CCRMA Restricted WWW Page Topics
Overview of Topics
FFT-Based Digital Audio Compression
FFT Signal Processing: The Filter-Bank Summation (FBS) Method for Fourier Analysis, Modification, and Resynthesis
Principles of Multirate Systems
Downsampling and Upsampling
FFT Implementation of Linear Systems
Multirate Filter Banks
FFT Signal Processing: The Overlap-Add
Sinusoidal Modeling and the Phase Vocoder
Introduction to Linear Predictive Coding (LPC)
Time-Scale Modification and Critically Sampled Filter Banks
Virtual Analog Sound Synthesis
Introduction to Wavelet Transforms
The Window Method for FIR Digital Filter Design
Digital Audio Compression
FFT-Based Digital Audio Compression
Subband Coding
Transform Coding
Princen-Bradley Filter Bank
Dolby AC-2 and AC-3
MUSICAM
JPEG Image Compression
``FFT-Based Digital Audio Compression''
References
Short-Time Fourier Transform Processors: Overlap-Add Interpretation
``FFT Signal Processing: The Overlap-Add (OLA) Method for Fourier Analysis, Modification, and Resynthesis''
Linear Convolution of Finite Duration Signals
FFT Convolution
FFT Convolution vs. Direct Convolution
Audio FIR Filters
Examples
Example 1: Low Pass Filtering
Example 2: Time Domain Aliasing
Infinite-Length signals
Example 3: Overlap-Add Convolution
Summary
Time Varying Modifications
Block Diagram Interpretation
Length L FIR Frame Filters
Nonlinear Modifications
Poisson Summation
Poisson Summation Formula
Constant-Overlap-Add (COLA) Cases
Quick Summary of Zero Padding
About this document
Short-Time Fourier Transform Processors: Filterbank-Summation Interpretation
Two Views of the Short Time Fourier Transform
Filter Bank Summation (FBS)
FFT Signal Processing: The Filter-Bank Summation (FBS) Method for Fourier Analysis, Modification, and Resynthesis
OLA
Filterbank Interpretation of the STFT
Window Constraints
Nyq(N) Windows
Downsampling Factor R
Fixed Modifications
Time Varying Modifications in FBS
OLA and FBS duality
STFT Analysis
FBS Analysis Filter Bank
STFT Re-Synthesis
STFT Fixed Spectral Modification
STFT Time Varying Spectral Modification
Portnoff Windows
Introduction to Wavelets and Perfect Reconstruction Filter Banks
Geometric Signal Theory
Examples Basis Signals
Wavelets
Discrete Wavelet Transform
Discrete Wavelet (Dyadic) Filterbank
Generalized STFT
Discrete Wavelet Filterbank
Application Example: Cross-Synthesis
Spectral Envelope Extraction
Cepstral Smoothing
Linear Prediction Spectral Envelope
LPC Envelope Example: Speech vowel ``ah'' [a
About this document
``FFT Signal Processing: The Filter-Bank Summation (FBS) Method for Fourier Analysis, Modification, and Resynthesis''
Fourier Implementation of LTI systems (Overlapp add summation)
Linear Convolution of finite length signals
Infinite Length signals
Multirate Filterbanks
``Multirate Filter Banks''
Upsampling and Downsampling
Multirate Noble Identities
Example: Filtering and Downsampling
Polyphase Filtering
Filtering and Downsampling, Revisited
Perfect Reconstruction Filter Banks
``Principles of Multirate Systems''
DFT Filter Banks
Relationships bewteen OLA,LOT, & ELT
Pseudo-QMF Cosine Modulation Filter Bank
Perfect Reconstruction Cosine Modulated Filter Banks
MPEG Layer III Filter Bank
References
Linear Prediction
``Introduction to Linear Predictive Coding (LPC)''
LPC Motivation and Overview
Basic Principles of LPC
Goal of Linear Prediction
Notes and Discussion
Statistical Interpretation of LPC
Predicting the random process
Solution to the MMSE Linear Prediction Problem
Infinite Memory Linear Prediction
Objective of Prediction
Computation of LPC Parameters
