This presentation was part of "Mini Teaching Session" of Signal and Systems course.

1. Nishant Kumar
Regn No:-CSE/10114017
Indian Institute Of Information Technology,Kalyani
Email:-nishantkr@iiitkalyani.ac.in
Topic :- Size of Signal

2. Size of Signal
Size- It is a quantity that indicates largeness or strength of any entity.
Signal-As the term implies, is a set of information or data.
 Examples of signal include:
 Electrical signals
– Voltages and currents in a circuit
 Mechanical signals
– Velocity of a car over time
 Video signals
– Intensity level of a pixel (camera, video) over time.
 Mathematically, signals are represented as a function of one or more
independent variables.
 For instance a black & white video signal intensity is dependent on x, y coordinates and time t
f(x,y,t)
 Here, we shall be exclusively concerned with signals that are a function of a single variable: time.
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Lets begin
t
g(t)
Types:- (a) Continuous-time Signal
(b) Discrete-time Signal
How can a signal exists with certain time interval with
varing amplitude be measured by one number that will
x(t) x[n]
(a) (b)t n

3. Signal Energy(Eg)
Such a measure must consider not only signal amplitude but also ,its duration.
We may consider ,the area under a signal g(t) as a possible measure of its
size,because it includes both amplitude of direction.
This will be defective measure because g(t) could be large signal,yet its +ve
and –ve areas could cancel each other,indicating a signal of small size.
This difficulty can be corrected by defining the signal size as the area
g2(t),which is always +ve.
We call this measure the signal energy Eg,defined (for real signals ) as
For complex valued signal g(t),
Eqn.1
Eqn.2
The signal energy must be finite for a meaningful measure of signal size,
otherwise the integral in Eqn 1 will not converge..
Necessary condition for finite energy,
Signal Amplitude→0,As |t|→∞ (Fig 1a)

4. Figure 1
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5. Signal Power
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 Assume condition,when amplitude of g(t) does not →0 as
|t|→0 (Fig.1b),the signal energy is infinite.
 A more meaningful measure of signal size in such a case would be
the time average of the energy(if it exists),which is the average
power Pg defined (for real signal) by
generalised defn. For complex signal g(t) as,
Obserbe the signal power Pg is the time average(mean)
of the signal amplitude squared,i.e mean-squared value of g(t).
Indeed the square root of Pg will be the familier RMS value of
g(t).
Eqn.3
Eqn. 4

6. Example.1
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Determine the suitable measure of signals in figure given below.
Fig. 2
(a) The signal in Fig 2(a)→0 as |t|→∞.so,suitable measure of this signal is Energy Eg
given by,
(b)The signal doesn’t →0 as |t|→∞.However it is periodic ,therefore its power exists.
So from eqn.3,Power Pg,
Signal power is square of its rms value .Therefore the rms value of the signal is 1/√3.

7. ANY QUESTIONS
?
Ask
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