BM2202 - Signals and Systems |
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,
time-scaling, multiplication, Parseval’s relation – differentiation – integration. Continuoustime
Fourier transform (CTFT) – properties of CTFT – linearity, time shifting, timereversal,
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 IIILaplace 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 IVDiscrete 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 –
sectional convolution – overlap-add method and overlap-save method – radix-2 fast
Fourier algorithm – decimation-in-time FFT – decimation-in-frequency FFT – inverse
FFT. |
UNIT VZ-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. |
Text Book |
1. Allan V. Oppenhein et al, “Signals and Systems”, Pearson Education, 2007 |
References |
1. Simon Haykin and Barry Van Veen, “Signals and Systems”, John Willey, 1999
2. Roger E. Zeimer et al, “Signals and Systems”, McMillan, 2nd Edition, 1999.
3. Douglas K. Linder, ““Signals and Systems”, McGraw-Hill, 2nd Edition, 1999. |
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