THE DISCRETE FOURIER TRANSFORM: ITS PROPERTIES AND
APPLICATIONS: Frequency Domain Sampling: The Discrete Fourier
Transform: Frequency Domain Sampling and Reconstruction of Discrete-
Time Signals, The Discrete Fourier Transform (DFT), The DFT as a Linear
Transformation, Relationship of the DFT to other Transforms. Properties of
the DFT: Periodicity, Linearity and Symmetry Properties, Multiplication of
Two DFT’s and Circular Convolution, Additional DFT Properties; Linear Filtering Methods Based on the DFT: Use of the DFT in Linear Filtering,
Filtering of Long Data Sequences; Frequency Analysis of Signals using the
DFT.
UNIT 2
EFFICIENT COMPUTATION OF THE DFT: FAST FOURIER
TRANSFORM ALGORITHMS: Efficient Computation of the DFT: FFT
Algorithms: Direct Computation of the DFT, Divide-and-Conquer Approach
to Computation of the DFT, Radix-2 FFT Algorithms, Radix-4 FFT
Algorithms, Split-Radix FFT Algorithms, Implementation of FFT
Algorithms. Applications of FFT Algorithms: Efficient computation of the DFT of Two
Real Sequences, Efficient computation of the DFT of a 2N-Point Real
Sequence, Use of the FFT Algorithm in Linear filtering and Correlation. A
Linear filtering approach to Computation of the DFT: The Goertzel
Algorithm, The Chirp-Z Transform Algorithm. Quantization Effects in the
Computation of the DFT: Quantization Errors in the Direct Computation of
the DFT, Quantization Errors in FFT Algorithms.
UNIT 3
IMPLEMENTATION OF DISCRETE-TIME SYSTEMS – 1: Structures
for the Realization of Discrete-Time Systems. Structures for FIR Systems:
Direct-Form Structures, Cascade-Form Structures, Frequency-Sampling
Structures, Lattice Structure. Structures for IIR Systems: Direct-Form
Structures, Signal Flow Graphs and Transposed Structures, Cascade-Form
Structures, Parallel-Form Structures, Lattice and Lattice-Ladder Structures
for IIR Systems.
UNIT 4
IMPLEMENTATION OF DISCRETE-TIME SYSTEMS – 2 : State-
Space System Analysis and Structures: State-Space Descriptions of Systems
Characterized by Difference Equations, Solution of the State-Space
Equations, Relationships between Input-Output and State-Space
Descriptions, State-Space Analysis in the Z-Domain, Additional State-Space
Structures. Representation of Numbers: Fixed-Point Representation of
Numbers, Binary Floating-Point Representation of Numbers, Errors
Resulting from Rounding and Truncation.
PART – B
UNIT 5
IMPLEMENTATION OF DISCRETE-TIME SYSTEMS - 3: Quantization of Filter Coefficients: Analysis of Sensuitivity to Quantizatior of Filter Coefficients, Quantization of Coefficients in FIR Filters. Round-Off
Effects in Digital Filters: Limit-Cycle Oscillations in Recursive Systems,
Scaling to Prevent Overflow, Statistical Characterization of Quantization
effects in Fixed-Point Realizations of Digital Filters.
UNIT 6
DESIGN OF DIGITAL FILTERS – 1: General Considerations: Causality
and its Implications, Characteristics of Practical Frequency-Selective Filters.
Design of FIR Filters: Symmetric And Antisymetric FIR Filters, Design of
Linear-Phase FIR Filters Using Windows, Design of Linear-Phase FIR
Filters by the Frequency-Sampling Method, Design of Optimum Equiripple
Linear-Phase FIR Filters, Design of FIR Differentiators, Design of Hilbert
Transformers, Comparison of Design Methods for Linear-Phase FIR filters.
UNIT 7
DESIGN OF DIGITAL FILTERS – 2: Design of IIR Filters from Analog
Filters: IIR Filter Design by Approximation of Derivatives, IIR Filter Design
by Impulse Invariance, IIR Filter Design by the Bilinear Transformation, The
Matched-Z Transformation, Characteristics of commonly used Analog
Filters, Some examples of Digital Filters Designs based on the Bilinear
Transformation.
UNIT 8
DESIGN OF DIGITAL FILTERS – 3: Frequency Transformations:
Frequency Transformations in the Analog Domain, Frequency
Transformations in the Digital Domain. Design of Digital Filters based on
Least-Squares method: Padé Approximations method, Least-Square design
methods, FIR least-Squares Inverse (Wiener) Filters, Design of IIR Filters in
the Frequency domain.
REFERENCE
TEXT BOOKS:
1. Digital Signal Processing – John G. Proakis and Dimitris G.
Manolakis, 3rd Edition, Pearson Education, 2003.
Reference Books
1. Digital Signal Processing: System Analysis and Design – Paulo S.
R. Diniz, Eduardo A. B. da Silva and Sergio L. Netto, Cambridge
University Press, 2002.
2. Digital Signal Processing: A Computer Based Approach – Sanjit
K. Mitra, Tata McGraw-Hill, 2001.
3. Digital Signal Processing - Alan V.Oppenheim and Ronald
W.Schafer, Pearson Education, 2003.