# power & energy signals

Started by April 16, 2005
```pls can any body make me understand difference between power signals &
Energy signals.
why  r random signals called power signals.

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```
```geeez i wish the chat-room lingo would stay in the chat room.

in article VeidnVJa8dkOkfzfRVn-uw@giganews.com, shikha at
shikhadrdo@yahoo.co.in wrote on 04/16/2005 09:01:

>
> pls can any body make me understand difference between power signals &
> Energy signals.

a finite energy signal:

+inf
total energy = integral{ x(t)^2 dt}   < infinity
-inf

a finite power signal:

+T/2
average power = lim  1/T  integral{ x(t)^2 dt}   < infinity
T->inf       -T/2

> why  r random signals called power signals.

because, like a sine wave, if they are left turned on forever, they will
deliver an infinite amount of energy.  but their average power is finite.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```shikha wrote:
> pls can any body make me understand difference between power signals
&
> Energy signals.
> why  r random signals called power signals.

Trying to make it easy:

An energy signal has a finite energy. Signals of a limited length
also carry a finite energy, and so they are energy signals. A signal
that decays exponentially, for example, also has a finite energy.

A power signal is not limited in time (it is *always* on, from the
Big-Bang to Judgement Day and beyond), and has an *infinite* energy.
Since an infinite energy has no meaning for us, then we use the energy
per unit of time, i.e., power.

Examples:
A square pulse is an energy signal.
A square wave of infinite length is a power signal.

```
```"shikha" <shikhadrdo@yahoo.co.in> wrote in message
news:VeidnVJa8dkOkfzfRVn-uw@giganews.com...
>
> pls can any body make me understand difference between power signals &
> Energy signals.
> why  r random signals called power signals.
>

Well, first of all, this is the first time I can recall ever hearing of
signals labeled like this.  So, I would suspect the labeling "energy
signals" and "power signals".  Signals are signals as functions are
functions as sequences are sequences.  But maybe I've missed something along
the way.

Robert suggested something in adding "finite" to his definitions.  Now that
changes things a lot!   Mind well.

Oh darn!  Now I find that folks have been using these terms.  Here is one
from Stanford at:
http://www.stanford.edu/class/ee179/lecture7.pdf

VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV
1. Energy and Power Signals

An energy signal x(t) has 0 < E < 1 for average energy

inf
E = int[|x(t)|^2]dt
-inf

A power signal x(t) has 0 < P < 1 for average power

inf
P = lim [1/2T]*int[|x(t)|^2]dt
T>inf      -inf

- Can think of average power as average energy/time.

- An energy signal has zero average power. A power signal has infinite
average energy.
Power signals are generally not integrable so don&#2013266066;t necessarily have a
Fourier transform.

- We use power spectral density to characterize power signals that don&#2013266066;t

have a Fourier
transform.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Oh my ... and where did those 1's come from?  I guess I'd have to do a bit
of studying on this because it doesn't make any sense to me right off.  I
see an equation for E that doesn't involve time - OK.  Then I read a
description that says "average".
I always thought that power was energy per unit time.  Now we have "average
power as average energy/time"  Well the two aren't exactly inconsistent but
power=energy per unit time is already an expression of an average isn't it?
So now we have?:

average power is average average energy???  For this to be the case, there
have to be two time frames otherwise average average energy (aae) is what?

aae=[1/T]*sum[(1/T)*sum|x(t)|^2] or [1/T^2]*sumsum[|x(t)|^2]
T         T                       T  T

I'm supposed to know better than to waste time on silly things.

Here's another description from:
http://www.signal.uu.se/Courses/CourseDirs/ModDemKod/2005/Lectures/lecture1/slides.ppt#14

A signal is an "energy signal" if, and only if, it has nonzero but finite
energy for all time 0<Ex<inf:

T/2               inf
Ex =lim   int[|x(t)|^2]dt = int[|x(t)|^2]dt
T>inf -T/2             -inf

A signal is a "power signal" if, and only if, it has finite but nonzero
power for all time 0 < Px < inf:
T/2
Px =lim   (1/T)int[|x(t)|^2]dt
T>inf     -T/2

General rule: Periodic and random signals are power signals. Signals that
are both deterministic and non-periodic are energy signals.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

It seems this is supposed to help when looking at the autocorrelation and
spectral densities.  So, OK.

