DSP related applied math ramblings.

This is a collection of misc notes about applied math, algorithms and
circuits, somewhat related to programs I'm writing and projects I'm
working on, but deserving a place of their own.

For more http://zwizwa.be/ramblings

20200723 smoothing transaction graph
20200705 Third order
20200704 Higher order sigma-delta
20200618 The 'd' transform
20200613 Low frequency non-linear model updates
20200607 Computing logarithm
20200524 Gyrator, Symplectic
20200518 SVF vs. biquad
20200509 The D-transform
20200216 protocol analyzer
20191116 Financial transactions and density
20191023 CRC
20190826 Different sync encoding
20190512 The importance of reframing
20190506 Mapping fractions to integers
20190411 autodiff and recursive eval
20190404 Embedding manifolds
20190326 Bezier Curves
20190228 Transaction matching
20190222 Universal coalgebra: a theory of systems
20190112 Dobble Beach
20181126 clustering is not well defined
20180918 Gravity peak detection
20180914 Kalman filter
20180705 intuitionistic type theory
20180626 Constructive analysis
20180621 correctness proofs
20180616 Intuitionistic logic
20180615 Brouwer
20180527 Sums and Products..
20180315 Sums and Products
20180212 The important part is concepts
20180105 sparsity
20171229 Agda, coproducts
duality: product and coproduct
20171228 De Morgan vs. product/coproduct
20171118 duality
20170908 On intuition
20170519 woven balls
20170411 Merging
20170102 Running mean/variance
20160902 Category Theory lectures - Bartosz Milewski
20160829 Packetized TDM as coordinate transformations
Inplace matrix transposition
20160814 What is it like to understand advanced mathematics?
20160806 Linear Logic - Session Types
20160518 Cascaded integrator-comb filter
20160225 base64
20160123 Colliding point masses.
Biliart ball chaos
Hamiltonian signals
20160111 CT and declarative programming
20151120 Bisecting intervals with gaps
20151004 Complex derivative hack
20150916 category theory / algebraic topology
20150802 Commutation
20150705 deep learning
20150525 DPW
20150307 PLL stability
20141229 computation is topology
20141216 Simplest symplectic manifolds
Hamiltonian matrix
LU, Cholesky and Hamiltonians
20141214 Symplectic Integration
20141107 Coming together
20141104 Conjugate gradient
20141026 About static nonlinearities and aliasing
20141021 Spinor Fourier Transform
Circuits: is connection essential?
A slowed-down diode
V/I Duality
Circuit sim, a-symmetry of static NL transformation
20141020 Circuit simulation
20141019 Manifold music
20140906 Settable and Non-Interfering Signal Functions for FRP - Daniel Winograd-Cort
Compsable or Separable?
20140706 Add a little frequency or a little period?
20140510 Exponential IDAC (EIDAC)
20140128 Integers don't exist
Where > and >= are the same.
20140109 I am a Strange Loop
20131220 Impedance
Transistor model
20131216 The absurdity of categories (histograms)
Image Processing Primer
20131213 Power-efficient variable-rate signal processing
20131106 Making things with maths - Steven Wittens
20130927 Potential wells / nondeterministic chaos
20130606 Distance in high-dimensional vector spaces
20130522 Simulating reverb tail
20130517 Environmental synth
20130512 FDN Reverberation
20130507 SVF revistited
Curious involution
Gain knob
20130506 Derivative of log
20130503 Stretched exponentials: scaling attack & decay times
20130429 All-pole
20130424 Equalizers
Symplectic integrator
20130421 Symplectic update. What to learn?
SVF decay
Determinant 1
SVF and Symplectic Update
20130420 Logarithmic oversampling
Stilson's Root Locus Adventure
20130419 Efficiency tradeoff for block-based FFT FIR implementation
White minimal amplitude, periodic
IRT - impulse response truncation & Gibbs
All-pole filter designer GUI
Transposition of realizations
Levinson-Durbin algorithm
20130418 Lattice, Ladder and Waveguide
20130417 Inverse Lattice
Waveguide, Ladder, Lattice
20130416 Equalizers
Ladder vs. Lattice?
