**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
- Optionally peruse the Music 421 overheads
pertaining to acyclic convolution
- Assignment 1

- Chapters 1 and 2
of
**Lecture Videos (Total Viewing Time 2 Hours):**- Linear Time-Invariant (LTI) Filters,
Convolution, Ideal Lowpass, Guard 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]
- 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]
- 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, Ideal Lowpass, Guard 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