Autocorrelation Method
Levinson-Durbin Algorithm
Levinson-Durbin algorithm
Notes
Covariance Method
LPC Equations for the Covariance Method
Cholesky Decomposition Solution for the Covariance Method
Outline of the Cholesky Decomposition Method
Stability issues
Frequency Domain Interpretations of LPC Analysis
Power Spectrum Envelope Matching
Perfect Reconstruction of the Signal Spectrum
Spectral Matching Properties of LPC
Envelope following property of LPC
Smoothness as a Function of Prediction Order
Frequency Selective Linear Prediction
Selective Linear Prediction: Procedures
Applications of LPC
References
Spectral Modeling Synthesis and the Phase Vocoder
``Sinusoidal Modeling and the Phase Vocoder''
Motivation and Overview
Resolution Bandwidth (resolving sinusoids)
Resolution of Harmonic Signals
Choice of Window Length M
Zero Padding
spectral interpolation
Parabolic Interpolation
Additive Synthesis
Spectral Analysis of Sinusoids
SMS and PVC Overview
Vocoders
Computing the Vocoder Parameters
Tracking Sinusoidal Peaks in a Sequence of FFTs
Peak Tracking across Frames
McAulay and Quatieri Sinusoidal Speech Modeling
Sines+Noise Modeling
Analysis
Synthesis
About this document
Time Compression/Expansion
Compressed Data Requirements
Time Domain Methods
Frequency Domain Methods
Time Scale Modification Sound Examples
Subband Time Scale Modification
OLA Sound Examples
About this document
``Time-Scale Modification and Critically Sampled Filter Banks''
Virtual Analog Sound Synthesis
``Virtual Analog Sound Synthesis''
What is ``Virtual Analog'' Synthesis?
Subtractive Synthesis
Goals of Virtual Analog Design
Design Issues
Analog Synthesis Modules
First Attempt at Digital Versions
But if you want to get picky
Bandlimited Signal generation
Simplicity of Classic Analog Waveforms
Multiple-Integration
More on Multiple Integration
DC Blocking Filters
The Bandlimited Impulse Train (BLIT)
BLIT Methods
Additive Methods for BLIT Synthesis
DSF
SincM
Wavetable, Wavetable Bank
Sum-of-Windowed Sincs (SWS)
Comparisons: Frequency input cost
Flexibility Comparison
Trouble at the Nyquist Limit
Fixing the Nyquist Entrance/Exit Click
Pictures of Frequency Sweeps
Amplitude, Loudness
Fixed-Cost vs. Variable Cost
Mixed-Algorithm Oscillator
Calculating Steady-State Waveform vs. Calculating Events
Digital VCF
Variable Filter Design
Closed-Form Coefficient Functions
Multiple Static Designs/Coefficient Interpolation
Outer Product Expansion
Spectrum Warping
Heterodyne Filters
General Advice
The Moog VCF
Root Locus
Back to the MoogVCF
More on the MoogVCF
Root-Locus Filters
Discrete-Time Moog VCF
Separation Table
More cases
Various Comments
zeros at z=0.3
Other root-locus filters
Wavelets
Introduction to Wavelet Transforms
Geometric Signal Theory
Introduction to Wavelet Transforms
Example Basis Signals
Discrete Wavelet Transform
Discrete Wavelet (Dyadic) Filterbank
Generalized STFT
Discrete Wavelet Filterbank
The Window Method for Digital Filter Design
The Window Method for FIR Digital Filter Design
FIR Digital Filter Design
Matlab hilbert() function
Filter Specifications
Ideal Lowpass Filter
Example
Other Types of Filters
Hilbert Transform Filter Design: A Case Study in FIR Filter Design
Problem Statement
Kaiser Window
Oversimplified Window Method
Window Method applied to Bandlimited Ideal Impulse Response
Remez Multiple Exchange Method
Summary of Trade-Offs
©2000 CCRMA, Stanford University. All Rights Reserved.
Created and maintained by Gary P. Scavone,
gary@ccrma.stanford.edu
CCRMA Restricted WWW Page Topics
CCRMA Restricted WWW Page Topics