## BM 2202 SIGNALS AND SYSTEMS Lecture Notes for BME - Third (3rd) semester

BM2202 Lecture Notes

UNIT I CLASSIFICATION OF SIGNALS AND SYSTEMS
Classification of signals – Continuous-time signal and discrete-time signals – periodic and
aperiodic signals – even and odd signals – energy and power signals – deterministic and
random signal. Basic operations on signals – arithmetic operations – reflections – time
shifting – time scaling. Types of signals – exponential, sinusoidal, step, impulse and ramp.
System - impulse response of the system. Classification of systems – stable – memory –
invertible – time invariant – linear – causal. Convolution integrals and its properties.
Sampling theorem.

UNIT II FOURIER SERIES AND FOURIER TRANSFORM
Continuous-time Fourier series (CTFS) – Exponential and trigonometric representation of
CTFS. Dirichlet condition. Properties of CTFS – linearity, time-shifting, time-reversal, timescaling,
multiplication, Parseval’s relation – differentiation – integration. Continuous-time
Fourier transform (CTFT) – properties of CTFT – linearity, time shifting, time-reversal,
time-scaling, multiplication, convolution, Parseval’s relation – differentiation in time and
frequency domains– integration. Application to systems - solution to differential equation
using CTFT.
Discrete-time Fourier series (DTFS) and Discrete-time Fourier transform (DTFT) –
properties – linearity, time-shifting, time-reversal, time-scaling, multiplication, Parseval’s
relation – difference – accumulation. Application to systems - solution to difference
equation using DTFT.

UNIT III LAPLACE TRANSFORM
Unilateral and bilateral Laplace transform (LT) – region of convergence (ROC) - properties
of LT – linearity, time-shifting, time-reversal, time-scaling, multiplication, convolution,
Parseval’s relation – differentiation in time and frequency domain – integration – initial
value and final value theorem – inversion of LT – solution to differential equation using LT
– analysis of passive network using LT.

UNIT IV DISCRETE FOURIER TRANSFORM (DFT) AND
FAST FOURIER TRANSFORM (FFT)
Discrete Fourier transform – properties of DFT – linearity, circular-shifting in time and
frequency domains, time-reversal, time-scaling, circular correlation, multiplication,
convolution, parseval’s relation – circular convolution – circle method, matrix method –
Fourier algorithm – decimation-in-time FFT – decimation-in-frequency FFT – inverse FFT.

UNIT V Z-TRANFORM AND STATE MATRIX
Z-transform (ZT) – region of convergence (ROC) - properties of ZT – linearity, timeshifting,
time-reversal, time-scaling, multiplication, convolution, parseval’s relation –
differentiation in time and frequency domain – integration – initial value and final value
theorem – inversion of ZT – power series method, partial-fraction method, residual method
- solution to difference equation using ZT.
State variable description for LTI system – determination of transfer function from state
model – discrete-time model.