EE41013, EE60033 | Autumn 2018

Announcements	Digital Signal Processing	Quick Links
Now in OBE format! OBE is outcome-based education according to Washington Accord 12 July 2018* Classes start on Tue, 17 July 2018. 12 July 2018 Sample question papers: Mid Term, End Term	EE41013, EE60033 Autumn 2018 Subject Type: Elective \| LTP: 3-1-0 \| Credits: 4 Location: NC333, Nalanda Lecture Hall Complex, IIT Kharagpur Time: Slot A + S(1) / Mon (8:00 AM - 09:55 AM) + Mon (05:00 PM - 05:55 PM) + Tue (12:00 PM - 12:55 PM) Instructor: Dr. Debdoot Sheet Tutoring: N240, SIP Lab, Electrical Engg. Rachana Sathish, Saurabh Sharma Grading: Attendance 10%, Coding Tutorials 10%, Online Assignments 20%, Mid-Term 20%, End-Term 40%	Linear Algebra - Gilbert Strang Digital Signal Processing - Alan V. Oppenheim Discrete-Time Signal Processing - Alan V. Oppenheim A Gentle Introduction to Programming Using Python - Sarina Canelake Design and Analysis of Algorithms - Dana Moshkovitz and Bruce Tidor Introduction To MATLAB Programming - Yossi Farjoun Tools of the Trade: Anaconda Python 2.7 & 3.6 \| Matlab SDK \| MikTex LaTex compiler \| ShareLaTex online compiler \| Git version control

Why this subject?	Listen from Prof. Sanjit K. Mitra on DSP as Road to the Future
Signal is quite often referred to as the physical manifestation of a function of independent variables such as time, distance, position, temperature, pressure, etc. Examples include speech or music signals which represent air pressure variation as a function of time at a point in space. Digital Signal Processing (DSP) is the field that deals with use of digital processing technology viz. digital computers and processors to perform a wide variety of operations to alter and process digitally recorded signals. DSP as a subject lays down foundation to be able to gain understanding of specialized subjects like Digital Image Processing (DIP), Computer Vision (CV), Pattern Recognition (PR), Statistical Signal Processing (SSP), Machine Learning (ML), Deep Learning (DL), Probabilistic Graphical Models (PGM), etc. If you are looking forward to a career in signal processing technology, audio and speech processing, image processing, smart cameras and smartphones, image sensors, internet of things, digtal multimedia, visualization, augmented reality, gaming, automotive and navigation system, this a foundation subject you should definitely opt for. Text books: [1]. S. K. Mitra, Digital Signal Processing - A computer based approach, 4 Ed, McGraw Hill Education (India), 2013. [2]. J. Unpingco, Python for Signal Processing, Springer, 2014. Measure of Outcome: A student undertaking this subject would be graded based on perfromance in all of the following: (1) Regular participation in class activity. (2) Timely submission of all online assignments to be submitted in class. (3) Participation in coding tutorials in class. (4) Appear for all the exams.

Why this subject?

Listen from Prof. Sanjit K. Mitra on DSP as Road to the Future

Signal is quite often referred to as the physical manifestation of a function of independent variables such as time, distance, position, temperature, pressure, etc. Examples include speech or music signals which represent air pressure variation as a function of time at a point in space. Digital Signal Processing (DSP) is the field that deals with use of digital processing technology viz. digital computers and processors to perform a wide variety of operations to alter and process digitally recorded signals. DSP as a subject lays down foundation to be able to gain understanding of specialized subjects like Digital Image Processing (DIP), Computer Vision (CV), Pattern Recognition (PR), Statistical Signal Processing (SSP), Machine Learning (ML), Deep Learning (DL), Probabilistic Graphical Models (PGM), etc.

If you are looking forward to a career in signal processing technology, audio and speech processing, image processing, smart cameras and smartphones, image sensors, internet of things, digtal multimedia, visualization, augmented reality, gaming, automotive and navigation system, this a foundation subject you should definitely opt for.

Text books:
[1]. S. K. Mitra, Digital Signal Processing - A computer based approach, 4 Ed, McGraw Hill Education (India), 2013.
[2]. J. Unpingco, Python for Signal Processing, Springer, 2014.

Measure of Outcome:
A student undertaking this subject would be graded based on perfromance in all of the following:
(1) Regular participation in class activity.
(2) Timely submission of all online assignments to be submitted in class.
(3) Participation in coding tutorials in class.
(4) Appear for all the exams.

**Module I**: Signals and Signal Processing
1. Signal characterization	Continuous and discrete time signals, continuous valued and discrete valued signals.	[1]. 1.1
2. Signal processing operations	Time domain operations, filtering, generating complex valued signals, amplitude modulation, signal multiplexing and demultiplexing, signal generation.	[1]. 1.2 [2]. 1

**Module II**: Discrete-Time Signals in the Time Domain
1. Time-domain representation	Time domain representation of continuous and discrete signals, length of a discrete-time signal, strength of signal.	[1]. 2.1 [2]. 2
2. Operations on sequences	Elementary operations, combination of operations, convolution, circular time reversal, circular shift, symmetry based classification, periodic and aperiodic sequences, energy and power signals.	[1]. 2.2-2.3
3. Typical sequence representation	Some basic sequences viz. unit sample, step, sinusoidal and exponential, windowed sequence, fundamental and harmonic components, representation of arbitrary sequence.	[1]. 2.4
4. Sampling process, aliasing and correlation	Discrete time representation of continuous time signals and illustration of aliasing, auto-correlation and cross-corelation of sequences, normalized forms of correlation.	[1]. 2.5-2.6

