Unit-I | Classification of Signals & systems: Introduction, Continuous Time and discrete time signals, classification of signals, simple manipulations of discrete time signals, amplitude and phase spectra, classification of systems, analog to digital conversion of signals
Introduction, trigonometric Fourier series, Complex or exponential form of Fourier series, Parsevals identity for Fourier series, Power spectrum of a periodic function. Fourier transform and its properties, Fourier transforms of some important signals, Fourier transforms of power and energy signals |

Unit-II |
Introduction, definition, region of convergence (ROC) LT of some important functions, Initial and final value theorems, convolution integral, Table of Laplace transforms, partial fraction expansions, network transfer function. S-plane Poles and zeros. LT of periodic functions. Application of LT in analysing networks. |

Unit-III |
Introduction, definition of z-transform, properties of z-transform, evaluation of inverse z-transform. |

Unit-IV |
Introduction, properties of DSP system, Discrete convolution, solution of linear constant coefficient difference equation. Frequency domain representation of discrete time signals and systems. Difference equation and its relationship with system function, impulse response and frequency response |

Unit-V |
Introduction, discrete Fourier series, Discrete time Fourier transform (DTFT), Fast Fourier transform (FFT), Computing an inverse DFT by doing direct DFT, Composite radix FFT, Fast (Sectioned) convolution, Correlation. |

Unit-VI |
Introduction, magnitude response and phase response of digital filters, frequency response of linear phase FIR filters, Design techniques of FIR filters, design of optimal linear phase FIR filters.
Introduction, IIR filter design by approximation of derivatives, IIR filter design by impulse invariant method, IIR filter design by the bilinear transformation, Butterworth filters, Chebyshev filters, Elliptic filters, frequency transformation. |

**Practicals:**

1. Write a Scilab program to study and implement Discrete Time Signals and systems.

a. Unit Step Sequence

b. Unit Ramp Sequence

c. Exponential Sequence

d. Exponential Increasing Sequence

e. Exponential Decreasing Sequence

f. Even Signals

g. Odd Signals

2. Write a Scilab program to implement Z-Transforms.

a. Z-transform of Finite duration signals

b. Time shifting property of Z transform

3. Write a Scilab program to demonstrate convolution property.

4. Write a Scilab program to demonstrate correlation property.

5. Write a Scilab program to implement Frequency Response of First order Difference Equation.

6. Write Scilab program to

a. Determine N-Point DFT.

b. Find DFT and IDFT of the given sequence.

7. Write a Scilab program to implement circular convolution using DFT

8. Write Scilab program to perform linear filtering (linear convolution using DFT).

9. Write Scilab program to implement/Design of FIR Filter using Frequency Sampling Technique.

10. Write Scilab program to implement low pass, high pass and band pass filters.

**Books:**

**B1:** Digital Signal Processing by S. Salivahanan, C. Gnanapriya Second Edition, TataMcGrawHill **(Unit I: Chapter 1,2, Unit II: Chapter 3, Unit III: Chapter 4, Unit IV: Chapter 5, Unit V:**

**Chapter 6, Unit VI: Chapter 7, 8)**

**References:**

Digital Signal Processing by Sanjit K. Mitra, Third Edition, Tata McGrawHill

Signals and Systems by Alan V. Oppenheim and Alan S. Willsky with S. Hamid Nawab, Second Edition, PHI (EEE)

Signals and Systems by A. Anand Kumar, EEE, PHI.

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