7/25/2019 Power and Energy of a Signal
1/5
(9votes, average: 3.89out of 5)
Calculating the energy and power of a signal was discussed in one of
the previous posts. I have received numerous queries on this topic. I
intend to elaborate on this topic a little more here.
In signal processing, a signal is viewed as a function of time. The termsizeof a signal is used to represent strength of the signal. It is
crucial to know the size of a signal used in a certain application. For
example, we may be interested to know the amount of electricity
needed to power a LCD monitor as opposed to a CRT monitor. Both
of these applications are different and have different tolerances. Thus
the amount of electricity driving these devices will also be different.
A given signals size can be measured in many ways.Given a
mathematical function (or a signal equivalently), it seems that the
area under the curve, described by the mathematical function, is a
Mathuranathan December 20, 2013 Latest Articles, Signal Processing,Tips & Tricks, Tutorials 5 Comments
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good measure of describing the size of a signal. A signal can have
both positive and negative values. This may render areas that are
negative. Due to this effect, it is possible that the computed values
cancel each other totally or partially, rendering incorrect result. Thus
the metric function of area under the curve is not suitable for
defining the size of a signal. Now, we are left with two options :either 1) computation of the area under the absolute value of the
function or 2) computation of the area under the square of the
function. The second choice is favored due to its mathematical
tractability and its similarity to Euclidean Norm which is used in
signal detection techniques (Note: Euclidean norm otherwise called
L2 norm or 2-norm is often considered in signal detection
techniques on the assumption that it provides a reasonable measure
of distance between two points on signal space. It is computed as
Euclidean distance in detection theory).
Going by the second choice of viewing the size as the computation
of the area under the square of the function, the energy of a
continuous-time complex signal is defined as
If the signal x(t) is real, the modulus operator in the above equation
does not matter.
This is called Energy in signal processing terms. This is also a
measure of signal strength. This definition can be applied to any
signal (or a vector) irrespective of whether it possesses actual energy
(a basic quantitative property as described by physics) or not. If the
signal is associated with some physical energy, then the above
definition gives the energy content in the signal. If the signal is an
electrical signal, then the above definition gives the total energy of the
signal (in Joules) dissipated over a 1 Ohm resistor.
To know the actual energy of the signal , one has to know the value
of load the signal is driving and also the nature the electrical signal
[1]
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Gaussian
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Follo
Simulation of Digital
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Using Matlab [eBook]
Second Edition -
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and Cosine waves
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(voltage or current). For a voltage signal, the above equation has to be
scaled by a factor of .
For current signal, it has to be scaled by .
Here, is the impedance driven by the signal , is the signal
energy (signal processing term) and is the Energy of the signal
(physical quantity) driving the load
In the discrete domain, the energy of the signal is given by
The energy is finite only if the above sum converges to a finite value.
This implies that the signal is squarely-summable. Such a signal is
called finite energy signal.
What if the given signal does not decay with respect to time (as in a
continuous sine wave repeating its cycle infinitely) ? The energy will
be infinite and such a signal is not squarely-summable in other
words. We need another measurable quantity to circumvent thisproblem.This leads us to the notion of Power
Power is defined as the amount of energy consumed per unit time.
This quantity is useful if the energy of the signal goes to infinity or the
signal is not-squarely-summable. For non-squarely-summable
signals, the power calculated by taking the snapshot of the signal over
a specific interval of time as follows
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1) Take a snapshot of the signal over some finite time duration
2) Compute the energy of the signal
3) Divide the energy by number of samples taken for computation
4) Extend the limit of number of samples to infinity . This
gives the total power of the signal.
In discrete domain, the total power of the signal is given by
Following equations are different forms of the same computation
found in many text books. The only difference is the number of
samples taken for computation. The denominator changes according
to the number of samples taken for computation.
A signal can be classified based on its power or energy content.
Signals having finite energy are energy signals. Power signals have
finite and non-zero power.
