What is the energy and power os signal mean in real...??

[audioguru]

I think the Frequency Domain graph is wrong.
The amplitude should be 1.0 (not 0.1) so you can easily see the amplitude of the harmonics. The frequency of the fundamental (60Hz) should be 1 and the harmonics should be 180Hz= 3, 300Hz= 5, 420Hz= 7 etc.

 

[crutschow]

If we talk about digital filters and analog filter ( like Low pass RC filter).
IIR is digital filter, what the basic diff. both of them?? and why digital signal are not passed through analog filters.

A digital filter requires the signal to be a series of digital values representing the analog signal (such as when the analog signal is converted to digital by an analog-to-digital converter). An analog filter works directly on the analog signal.

So obviously digital signals are not passed through an analog filter because analog filters are designed for analog signals, not digital.

It would appear you don't understand the basic difference between analog and digital signals. I suggest you do some study on that.

 

[koolguy]

In IIF there come poles and zero concept.....
while they represent the stability,etc of system. But if we talk about them in real what they refers and what does stabilty exactly mean what stabilty are we talking about???
At last why should we bothers about Poles and zero....??

 

[carbonzit]

I was just reading about this last night in my engineering textbook. (I should point out that most of this stuff is waaaaay over my head!)

You might look into exploring root-locus analysis (developed by W.R. Evans in the 1940s), like this page and this page. It has everything to do with determining the stability of a system, using the locus (location) of the system's poles and zeroes in the s-plane (which, as I said, I don't yet fully understand; I'm guessing that the O.P. doesn't either).

 

[crutschow]

Poles and zeros are used to determine the stability and transfer function of a system. The stability of a system is a measure of its tendency to oscillate or ring in response to an input. Pole-zero analysis was originally developed for characterizing analog control and feedback systems as well as to describe filter response. Since much digital processing, such as digital filters and digital control loops, are basically mimicking analog functions with digital processing, the same pole-zero analysis can be used to define and analyze the response of the digital loops.

 

[koolguy]

OK, but how we came to know that the poles and zero are unstable in right hand side...
and what does Poles and zero came from, they real meaning why we say them poles and zero..??

 

[crutschow]

If they are in the right hand plane it means the feedback in the system is becoming more positive instead of negative, which indicates instability.

A pole is where the value of the system transfer function goes to infinity (denominator goes to zero). A zero is where the value of the system transfer function goes to zero (numerator goes to zero).

For more info Google "poles and zeros" or read this.

 

[koolguy]

If they are in the right hand plane it means the feedback in the system is becoming more positive instead of negative

OK, if the poles and zero in right side the feedback decrease..but why we consider right side ant left or up and down...??
Is there any specific reason for that??

and what types of system we can consider in poles and zero..??
like amplifiers, computers circuits,etc...
can't we find stability without considering poles and zero...??

 

[carbonzit]

Moderated Abusive Comment.

 

[koolguy]

Hey carbo,
don't play with forum be like gentle man...

 

[MrAl]

Hi,


The poles and zeros of a function lie in the complex plane. It's called the complex
plane because it maps a complex number to an x and y axis. The x axis is the 'real'
part and the y axis is the 'complex' part. The y axis component of the number is
denoted by placing a "j" in front of the number like: j5. The complex number is
then represented like for example a complex number (1,2) would be 1+2j. That maps
to the complex plane 1 unit to the right of the y axis and 2 units up from the x
axis. It's just like any other plane where we plot things like a point (x,y).
The y axis is sometimes called the "jw" axis or the "imaginary" axis.

With a system there is a lot of significance where the point maps to. For example,
the point 1+2j maps to the right half plane (the right half plane is the first and
fourth quadrants) and is said to be 'unstable' because the real part (1) is positive.
The point -1+2j maps to the left half plance (the left half plane is the second and
third quadrants) and is said to be stable because the real part (-1) is negative.
So you see just by knowing which side the pole is on we know something about the
system. Sometimes there is pole zero cancelation, where the pole gets canceled by
the zero, so that's something to consider as well.