**Module III**: Discrete-Time Signals in the Frequency Domain
1. Continuous-time Fourier transform	Revision of basics and transform of some common functions, energy density spectrum, transform of band limited signals.	[1]. 3.1.
2. Discrete-time Fourier transform	Definition and transform of some common functions, basic properties, symmetry relations, convergence condition, some commonly used discrete-time Fourier transform (DTFT) pairs, DTFT theorems, energy density spectrum.	[1]. 3.2-3.7 [2]. 3
3. Digital processing of continuous-time signals	Overview of the approach, effects of time-domain sampling in the frequency domain, recovery of the analog signal, sampling a bandpass signal, effect of sample and hold operations.	[1]. 3.8-3.10 [2]. 4

**Module IV**: Discrete-Time Systems
1. Some discrete time systems	Accumulator, moving-average filter, weighted moving-average filter, interpolator, median filter.	[1]. 4.1
2. Classification of discrete-time systems	Linear, shift invariance, causal, stable, passive and lossless systems, impulse and step response of systems.	[1]. 4.2-4.3
3. Time-domain characterization of LTI discrete-time systems	Input-output relationship, convolution sum computation in tabular method, stability condition, causality condition, cascade and parallel connection of systems.	[1]. 4.4-4.5
4. Finite-dimensional LTI discrete-time systems	Implementation, total sum calculation, zero-input and zero-state response, impulse response calculation, classification of systems.	[1]. 4.6-4.7
5. Frequency-domain representation of LTI discrete-time systems	Frequency response, frequency domain characterization, steady-state and transient response, response to causal exponential sequence, concept of filtering, phase and group delays.	[1]. 4.8-4.9

**Module V**: Finite-Length Discrete Transforms
1. Discrete Fourier transform	Orthoginal transforms, definition of discrete Fourier transform (DFT), computational complexity, matrix relationship, relation between DTFT and DFT and their inverses, DTFT from DFT, sampling the Fourier transform.	[1]. 5.1-5.3
2. Circular convolution	Definition and some operations, tabular method of circular convolution.	[1]. 5.4
3. Classification of finite-length sequences	Conjugate symmetry, geometric symmetry, DFT symmetry relations, DFT theorems, Fourier domain filtering.	[1]. 5.5-5.8
4. DFT of real sequences	N-point DFT, 2N-point DFT using single N-point DFT, linear convolution using DFT, linear convolution of a finite-length sequence with an infinite-length sequence.	[1]. 5.9-5.10
5. Short-time Fourier Transform	Definition, sampling in time and frequency dimensions, discrete cosine transform (DCT), Harr transform, energy compation properties.	[1]. 5.11-5.14

**Module VI**: Z-Transform
1. Definition and computation	Definition, existence, region of convergence, rational z-transform.	[1]. 6.1-6.3
2. Inverse z-transform	General expression, inversion by table look-up, inversion by partial-fraction expansion, inverse transform via long division, inverse transform theorems.	[1]. 6.4-6.5
3. Computing convolution sum of finite-length sequences	Linear convolution using polynomial multiplication, circular convolution using polynomial multiplication, transfer function, frequency response computation, stability condition.	[1]. 6.6-6.7 [2]. 5.3

**Module VII**: LTI Discrete-Time System in Transform Domain
1. Classification of transfer functions	Classification based on magnitude and phase characteristics, types of linear-phase FIR transfer functions.	[1]. 7.1-7.3
2. Simple digital filters	Simple FIR digital filters, simple IIR digital filters, digital integrators, digital differentiators, DC blockers, comb filters.	[1]. 7.4
3. Complementary transfer functions	Delay complementary transfer functions, allpass complementary transfer functions, power symmetric and conjugate quadrature filters.	[1]. 7.5
4. System inversion and identification	Convolution operation represented in the z-domain, deconvolution operation, system identification.	[1]. 7.6-7.7

**Module VIII**: Digital Filter Structures
1. Representation and structures	Block diagram representation, equivalent structures.	[1]. 8.1-8.2
2. FIR Digital Filter Structures	Basic structure of a FIR digital filter.	[1]. 8.3 [2]. 5
3. IIR Digital Filter Structure	Basic structure of an IIR digital filter, all-pass filters.	[1]. 8.4, 8.6
4. Tunable low-order IIR digital filter	Tunable first-order lowpass filter, highpass filter, second-order bandpass and bandstop filters, IIR tapped cascaded lattice structures.	[1]. 8.7-8.8
5. FIR cascaded lattice structures	Realizing a pair of arbitrary functions.	[1]. 8.9

**Module IX**: DSP Algorithm Implementation
1. Basic approaches	Matrix representation of digital filter structure, precedence graph, structure verification.	[1]. 11.1
2. DFT computation and the Fast Fourier Transform (FFT)	Goertzel's algorithm, Cooley-Tukey Fast Fourier Transform (FFT) algorithm, decimation in time (DIT) FFT and decimation in frequence (DIF) FFT, fast DFT based on index mapping, general form of the Cooley-Tukey FFT algorithm.	[1]. 11.4

Pedagogical Objectives

The aim is to teach students fundamentals of Digital Signal Processing. It would be beneficial to students opting for specialization in signal processing technology, audio and speech processing, image processing, smart cameras and smartphones, image sensors, internet of things, digtal multimedia, visualization, augmented reality, gaming, automotive and navigation system, who can use the gained skills in order to develop newer technological innovations and regularize their high-throughput translation and usage.

On completion of the course, a student would be able to:
1. Explain and discuss the scientific principles of signal digitization, its digital and discrete time representation.
2. Demonstrate the ability of analyzing signals in digital domain using their foundations of linear algebra for implementing an equivalent response filter on a digital computer or processor.
3. Design and develop new techniques for improving digital signal processing based workflow with incorporation of digital signal processing and analysis in regular industrial and other usage.