20130415 Bultheel - Linear Prediction
Realizable transfer functions
Circle filter
20130408 Backwards vs. Forward difference
20130402 Natural gravitation points
Autodiff partial differentials
20130401 Root locus
Stilson's PhD meta
20130331 Iteration and polynomial interpolation
20130328 Static nonlinearities for discrete systems.
20130327 Rational squash functions
Phasor path
Exponentials: drift compensation.
20130326 Imaginary logarithm
Successive squaring for complex exponentials
Broad-range, weak approximation to 2^x
20130325 Exponential curve interpolation
Construct a low-pass filter from a discrete pole pair.
Constant-Q filter topologies
Constant-Q pole curves
20130321 Polynomial bumps and saturation functions
20130320 SVF discretization + compensation
The State Variable Filter
The Harmonic Oscillator and the Laplace Transform
Saturation update
Applying the N-R method for function evaluation
Newton-Raphson method
20130319 Cheaper filter?
What does an LP/HP/BP response look like?
Bilinear vs. impulse invariance
CT -> DT
Partial fraction forms
CT proto 2nd order filters.
Impulse-invariant high-pass filter: what does it mean?
Complex 1-poles
Standard filters from pole positions.
20130315 Normalization: Fast inverse square root
Normalization: a-symmetric
Exponentials: computing the log of |p| ~= 1
Exponentials: final word
20130314 Direct computation of 2D series
20130313 Composition of series expansion
Exponentials: stable update
20130312 Exponentials: update
20130309 Exponentials: pole interpolation: linear vs. exp(linear) ?
Synth sampling
Exponentials: exp(x) vs exp(x/2)^2
Exponentials: compute exp(x) and exp(iy) separately?
Exponentials: soft reset (lowpass)
Exponentials: push drift compensation upward
Exponentials: Reset + Nth root
Exponentials: reset at border
20130308 Exponentials: approximation error should not introduce instability
Exponentials: exp(spline(t))
20130307 Conservative nonlinearities - hamiltonian systems?
Filter transforms
20130228 Time-variant filters
20130224 Quantum Information
20130121 Faust, or point-free DSP
20130120 Hoeldrich method for phase generation
20130123 Integrated wavetable
20130113 Declarative line rendering
20130111 Synchronizing "simultaneous" distributed updates.
20130104 Relational anti-aliased rendering
20130103 Using bilinear texture sampling for anti-aliasing
20121111 Oversampled signals
20121107 2 forms of LFSRs
20121002 Dynwav
20120906 Approximation of error analysis
20120905 Closed form expression for A1 modulator output + Fourier spectrum
20120904 How to make a good density plot?
Plotting the approximation error
S/D conclusions
Diagrams of x/11
Decorrelation through addition of state noise
Approximaton as low-denominator rationals
Ergodic theory
Where is the low frequency noise in S/D approximation?
20120902 Stochastic vs. Deterministic
The Joy of Cats
20120825 Meaning
20120814 Phases of 60 seconds
20120810 New method for solving linear equations over finite fields F_p, p prime
20120809 Expected value of maximum
20120808 Smoothing threshold detections
20120807 Amplitude vs. frequency distribution
20120730 Random book?
20120729 Combine S/D mod + decorrelator
20120728 The non-deterministic S/D modulator
S/D notes
20120723 Mean/variance estimator
20120722 Smoothing financial data
20120714 FFT: recursive construction of analysis functions
20120711 Counter bitswapper
20120710 Inverse of 7 mod 2^32
Analog Synth using Sigma/Delta signals
Density of monetary transactions
Understanding Density
20120708 Basic Hypothesis Testing
20120704 Haskell & simulation
Usable spectrum in a Sigma/Delta signal
Pulse counters as grey code?
