**Demos:**- Interactive display and hearing of classic
*digital filters*by`java@falstad.com`

- Interactive display and hearing of classic
**Reading:**- Chapters 1 and 2
of
**Introduction to Digital Filters** - Chapter 4 (Linearity and Time Invariance)
and

Chapter 5 (Time Domain Filter Representations) of**Introduction to Digital Filters** - First section of Chapter 9 (Implementation
Structures)
on the Four
Direct Forms
- Matrix Filter Representations
- Optionally peruse the Music 421 overheads
pertaining to acyclic convolution
- Supplementary: Audio Signal Processing in FAUST
- Assignment 1

- Chapters 1 and 2
of
**Lecture Videos (Total Viewing Time 2 Hours):****IMPORTANT NOTICE:**The videos are hosted on YouTube and they use*annotations*for corrections and supplementary information. These annotations are*not supported on mobile devices*. It is therefore unfortunately important to view these videos*in a Web browser on a desktop/laptop computer*.- Linear Time-Invariant (LTI) Filters,
Convolution, Linearity, Nonlinear Example, Time-Varying Example,
Ideal Lowpass Filter, Pass Band, Cutoff Frequency, Guard Band, Stop
Band, Transition Band, Simplest Lowpass Filter, Impulse Response,
DTFT, Frequency Response, Amplitude Response, Phase Response, Linear
Phase, Sinewave Analysis
[38:36]
- Derivation of Convolution from Linearity and Time-Invariance (LTI)
(Superposition) [2015]
[29:08]
- General Linear [Causal] [Time-Invariant] Filters -- Matrix Representations
[19:03]
- Recursive Filters, Simplest Lowpass,
Phase Delay, Group Delay
[28:01]
- Supplementary: FAUST in the Classroom
[41:00]
- Supplementary: FAUST Intro
[26:00]
- Supplementary: FAUST Implementation of the Simplest Lowpass Filter
[18:22]
- Simplest RECURSIVE LPF, Pole Gain, PFE,
Time-Constant of a Pole, Stability Pole, Bandwidth, Laplace Transform,
s-plane poles and zeros, s-plane pole corresponds to exponential
[38:37]
- What does the Laplace Transform really tell us? A visual explanation (plus applications)
[20:24]

Nice 3D plot of two poles at t=512 [] - Direct Form Digital Filters, Transposing a Flow
Graph, Transposed Direct Forms 1 and 2, Direct Form 1 Biquad, Direct
Form 2 Biquad, Transposed Direct Form 2 Biquad, Interpolated
Delay-Line Read, Interpolated Delay-Line Write = Transpose of
Read
[14:35]
- Simplest Mechanical LPF: Ideal Mass on
Frictionless Surface, Newton's law of motion f=ma, Analog Transfer
Function for Driving-Force Input, Velocity Output, Admittance
(Mobility) of a Mass
[5:31]
- Simplest Mechanical LPF: Ideal Mass on
Frictionless Surface, Differentiation Theorem for Laplace
Transforms, Transfer Function of the Force-Driven Mass: Frequency
Response, Poles and Zeros,, Amplitude Response, 6dB per octave roll
off, Bode Plot, Harald Bode, Phase Response
[27:29]

- Linear Time-Invariant (LTI) Filters,
Convolution, Linearity, Nonlinear Example, Time-Varying Example,
Ideal Lowpass Filter, Pass Band, Cutoff Frequency, Guard Band, Stop
Band, Transition Band, Simplest Lowpass Filter, Impulse Response,
DTFT, Frequency Response, Amplitude Response, Phase Response, Linear
Phase, Sinewave Analysis
[38:36]

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University