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3-0-2-8 Credit Elective Course
S. R. M. Prasanna

Dept of ECE,
IIT Guwahati,
prasanna@iitg.ernet.in

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Course Planning for Jan-Apr 2008
Multirate Signal Processing (MSP)
Time Frequency Analysis (TFA)
Audio Coding (AC): Application of MSP & TFA
Theory Lectures
MSP: 14
TFA: 14
AC: 14
Total: 42

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Course Planning (contd.)
Laboratory
MSP: 03
TFA: 03
AC: 03
Total: 09
Written Assignments
MSP: 02
TFA: 02
AC: 02
Total: 06

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Time-Table & Evaluation
Time-Table
3 Lectures / week
1 L for MSP (Tuesday, 9-10)
1 L for TFA (Wednesday, 9-10)
1 L for AC (Friday, 12-13)
Lab: Wednesday, 15-17
Evaluation
Quiz: 20 Marks (10%) (End of Jan)
Mid-Sem: 40 Marks (25%) (End of Feb)
End-Sem: 60 Marks (40%) (End of Apr)
Laboratory & Assignments: Continuous (25%)
Total: 100%

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Overview of Signal Processing Area
Relation among different subjects
Signals & Systems is the foundation part of signal
processing area
DSP is the central part of signal processing area
ADSP is the peripheral part of signal processing
area

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Signals & Systems
Classiﬁcation of signals
Properties of systems
LTI System
Correlation & Convolution
Differential / Difference equation representation
Fourier representation: CTFS, CTFT, DTFS and DTFT
LT & ZT
Concepts of impulse response, frequency response,
system function & transfer function

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DSP
Sampling theorem: time and frequency domains
DFT and its properties
Circular shift and convolution
FFT methods for DFT computation
Analysis and design of IIR and FIR ﬁlters
Structures for realization of ﬁlters
Finite word length effects

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Multirate DSP
Time-frequency analysis
Statistical signal processing
Architecture of DSP processors
Speech, Audio, Image and Video processing
Biomedical signal processing
Signal processing for communication

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Focus of EC 623 Course
Multirate DSP (MSP)
Time-frequency analysis (TFA)
Audio coding (AC): Applications of MSP & TFA

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Topics from MSP
Introduction and Applications of MSP.
Decimation, Interpolation and Fractional Rate.
Polyphase Representation for MSP.
Introduction to Filter Banks.
Maximally Decimated Filter Banks.
Two QMF and M Channel Filter Banks.
Polyphase Representation of Filter Banks.
Perfect Reconstruction (PR) and Paraunitary PR.
Two and M Channel Paraunitary Filter Banks.
Linear Phase PR QMF Banks.
Cosine Modulated Filter Banks and Pseudo QMF Bank.
Recent trends in the Design of Filter Banks.
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Topics from TFA
Introduction and Applications of TFA.
Time and Frequency Description of Signals.
Instantaneous Frequency and the Complex Signal.
The Uncertainty Principle.
Densities and Characteristic Functions.
Time-Frequency Distributions: Fundamental Ideas.
TFA using STFT and Wavelets.
Wigner and Wigner-Ville Distribution.
General and Kernel Method for designing TFDs.
TFDs based on Kernel Methods.
Comparison of Various TFDs.
Recent Trends in TFA.
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Topics from AC
Introduction to Audio Coding.
Psychoacoustic Principles for Audio Coding.
Filter Banks for Audio Coding.
Transform Coders for Audio Coding.
Subband Coders for Audio Coding.
Sinusoidal Coders for Audio Coding.
Audio Coding Standards and Algorithms.
Lossless Audio Coding.
Quality Measures for Perceptual Audio Coding.
Recent Trends in Audio Coding.

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Books (Text/ References)
P. P. Vaidyanathan, "Multirate systems and ﬁlter banks",
Pearson, Delhi, 2004.
L. Cohen, "Time-Frequency analysis", Prentice hall, NJ,
USA, 1995.
B. Boashash, "Time-frequency signal analysis and
processing" Elsivier, 2003.
A. Spanias, et. al., "Audio signal processing and
coding", Wiley-Interscience, NJ, USA, 2007.

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Unirate v/s Multirate DSP
Unirate: Processing of signals at one sampling rate.
Multirate: Processing at multiple sampling rates.
Merits of Multirate DSP.
Reduced complexity & distortion.
All digital implementation.
No distortion due to ADC & DAC.
Sampling rate conversion.
Reduced transmission rate / storage requirement.
On an average reduced number of bits / sample.
Subband coding.

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Applications of Multirate DSP
Theory of ﬁlter banks and their application.
Signal compression: subband coding.
All digital sampling rate conversion.

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Time-Frequency Analysis
Time Domain Analysis:
Amplitude v/s time
Localization in time domain
Good resolution in time domain
Poor resolution in frequency domain
Frequency Domain Analysis:
Amplitude v/s frequency
Localization in frequency domain
Good resolution in frequency domain
Poor resolution in time domain

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Time-Frequency Analysis (contd.)
Time-Frequency Analysis:
Amplitude v/s time and frequency.
Localization in time and frequency domains.
Ideally good resolution in both the domains.
Simultaneous good resolution is not possible.
Good resolution in one domain with a compromise
on resolution in other domain.

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Tools for Time-Frequency Analysis
Short Term Fourier Transform (STFT).
Wavelets.
Time-frequency distributions (TFDs).

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Audio Coding
Audio: Signals in AF (20 Hz - 20 kHz) range.
Speech and music signals.
Speech: 20 Hz - 8 kHz with max energy up to 4 kHz.
Music: 20 Hz - 20 kHz.
Audio processing: Mainly processing music signals.
Audio coding: Different audio compression methods.
Finds immense application in entertainment industry.
MSP and TFA concepts are being extensively used in
audio coding methods.