A finite energy signal will have zero TOTAL power. Lets investigate
this statement in detail. When the energy is finite, the total power will
be zero. Check out the denominator in the equation for calculating
the total power. When the limit , the energy dilutes to zero
over the infinite duration and hence the total power becomes zero.
Signals whose total power is finite and non-zero. The energy of the
power signal will be infinite. Example: Periodic sequences like
sinusoid. A sinusoidal signal has finite, non-zero power but infinite
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Karnaugh Map walks
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over Fading Channels
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system over a Rayleigh Fading
channel Simulation in
Matlab
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a fading channel
Characterizing a MIMO
channel Channel State
Information (CSI) and
Condition number
MIMO Diversity and Spatial
Multiplexing
Introduction to Multiple
Antenna Systems
Chirp Signal Frequency
Sweeping FFT and power
spectral density
Generating Basic Signals
Gaussian Pulse and Power
Spectral Density using FFT
Generating Basic signals
Rectangular Pulse and Power
Spectral Density using FFT
Generating Basic signals
Square Wave and Power
Spectral Density using FFT
sakshama ghoslya - Hello Sir,
> Your final expression for
transmi...
Mathuranathan - Thanks for
spotting that. Will correct the
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5/5
energy.
A signal cannot be both an energy signal and a power signal.
Signals can also be a cat on the wall neither an energy signal nor a
power signal. Consider a signal of increasing amplitude defined by
For such a signal, both the energy and power will be infinite. Thus, it
cannot be classified either as an energy signal or as a power signal.
Calculation of power and verifying it through Matlab is discussed
here.
For details on RMS value of a signal (another measure for the
strength of the signal) click here
[1] Sanjay Lall,Norm and Vector spaces,Information Systems
Laboratory,Stanford University
( ) =
mistake...
PTM - I think there is a little
mistake in code comments...
Mathuranathan - Thanks for
your comment...
Mathuranathan - Thanks foryour comment....
Hao Yi - the two sources of
spectral leakage have confused
...
Mathuranathan - Thanks for
pointing it out...
Mathuranathan - I was
plotting the NON-normalized
magnitude spectr...
Yamuna - Hi Sir, In the above
example when I gave the ...
JAYAPRAKASH P - Hi, i am
doing my m tech final year
http://www.gaussianwaves.com/2013/07/channel-modeling-an-introduction/comment-page-1/#comment-28914http://www.gaussianwaves.com/2014/07/how-to-plot-fft-using-matlab-fft-of-basic-signals-sine-and-cosine-waves/comment-page-1/#comment-28950http://www.gaussianwaves.com/2014/07/how-to-plot-fft-using-matlab-fft-of-basic-signals-sine-and-cosine-waves/comment-page-1/#comment-28952http://www.gaussianwaves.com/2014/07/how-to-plot-fft-using-matlab-fft-of-basic-signals-sine-and-cosine-waves/comment-page-1/#comment-28954http://www.gaussianwaves.com/2011/01/fft-and-spectral-leakage-2/comment-page-1/#comment-28996http://www.gaussianwaves.com/2011/01/fft-and-spectral-leakage-2/comment-page-1/#comment-29004http://www.gaussianwaves.com/2011/01/fft-and-spectral-leakage-2/comment-page-1/#comment-29005http://www.gaussianwaves.com/2014/07/sampling-a-signal-in-matlab/comment-page-1/#comment-29006http://www.gaussianwaves.com/2014/07/sampling-a-signal-in-matlab/comment-page-1/#comment-29007http://www.amazon.jp/exec/obidos/ASIN/013280803X/gausswb-20http://www.amazon.jp/exec/obidos/ASIN/0966017633/gausswb-20http://lall.stanford.edu/svn/engr207c_2010_to_2011_autumn/data/norms_2008_10_07_01.pdfhttp://www.gaussianwaves.com/2013/12/power-and-energy-of-a-signal/%20http://www.gaussianwaves.com/2015/07/significance-of-rms-root-mean-square-valuehttp://www.gaussianwaves.com/2013/12/computation-of-power-of-a-signal-in-matlab-simulation-and-verification