As you are now reading this page, you see before you a two dimensional field of graphics.
Imagine if you only had a one dimensional field...you wouldnt be able to make out any
characters. Add that second dimension however, and things change radically. Suddenly you
can read entire paragraphs and that in turn leads to immense communications which allows
you to convey information about almost anything you than think of, as well as receive
information about almost anything we can think of. Well, the complex plane, because it has
two dimensions, allows us to 'see' a system in much more detail than if we looked at a
single number like the amplitude. That's how the complex plane helps, by allowing us to
visualize more than what we could ever see with just numbers alone.


The reason we consider up or down is because that shows us the frequency, because the
y axis is jw which is j*w. Thus the point (0,1) oscillates more slowly than the point
(0,2), because the '1' is less than the '2'. Since that '2' is really the angular
frequency 'w', the frequency in Hertz is 2/2pi=1/pi in this case.

So now you know the basic reason we consider left or right, because in most cases we know
something about the stability of the system. You also now know that the up and down
tells us something about the frequency. And there's more to it than that as indicated above.

If the point is in the left half plane, that means that the response is decreasing
exponentially. If the point is in the right half plane that means the response is
increasing exponentially, and so is considered to be unstable. If the point is right on
the jw (imaginary) axis then the system is an oscillator unless it is right at (0,0).
If the point is not on the real axis then the frequency is non zero, and closer to the
real axis the frequency is less than the frequency when it is farther away from the
real axis. The frequency in the left half plane is often the 'ringing' we see on a
waveform, where it jumps up and then oscillates for a while, then dies down to
some steady DC level.

So what does all this do for us?
We can look at a system to see if it will break into oscillation when certain parameters
change. For example, if we have a feedback system that has a forward gain K, we might
want to know if increasing that gain will ever cause oscillation or if it will be stable
for any gain K. What we do in this case is look at the roots of the characteristic
equation and see if any roots cross the jw axis while the K increases. I've included a
small diagram of a typical system where the roots, for some gain K, cross the jw axis
(the vertical axis in the center) and since they do that would mean that we would have
to find a way to prevent the gain K from increasing beyond that point in the real life
system or else it would break into oscillation or simply max out and saturate. That would
make the system unusable at that point.

In the diagram, the gain K increases as shown by the arrows. There are three roots to
this system so we track the path of all three roots. Two of the roots cross the jw axis, and
only one of them doesnt. The gain K starts out at zero where the very small white dots
appear, and end at the red dots at some large value of gain.
The plot in the diagram is called a "Root Locus" diagram, and you can look that up on the
web and find out how to do the "Root Locus Procedure" and that will help you analyze systems
that have feedback.

Other methods for investigating stability are Phase Margin, and Gain Margin. There are numerous
other methods too though.

 

[koolguy]

In the diagram, the gain K increases as shown by the arrows. There are three roots to
this system so we track the path of all three roots. Two of the roots cross the jw axis, and
only one of them doesnt. The gain K starts out at zero where the very small white dots
appear, and end at the red dots at some large value of gain.
The plot in the diagram is called a "Root Locus" diagram, and you can look that up on the
web and find out how to do the "Root Locus Procedure" and that will help you analyze systems
that have feedback.

The two arrows are crossing jw (imaginary axis) from left to right side. if the arrows will remain left hand side...then what will be the conclusion...

 

[MrAl]

Hi,

The arrows are not crossing anything, it's the green line that is crossing the jw axis but i think that's what you meant to say anyway. The green line is made up of points that have been found to be the complex roots of the characteristic equation as the gain K takes on larger and larger values. The arrows indicate the path the roots map out as the gain K increases.

