1 
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 unitstep functions 
2 
Continuous LTI system timedomain response
Sinusoidal response of LTI continuous systems

Class handouts: Convolution, sinusoidal frequency response 
3 
The Fourier series and transform
Periodic input functions — the Fourier series
Aperiodic input functions — the Fourier transform

Class handout: Frequency domain methods 
4 
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


5 
The onesided Laplace transform
The transfer function
Poles and zeros of the transfer function
Frequency response and the polezero plot

Class handouts: The Laplace transform, understanding poles and zeros, sinusoidal frequency response of linear systems 
6 
Poles and zeros of filter classes
The decibel
Lowpass filter design

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

Class handout: Introduction to continuous time filter design 
8 
Secondorder filter sections
Transformation of lowpass filters to other classes
Statevariable active filters

Class handouts: Introduction to continuous time filter design, introduction to operational amplifiers, opamp implementation of analog filters 
9 
Operationalamplifier based statevariable filters
Introduction to discretetime signal processing

Class handout: Introduction to the operational amplifier, opamp implementation of analog filters 
10 
The sampling theorem
The discrete Fourier transform (DFT)

Class handout: Sampling and the discrete Fourier transform
P&M, sections 6.16.3 and 7.1
OS&B, sections 4.14.3 and 8.18.5

11 
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 89

12 
The fast Fourier transform (cont.)
Spectral leakage in the DFT and apodizing (windowing) functions

Class handout: The fast Fourier transform
P&M, sections 8.18.3
OS&B, sections 9.09.3

13 
Introduction to timedomain digital signal processing
The discretetime convolution sum
The ztransform

P&M, chapter 3
OS&B, chapter 3

14 
The discretetime transfer function
The transfer function and the difference equation
Introduction to zplane stability criteria
The frequency response of discretetime systems
The inverse ztransform


15 
Frequency response and poles and zeros
FIR lowpass filter design

P&M, chapter 7
OS&B, chapter 10
Cartinhour, chapters 6 and 9

16 
FIR lowpass 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

17 
Frequencysampling filters
FIR filter design using optimization

Class handout: Frequencysampling filters
P&M, sections 10.2.3 and 10.2.4
OS&B, section 7.4
Cartinhour, chapter 9

18 
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

20 
Directform filter structures
Transversal FIR structure
IIR direct form structures
Transposed direct forms
Coefficient sensitivity in direct form filters

Class handout: Directform digital filter structures
P&M, section 9.19.3
OS&B, 6.06.5

21 
Interpolation and decimation
Introduction to random signals

Class handout: Interpolation (upsampling) and decimation (downsampling)
P&M, sections 11.111.5 and 12.1
OS&B, section 4.6, appendix a
Stearns and Hush, chapter 9

22 
The correlation functions (cont.)
Linear system input/output relationships with random inputs
Discretetime correlation

P&M, sections 12.112.2
Stearns and Hush, chapter 13

23 
Nonparametric power spectral density estimation 
P&M, sections 14.114.2
OS&B, sections 10.610.8
Stearns and Hush, 15.4 and 15.6

24 
Leastsquares filter design 
Class handout: MATLAB examples of leastsquares FIR filter design
P&M, sections 12.312.5
Stearns and Hush, chapter 14

25 
Adaptive filtering 
Class handouts: Introduction to leastsquares adaptive filters, introduction to recursiveleastsquares (RLS) adaptive filters
P&M, sections 13.113.3
