## Syllabus

UNIT- I

Signal  Analysis:  Analogy  between  vectors  and   signals,   Orthogonal   signal  space, Signal approximation using  orthogonal  functions,  Mean  square  error, Closed or complete set of orthogonal functions,  Orthogonality  in  complex functions, Exponential and sinusoidal signals, Concepts of Impulse function, Unit step function, Signum function.

UNIT-II

Fourier Transform: Deriving Fourier transform from Fourier series,  Fourier transform of arbitrary signal, Fourier transform of standard  signals,  Fourier transform of periodic signals, properties of Fourier transforms, Fourier transforms involving impulse function and Signum  function.  Introduction  to  Hilbert Transform.

UNIT-III

Signal Transmission Through Linear Systems: Linear system, impulse response, Response of a linear system, Linear time invariant  (LTI)  system,  Linear  time variant (LTV) system, Transfer function of a LTI system. Filter characteristics of linear systems. Distortion less transmission through a system, Signal bandwidth, system bandwidth, Ideal LPF, HPF and BPF characteristics, Causality and Poly- Wiener criterion for physical realization, relationship between bandwidth and rise time.

UNIT–IV

Convolution & Correlation of Signals: Concept of convolution in time domain and frequency domain, Graphical representation of convolution, Convolution property of Fourier transforms. Cross correlation and auto correlation of functions, properties of correlation  function,  Energy  density  spectrum,  Parseval’s  theorem,   Power density spectrum, Relation between auto correlation function and energy/power spectral density function. Relation between convolution and correlation, Detection of periodic signals in the presence of noise by correlation, Extraction of signal from noise by filtering.

UNIT- V

Z-Transform: Fundamental difference between  continuous  and  discrete  time signals, discrete time signal representation using complex  exponential  and  sinusoidal components, Periodicity of discrete time using complex exponential  signal, Concept of Z- Transform of a discrete sequence.  Distinction  between Laplace, Fourier and Z transforms. Region of convergence in Z-Transform, constraints on ROC for various  classes  of  signals,  Inverse  Z-  transform,  properties of Z-transforms.