DIGITAL SIGNAL PROCESSING
COURSE OBJECTIVES:
- To learn discrete fourier transform, properties of DFT and its application to linear filtering
- To understand the characteristics of digital filters, design digital IIR and FIR filters and apply these filters to filter undesirable signals in various frequency bands
- To understand the effects of finite precision representation on digital filters
- To understand the fundamental concepts of multi rate signal processing and its applications
- To introduce the concepts of adaptive filters and its application to communication engineering
UNIT I DISCRETE FOURIER TRANSFORM 9
Sampling Theorem, concept of frequency in discrete-time signals, summary of analysis & synthesis equations for FT & DTFT, frequency domain sampling, Discrete Fourier transform (DFT) – deriving DFT from DTFT, properties of DFT – periodicity, symmetry, circular convolution. Linear filtering using DFT. Filtering long data sequences – overlap save and overlap add method. Fast computation of DFT – Radix-2 Decimation-in-time (DIT) Fast Fourier transform (FFT), Decimation-in-frequency (DIF) Fast Fourier transform (FFT). Linear filtering using FFT.
UNIT II INFINITE IMPULSE RESPONSE FILTERS 9
Characteristics of practical frequency selective filters. characteristics of commonly used analog filters
- Butterworth filters, Chebyshev Design of IIR filters from analog filters (LPF, HPF, BPF, BRF)
- Approximation of derivatives, Impulse invariance method, Bilinear transformation. Frequency transformation in the analog domain. Structure of IIR filter – direct form I, direct form II, Cascade, parallel
UNIT III FINITE IMPULSE RESPONSE FILTERS 9
Design of FIR filters – symmetric and Anti-symmetric FIR filters – design of linear phase FIR filters using Fourier series method – FIR filter design using windows (Rectangular, Hamming and Hanning window), Frequency sampling method. FIR filter structures – linear phase structure, direct form realizations
UNIT IV FINITE WORD LENGTH EFFECTS 9
Fixed point and floating point number representation – ADC – quantization – truncation and rounding
– quantization noise – input / output quantization – coefficient quantization error – product quantization error – overflow error – limit cycle oscillations due to product quantization and summation – scaling to prevent overflow.
UNIT V DSP APPLICATIONS 9
Multirate signal processing: Decimation, Interpolation, Sampling rate conversion by a rational factor
– Adaptive Filters: Introduction, Applications of adaptive filtering to equalization-DSP Architecture- Fixed and Floating point architecture principles
PRACTICAL EXERCISES:
MATLAB / EQUIVALENT SOFTWARE PACKAGE/ DSP PROCESSOR BASED IMPLEMENTATION
- Generation of elementary Discrete-Time sequences
- Linear and Circular convolutions
- Auto correlation and Cross Correlation
- Frequency Analysis using DFT
- Design of FIR filters (LPF/HPF/BPF/BSF) and demonstrates the filtering operation
- Design of Butterworth and Chebyshev IIR filters (LPF/HPF/BPF/BSF) and demonstrate the filtering operations
- Study of architecture of Digital Signal Processor
- Perform MAC operation using various addressing modes
- Generation of various signals and random noise
- Design and demonstration of FIR Filter for Low pass, High pass, Band pass and Band stop filtering
- Design and demonstration of Butter worth and Chebyshev IIR Filters for Low pass, High pass, Band pass and Band stop filtering
- Implement an Up-sampling and Down-sampling operation in DSP Processor
COURSE OUTCOMES:
At the end of the course students will be able to:
CO1:Apply DFT for the analysis of digital signals and systems
CO2:Design IIR and FIR filters
CO3: Characterize the effects of finite precision representation on digital filters
CO4:Design multirate filters
CO5:Apply adaptive filters appropriately in communication systems
TOTAL:75 PERIODS
TEXT BOOKS:
- John G. Proakis and Dimitris G.Manolakis, Digital Signal Processing – Principles, Algorithms and Applications, Fourth Edition, Pearson Education / Prentice Hall, 2007.
- A. V. Oppenheim, R.W. Schafer and J.R. Buck, ―Discrete-Time Signal Processing‖, 8th Indian Reprint, Pearson, 2004.
REFERENCES
- Emmanuel Ifeachor& Barrie. W. Jervis, “Digital Signal Processing”, Second Edition, Pearson Education / Prentice Hall, 2002.
- Sanjit K. Mitra, “Digital Signal Processing – A Computer Based Approach”, Tata Mc Graw Hill, 2007.
- Andreas Antoniou, “Digital Signal Processing”, Tata Mc Graw Hill, 2006.
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