2.161 | Fall 2008 | Graduate
Signal Processing: Continuous and Discrete


Readings in this course are drawn from the course handouts and the following texts:

[P&M] Proakis, John G., and Dmitris K. Manolakis. Digital Signal Processing. 4th ed. Upper Saddle River, NJ: Prentice Hall, 2006. ISBN: 9780131873742.

[OS&B] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 9780137549207.

Cartinhour, Jack. Digital Signal Processing: An Overview of Basic Principles. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 9780137692668.

Stearns, Samuel D., and Don R. Hush. Digital Signal Analysis. 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 1990. ISBN: 9780132131179.


Introduction to signal processing

Properties of LTI continuous filters

The Dirac delta function

Properties of the delta function

Practical applications of the Dirac delta function

Class handout: The Dirac delta and unit-step functions

Continuous LTI system time-domain response

Sinusoidal response of LTI continuous systems

Class handouts: Convolution, sinusoidal frequency response

The Fourier series and transform

Periodic input functions — the Fourier series

Aperiodic input functions — the Fourier transform

Class handout: Frequency domain methods

Review of development of Fourier transform

The frequency response of a linear system defined directly from the Fourier transform

Relationship between the frequency response and the impulse response

The convolution property


The one-sided Laplace transform

The transfer function

Poles and zeros of the transfer function

Frequency response and the pole-zero plot

Class handouts: The Laplace transform, understanding poles and zeros, sinusoidal frequency response of linear systems

Poles and zeros of filter classes

The decibel

Low-pass filter design

Class handouts: Sinusoidal frequency response of linear systems, sections 6.1 and 7, introduction to continuous time filter design

Butterworth filter design example

Chebyshev filters

Class handout: Introduction to continuous time filter design

Second-order filter sections

Transformation of low-pass filters to other classes

State-variable active filters

Class handouts: Introduction to continuous time filter design, introduction to operational amplifiers, op-amp implementation of analog filters

Operational-amplifier based state-variable filters

Introduction to discrete-time signal processing

Class handout: Introduction to the operational amplifier, op-amp implementation of analog filters

The sampling theorem

The discrete Fourier transform (DFT)

Class handout: Sampling and the discrete Fourier transform

P&M, sections 6.1-6.3 and 7.1

OS&B, sections 4.1-4.3 and 8.1-8.5


The discrete Fourier transform (cont.)

The fast Fourier transform (FFT)

Class handouts: Sampling and the discrete Fourier transform, the fast Fourier transform

P&M, chapter 7

OS&B, chapters 8-9


The fast Fourier transform (cont.)

Spectral leakage in the DFT and apodizing (windowing) functions

Class handout: The fast Fourier transform

P&M, sections 8.1-8.3

OS&B, sections 9.0-9.3


Introduction to time-domain digital signal processing

The discrete-time convolution sum

The z-transform

P&M, chapter 3

OS&B, chapter 3


The discrete-time transfer function

The transfer function and the difference equation

Introduction to z-plane stability criteria

The frequency response of discrete-time systems

The inverse z-transform


Frequency response and poles and zeros

FIR low-pass filter design

P&M, chapter 7

OS&B, chapter 10

Cartinhour, chapters 6 and 9


FIR low-pass filter design by windowing

Window FIR filters or other filter types

The zeros of a linear phase FIR filter

P&M, section 10.2

OS&B, chapter 7

Cartinhour, chapter 9


Frequency-sampling filters

FIR filter design using optimization

Class handout: Frequency-sampling filters

P&M, sections 10.2.3 and 10.2.4

OS&B, section 7.4

Cartinhour, chapter 9


FFT convolution for FIR filters

The design of IIR filters

P&M, sections 7.3.1, 7.3.2, and 10.3

OS&B, sections 8.7.3 and 7.1

19 The design of IIR filters (cont.)

P&M, section 10.3.3

OS&B, section 7.1


Direct-form filter structures

Transversal FIR structure

IIR direct form structures

Transposed direct forms

Coefficient sensitivity in direct form filters

Class handout: Direct-form digital filter structures

P&M, section 9.1-9.3

OS&B, 6.0-6.5


Interpolation and decimation

Introduction to random signals

Class handout: Interpolation (up-sampling) and decimation (down-sampling)

P&M, sections 11.1-11.5 and 12.1

OS&B, section 4.6, appendix a

Stearns and Hush, chapter 9


The correlation functions (cont.)

Linear system input/output relationships with random inputs

Discrete-time correlation

P&M, sections 12.1-12.2

Stearns and Hush, chapter 13

23 Non-parametric power spectral density estimation

P&M, sections 14.1-14.2

OS&B, sections 10.6-10.8

Stearns and Hush, 15.4 and 15.6

24 Least-squares filter design

Class handout: MATLAB examples of least-squares FIR filter design

P&M, sections 12.3-12.5

Stearns and Hush, chapter 14

25 Adaptive filtering

Class handouts: Introduction to least-squares adaptive filters, introduction to recursive-least-squares (RLS) adaptive filters

P&M, sections 13.1-13.3

Course Info
As Taught In
Fall 2008
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assignment Problem Sets
grading Exams with Solutions
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assignment Programming Assignments