| 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
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Class handout: The Dirac delta and unit-step functions |
| 2 |
Continuous LTI system time-domain response
Sinusoidal response of LTI continuous systems
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Class handouts: Convolution, sinusoidal frequency response |
| 3 |
The Fourier series and transform
Periodic input functions — the Fourier series
Aperiodic input functions — the Fourier transform
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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
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| 5 |
The one-sided Laplace transform
The transfer function
Poles and zeros of the transfer function
Frequency response and the pole-zero plot
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Class handouts: The Laplace transform, understanding poles and zeros, sinusoidal frequency response of linear systems |
| 6 |
Poles and zeros of filter classes
The decibel
Low-pass filter design
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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
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Class handout: Introduction to continuous time filter design |
| 8 |
Second-order filter sections
Transformation of low-pass filters to other classes
State-variable active filters
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Class handouts: Introduction to continuous time filter design, introduction to operational amplifiers, op-amp implementation of analog filters |
| 9 |
Operational-amplifier based state-variable filters
Introduction to discrete-time signal processing
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Class handout: Introduction to the operational amplifier, op-amp implementation of analog filters |
| 10 |
The sampling theorem
The discrete Fourier transform (DFT)
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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
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| 11 |
The discrete Fourier transform (cont.)
The fast Fourier transform (FFT)
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Class handouts: Sampling and the discrete Fourier transform, the fast Fourier transform
P&M, chapter 7
OS&B, chapters 8-9
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| 12 |
The fast Fourier transform (cont.)
Spectral leakage in the DFT and apodizing (windowing) functions
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Class handout: The fast Fourier transform
P&M, sections 8.1-8.3
OS&B, sections 9.0-9.3
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| 13 |
Introduction to time-domain digital signal processing
The discrete-time convolution sum
The z-transform
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P&M, chapter 3
OS&B, chapter 3
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| 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
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| 15 |
Frequency response and poles and zeros
FIR low-pass filter design
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P&M, chapter 7
OS&B, chapter 10
Cartinhour, chapters 6 and 9
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| 16 |
FIR low-pass filter design by windowing
Window FIR filters or other filter types
The zeros of a linear phase FIR filter
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P&M, section 10.2
OS&B, chapter 7
Cartinhour, chapter 9
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| 17 |
Frequency-sampling filters
FIR filter design using optimization
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Class handout: Frequency-sampling filters
P&M, sections 10.2.3 and 10.2.4
OS&B, section 7.4
Cartinhour, chapter 9
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| 18 |
FFT convolution for FIR filters
The design of IIR filters
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P&M, sections 7.3.1, 7.3.2, and 10.3
OS&B, sections 8.7.3 and 7.1
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| 19 |
The design of IIR filters (cont.) |
P&M, section 10.3.3
OS&B, section 7.1
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| 20 |
Direct-form filter structures
Transversal FIR structure
IIR direct form structures
Transposed direct forms
Coefficient sensitivity in direct form filters
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Class handout: Direct-form digital filter structures
P&M, section 9.1-9.3
OS&B, 6.0-6.5
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| 21 |
Interpolation and decimation
Introduction to random signals
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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
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| 22 |
The correlation functions (cont.)
Linear system input/output relationships with random inputs
Discrete-time correlation
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P&M, sections 12.1-12.2
Stearns and Hush, chapter 13
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| 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
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| 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
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| 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
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