# Lecture Notes

SES # TOPICS LECTURE NOTES
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

(PDF)
2

Continuous LTI system time-domain response

Sinusoidal response of LTI continuous systems

(PDF)
3

The Fourier series and transform

Periodic input functions — the Fourier series

Aperiodic input functions — the Fourier transform

(PDF)
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

(PDF)
5

The one-sided Laplace transform

The transfer function

Poles and zeros of the transfer function

Frequency response and the pole-zero plot

(PDF)
6

Poles and zeros of filter classes

The decibel

Low-pass filter design

(PDF)
7

Butterworth filter design example

Chebyshev filters

(PDF)
8

Second-order filter sections

Transformation of low-pass filters to other classes

State-variable active filters

(PDF)
9

Operational-amplifier based state-variable filters

Introduction to discrete-time signal processing

(PDF)
10

The sampling theorem

The discrete Fourier transform (DFT)

(PDF)
11

The discrete Fourier transform (cont.)

The fast Fourier transform (FFT)

(PDF)
12

The fast Fourier transform (cont.)

Spectral leakage in the DFT and apodizing (windowing) functions

(PDF)
13

Introduction to time-domain digital signal processing

The discrete-time convolution sum

The z-transform

(PDF)
14

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

(PDF)
15

Frequency response and poles and zeros

FIR low-pass filter design

(PDF)
16

FIR low-pass filter design by windowing

Window FIR filters or other filter types

The zeros of a linear phase FIR filter

(PDF)
17

Frequency-sampling filters

FIR filter design using optimization

(PDF)
18

FFT convolution for FIR filters

The design of IIR filters

(PDF)
19 The design of IIR filters (cont.) (PDF)
20

Direct-form filter structures

Transversal FIR structure

IIR direct form structures

Transposed direct forms

Coefficient sensitivity in direct form filters

(PDF)
21

Interpolation and decimation

Introduction to random signals

(PDF)
22

The correlation functions (cont.)

Linear system input/output relationships with random inputs

Discrete-time correlation

(PDF)
23 Non-parametric power spectral density estimation (PDF)
24 Least-squares filter design (PDF)