2. 4.2
Introduction to Signal
Signals are variables that carry information.
It is described as a function of one or more
independent variables.
Basically it is a physical quantity. It varies with
some independent or dependent variables.
Signals can be One-dimensional or
multidimensional
3. 4.3
Introduction to Signal
Signal: A function of one or more variables that
convey information on the nature of a physical
phenomenon.
• One-dimensional signals: function depends on a
single variable, e.g., speech signal
• Multi-dimensional signals: function depends on
two or more variables, e.g., image
4. 4.4
Classification Of Signals
Both continuous-time and discrete-time signals are further
classified as follows:
1. Deterministic and random signals
2. Periodic and non-periodic signals
3. Energy and power signals
4. Causal and non-causal signals
5. Even and odd signals
5. 4.5
Deterministic Signals
Behaviour of these signals is predictable w.r.t time
There is no uncertainty with respect to its value at any time.
These signals can be expressed mathematically.
For example x(t) = sin(3t) is deterministic signal
6. 4.6
Random Signals
Behavior of these signals is random i.e. not predictable w.r.t
time.
There is an uncertainty with respect to its value at any time.
These signals can’t be expressed mathematically.
For example: Thermal Noise generated is non deterministic
signal.
7. 4.7
Periodic and Non-Periodic Signals
Given x(t) is a continuous-time signal
• x (t) is periodic if x(t) = x(t+Tₒ) for any T and any integer n
• Example
– x(t) = A cos(ὠt)
– x(t+Tₒ) = A cos[ὠ(t+Tₒ)] = A cos( ὠ t+Tₒ)= A cos(ὠ t+2𝜋)
= A cos(ὠ t)
– Note: Tₒ =1/fₒ ; ὠ =2 𝜋 fₒ
8. 4.8
Periodic and Non-Periodic Signals
For non-periodic signals
x(t) ≠ x(t+Tₒ)
• A non-periodic signal is assumed to have a
period T = ∞
• Example of non periodic signal is an
exponential signal
9. 4.9
Energy Signal
A signal with finite energy and zero power is
called Energy Signal. i.e.for energy signal
0<E<∞ and P =0
Signal energy of a signal is defined as the area
under the square of the magnitude of the signal.
The units of signal energy depends on the unit of
the signal.
𝐸𝑥= −∞
∞
|𝑥 𝑡 |2𝑑𝑡
10. 4.10
Power Signals
Some signals have infinite signal energy. In
that case it is more convenient to deal with
average signal power.
For power signals
0<P<∞ and E = ∞
Average power of the signal is given by
𝑃𝑥= lim
𝑇→∞
1
𝑇 −𝑇/2
𝑇/2
|𝑥 𝑡 |2
𝑑𝑡
11. 4.11
Even and Odd Signals
Even signals xe( t ) and odd signals xo( t ) are defined as
xe( t ) = x e( -t ) and xo ( t ) = -xo ( -t ) .
Any signal is a sum of unique odd and even signals. Using
x( t ) = xe( t ) +xo( t) and x( - t ) = xe( t ) - xo( t ) , yields
xe( t ) = 0.5( x( t ) + x(- t) ) and xo( t ) =0.5( x( t ) - x( -t ) ) .
12. 4.12
Even:
x(-t) = x(t)
x[-n] = x[n]
Odd:
x(-t) = -x(t)
x[-n] = -x[n]
Any signal x(t) can be expressed as
x(t) = xe(t) + xo(t) )
x(-t) = xe(t) - xo(t)
where
xe(t) = 1/2(x(t) + x(-t))
xo(t) = 1/2(x(t) - x(-t))
Even and Odd Signals
13. 4.13
Causal and Non-Causal Signals
A discrete-time signal x(n) is said to be causal if x(n) = 0 for n
< 0, otherwise the signal is non-causal.
A discrete-time signal x(n) is said to be anti-causal if x(n) = 0
for n > 0.
A causal signal does not exist for negative time and an anti-
causal signal does not exist for positive time.
A signal which exists in positive as well as negative time is
called a non-casual signal.
u(n) is a causal signal and u(– n) an anti-causal signal,
whereas x(n) = 1 for – 2 <n < 3 is a non-causal signal.