If the roots (the green dots) stay on the left half plane and they are on the real axis, then the response is purely a decreasing exponential with no sinusoidal part (no oscillations in the response as it decreases in amplitude). If the roots stay on the left half plane and they are above (and below) the real axis, then the response is a decreasing exponential again but this time it also has a sinusoidal oscillation riding on that exponential, so it looks like a series of sine waves riding on another signal that decreases. The end result could be either zero or some constant DC value as long as the real part is negative.

The attached diagram shows a typical step response for a system with roots in the left half plane. Note that this would be the response for one single particular value of K in the root locus diagram previously posted. Thus you can see how much information the complex plane offers because it can help us visualize the response for many values of K, not just one single one like the diagram below on the left. The right side of the diagram shows a typical place where the complex roots might be located to get that kind of response on the left. The blue arrows point to the two roots that are shown as small red dots. There are two roots because they are complex conjugate roots.
If the root was on the real axis instead of above and below it, the response would look like a wave that starts out high and then gradually decreases but with no ripples in it.

 

[koolguy]

I don't understand how there comes half( under damped) sin waves?

 

[MrAl]

I don't understand how there comes half( under damped) sin waves?

Hi again,

Im not sure what you are asking, but here are a few diagrams that explain a little better left and right half plane and jw axis poles and damping.

 

[KeepItSimpleStupid]

crutschow:

Now your not making sense.

Power is really the ability to do work. Light a light bulb. Move a car. Plow a field.

Energy is how many gallons of gas did you use and it's the integral of power * time with respect to time. You pay for electricity in units of Killo-Watt-Hours.

 

[Jugurtha]

Hello,

I believe that Mr. RITESH KAKKAR means "energy" and "power" in a "Signal Processing" 'context'. (I think this is what he meant by "like in waves")

In the "topics" you are reading, is there any talking about "Finite Energy Signal", "Correlation", "Autocorrelation", "Spectral Density", Fourier Transform, ?

The Energy of a Signal (a finite one) is the integral from minus infinity to plus infinity of the squared module of this signal with respect to time.

The Power of a Signal , is the average of energy per unit of time. (Think Joule and Watt==Joule/Second).

Here you go, https://cnx.org/content/m10055/latest/

Please do report back if this is what you were looking for or not.

 

[carbonzit]

Hmm, I looked at your linked page ("Signal Energy vs. Signal Power"). Interesting.

1. In the first illustration (finding the energy of a signal), it looks as if all they did was take the absolute value of the signal and find its integral, not the square of the signal.

2. What's with all those "[Math Processing Error]"s all over the page? Javascript error messages?

 

[MrAl]

Hello,


Often a signal energy is referred to as the "1 ohm energy", which is found by integrating f(t)^2 from minus infinity to plus infinity. The Fourier Transform fits into this scenario by integrating (1/2pi)*|F(jw)|^2 from minus infinity to plus infinity, which gives the same results.

Thus we have Parseval's Theorem:

Integrate[-inf to +inf](f(t)^2) dt = (1/2pi)*Integrate[-inf to +inf](|F(jw)|^2) dw

or in Latex:

[LATEX]

\[\int_{-\infty }^{\infty }{\mathrm{f}\left( t\right) }^{2}dt=\frac{1}{2\,\pi}\,\int_{-\infty }^{\infty }{\left| \mathrm{F}\left( jw\right) \right| }^{2}dw\]

[/LATEX]


The energy in a given bandwidth is a slice of the second integral over a given w.

Energy is the ability to do work.
Power is like energy that hasnt done anything yet.
If energy was viewed as a solid like a long parallelepiped, power would be a cross section.

 

[Jugurtha]

Hmm, I looked at your linked page ("Signal Energy vs. Signal Power"). Interesting.

1. In the first illustration (finding the energy of a signal), it looks as if all they did was take the absolute value of the signal and find its integral, not the square of the signal.

2. What's with all those "[Math Processing Error]"s all over the page? Javascript error messages?

I don't know, the page is displayed without error here. And it's actually a squared signal, maybe there's a display error that kept the tiny ² from showing up Sneaky little ².