Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
This lecture is part of lecture series on Data Communication Systems. It was delivered by Prof. Prajin Ahuja at Birla Institute of Technology and Science. Its main points are: Domain, Analysis, Linear, System, Principle, Superpostion, Invariant, Deterministic, Random, Explicit
Typology: Slides
1 / 8
This page cannot be seen from the preview
Don't miss anything!
y(n) = T{x(n)} where T{.} is an operator that maps an input sequence x(n) into an output sequence y(n).
of superposition.
contains the sum of multiple signals then the output of this system is the sum of the system responses to each separate signal.
Linear System T{.}
input output
Superposition Example
y1 = T{u1}; y2 = T{u2} Y3 = T{u1 + u2} = y1 + y
ky1 = T(ku1)
Non-linear Systems: y(n) = x²(n) (i.e. T{.} = (.) ²) T{x 1 (n) + x 2 (n)} = x 1 ²(n) + x 2 ²(n) + 2x 1 (n)x 2 (n)
Linear System T{.}
u1 + u2 y1 + y
Linear System T{.}
au1 + bu2 ay1 + by
Linear Time Invariant System
time, i.e.: if y(n) = T {x(n)} implies y(n-k) = T {x(n-k)}
both linear and time-invariant (sometimes referred to as a Linear Shift-Invariant (LSI) system)
3. Analog and Discrete Signals
An analog signal x ( t ) is a continuous function of time; that is, x ( t ) is uniquely defined for all t
A discrete signal x ( kT ) is one that exists only at discrete times; it is characterized by a sequence of numbers defined for each time, kT, where k is an integer T is a fixed time interval.
4. Energy and Power Signals
Energy Signal
The performance of a communication system depends on the received signal energy; higher energy signals are detected more reliably (with fewer errors) than are lower energy signals
x ( t ) is classified as an energy signal if, and only if, it has nonzero but finite energy (0 < E (^) x < ∞) for all time, where:
E (^) x = lim ∫ x^2 (t) dt = ∫ x^2 (t) dt
An energy signal has finite energy but zero average power.
Signals that are both deterministic and non-periodic are classified as energy signals
T→∞ (^) -T/
T/
∞
Power is the rate at which energy is delivered.
A signal is defined as a power signal if, and only if, it has finite but nonzero power (0 < P (^) x < ∞) for all time, where
P (^) x = lim 1/T ∫ x^2 (t) dt
Power signal has finite average power but infinite energy.
As a general rule, periodic signals and random signals are classified as power signals
4. Energy and Power Signals
Power Signal
T→∞ (^) -T/
T/
6. Unit Step Function
Operations with Signals
-ve shift
+ve shift
Sifting property of δ(t)
X(t)
X(t0)
δ(t-t0) 1
X(t0)