I learned something, I hope Shikha did too!

Fred

```
```Fred Marshall wrote:

...

> - An energy signal has zero average power. A power signal has infinite
> average energy.

Huh? Power goes with the square of magnitude (into a resistive load). It
is a positive number for all non-zero magnitudes. To have zero average
power, a signal must be brief and averaged over all time, or everywhere
zero.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```Fred Marshall wrote:

> A signal is an "energy signal" if, and only if, it has nonzero but finite
> energy for all time 0<Ex<inf:

...

> A signal is a "power signal" if, and only if, it has finite but nonzero
> power for all time 0 < Px < inf:

Hunh? again. A sinusoid fits neither of those verbal descriptions.

...

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```"Jerry Avins" <jya@ieee.org> wrote in message
news:ieKdndZsCawKcf7fRVn-ug@rcn.net...
> Fred Marshall wrote:
>
>
>> A signal is an "energy signal" if, and only if, it has nonzero but finite
>> energy for all time 0<Ex<inf:
>
>   ...
>
>> A signal is a "power signal" if, and only if, it has finite but nonzero
>> power for all time 0 < Px < inf:
>
> Hunh? again. A sinusoid fits neither of those verbal descriptions.
>

Jerry,

First off, these were all "quotes" ...... and I was questioning the whole
thing from the get go.

Second, why doesn't a sinusoid have finite but nonzero power for all time?
er.... if I know what that even means!  Again, if power is energy per unit
time then finite for all time (in chunks of time) seems OK to me.

Fred

Fred

```
```Jerry Avins <jya@ieee.org> writes:

> Fred Marshall wrote:
>
>    ...
>
> > - An energy signal has zero average power. A power signal has
> > infinite average energy.
>
>
> Huh? Power goes with the square of magnitude (into a resistive
> load). It is a positive number for all non-zero magnitudes. To have
> zero average power, a signal must be brief and averaged over all time,
> or everywhere zero.

This is correct, Jerry, as I understand it. Any finite-temporal-extent
signal is considered a finite-energy, zero-power signal because of
the first reason you stated.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124
```
```Jerry Avins <jya@ieee.org> writes:

> Fred Marshall wrote:
>
>
> > A signal is an "energy signal" if, and only if, it has nonzero but
> > finite energy for all time 0<Ex<inf:
>
>
>    ...
>
> > A signal is a "power signal" if, and only if, it has finite but
> > nonzero power for all time 0 < Px < inf:
>
>
> Hunh? again. A sinusoid fits neither of those verbal descriptions.

Why don't you think a sinusoid has finite but non-zero power? When
Fred stated "... for all time..." I'm assuming he means "when averaged
over all time."
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124
```
```Fred Marshall wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message
> news:ieKdndZsCawKcf7fRVn-ug@rcn.net...
>
>>Fred Marshall wrote:
>>
>>
>>
>>>A signal is an "energy signal" if, and only if, it has nonzero but finite
>>>energy for all time 0<Ex<inf:
>>
>>  ...
>>
>>
>>>A signal is a "power signal" if, and only if, it has finite but nonzero
>>>power for all time 0 < Px < inf:
>>
>>Hunh? again. A sinusoid fits neither of those verbal descriptions.
>>
>
>
> Jerry,
>
> First off, these were all "quotes" ...... and I was questioning the whole
> thing from the get go.
>
> Second, why doesn't a sinusoid have finite but nonzero power for all time?
> er.... if I know what that even means!  Again, if power is energy per unit
> time then finite for all time (in chunks of time) seems OK to me.
>
> Fred

Fred,

I was questioning the quotes, not you. A sinusoid is sometimes positive,
sometimes negative. At the instant of transition, it is zero, violating
the condition "finite but nonzero power for all time".

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```