero?
That's indeed possible, at least in theory. Just come up with a signal which when squared and integrated diverges as $t\to\infty$, but slower than linearly. E.g.,
$$x(t)=\frac{1}{\sqrt[4]{|t|}}$$
$$\...
- 89k
4
votes
Accepted
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 $...
- 31.7k
4
votes
Significance of energy and power signals in real world
Energy can be a genuine motivation for real systems, when actual power is used. As said before by @Peter K. and @MBaz, in signal processing, most practical signals are time-limited, and thus energy-...
- 31.7k
4
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 ...
- 2,212
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 $...
- 28k
4
votes
Accepted
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 ...
- 2,212
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 ...
- 28k
4
votes
Accepted
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 ...
- 42.7k
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 ...
- 42.7k
3
votes
Accepted
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 ...
- 89k
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
$$\backslash f \mapsto f(a) \equiv ...
- 1,269
3
votes
Is the Dirac delta (impulse) signal a power signal or an energy signal?
You're right that the square of a Dirac delta impulse is undefined, so energy and power cannot be defined in the usual way for signals containing Dirac impulses.
However, in analogy with discrete-...
- 89k
3
votes
Accepted
Limiting bandwidth by adjusting sample rate
Depends on your signal. Typically we try to sample at the Nyquist rate, which is equal to two times the maximum frequency of your signal. If you sample less often than this, you will lose information ...
- 460
3
votes
Random signals as power signals
I think simple.
We want to model a random physical phenomenon for analysis purpose. One way is to model it by a stochastic process $X(t)$, i.e. a time series of random variables $\left\lbrace X(t_k) =...
- 6,080
3
votes
Accepted
Calculate the signal's average power
A signal either has finite energy, finite power or even infinite power. If it has finite energy, it will have zero average power, according to your definition
$$P_x=\lim_{T_0\rightarrow\infty}\frac{1}{...
- 6,208
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}^{...
- 89k
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)\...
- 20.2k
3
votes
Accepted
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 ...
- 312
3
votes
How can I shape my time channel response, in order to have Gaussian shaped Doppler Spread?
To spread in frequency with a Gaussian shape is to convolve the frequency domain on the waveform with the Gaussian shape. To convolve in frequency is to multiply in time the respective Fourier ...
- 48.9k
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