Sigma/Delta retake
20120703 Mixers and integrators
20120213 Accounting
20120101 Density of discrete entities
20111229 Distributivity vs. Commutation
20111223 Inference
20111218 Logic
20111031 Time varying filters
20111030 Human motion
20110712 Getting that book feel on an e-reader
20110707 A Primer of Infinitesimal Analysis
20110612 Programs and specifications
Code generation and quasi-particles
20110508 Queued Class-D DAC
20110505 Power spectrum as power of derivative of image
20110316 I don't know sound: 1. Pressure
20110315 Sound impedance
20110302 Fuzzy class D multi channel amp
20110220 Squirrels & robot control
20110121 Initial Algebra / Final Algebra
20110114 Factored FIR
20110111 Z-transform and generating functions
20110110 Dithering and "FAT" saw stacks
Matrix multiplication is quadratic?
20110106 Delta Operator
Model based control
20110105 2nd order 4-multiply ladder EQ
20110104 Nonlinear digital Moog VCF + bandlimited sawtooth.
Lattice and Ladder filters
Practical d-plane formulations
Difference Calculus
Tim Stilson PhD Introduction
20110102 The 7 divisions of the string.
Encoding finite sequences of numbers
Encoding pairs of numbers
Zeta function
Music: scales and intervals: almost equal composite numbers
20101227 A Signal-processing interpretation of the Riemann Zeta Function
Quantization and number theory
20101123 Impedance and Composite Circuits (What is a parallel impedance geometrically?)
Pink noise
20101122 Compensating small room low-frequency acoustic modes
20100814 Binary Tree Permutations
20100811 Size of GF(2^n) symmetry groups
20100808 Chirps from corrugated galvanised iron (golfplaat)
LFSR beacon detection
More PRN sequences: 1/x as fractional or p-adic number.
Finite Field Automorphisms
Schroeder phases and quadratic residue diffusors.
Peak compression
20100807 Quadratic Residues
20100803 Minimal erase counter
20100730 CRC algo
20100722 Binary clocked modulation & averages
20100708 Predict and Update
20100625 Displacement Rank & Generalized Schur
Superfast Toeplitz algorithms
20100624 Exponential sinusoidal modeling
20100622 Annoyed by Computer Modern
Digital Audio Restauration
Carette's Implicit Model Specialization
20100619 Maximum Likelihood estimation and the Kalman Filter
Subspace Identification
Exponential modeling
20100602 Exponential sinusoidal modeling
20100530 Wavelets : local trigonometric basis
Cleaning up PhD research papers
20100430 Differential Music
20100428 Spinors and Simplectic Geometry (Hamiltonian Mechanics)
20100418 d'Alembert Principle
20100412 Conservative Systems and Chaos
What is a differential?
20100410 Computer Algebra System (CAS)
Legendre Transform
20100409 Sussman about crappy notation
Euler-Lagrange equations
20100408 Rhythm & Dance
20100218 Binary Streams as Stochastic Variables (PDFs)
20100203 Never invert a matrix!
20100126 WSOLA - Waveform Similarity OverLap Add.
20091116 HSVD
20091017 Informal proofs are difficult
20090928 Material Derivative
20090707 MDCT
Binary Coding
Video Codecs
20090620 Complex Number Wave Shaping
20090619 Math and Music: Harmony vs. Melody
Matrix Multiplication
Matrix Decompositions
20090618 Implementing Fermat Prime order Galois Fields
Dynamic Wavetable Synthesis
Bandlimited Discontinuities with Infinite Response
Topics in Algebra
20090617 Binary Sound Synthesis
20090610 Using finite fields for music
SD and edge-triggered representation
Filters in SD space.
20090609 Music and almost integers
Symmetries of boolean functions
Sigma-Delta analog synth
20090607 Counting votes.
20090602 Analog vs. Digital
Throwing away the right information
20090511 Computer Modern is Too Thin
Counting votes.
20090506 Graceful degradation of integer values
20090222 Dual Numbers and Automatic Differentiation
20081119 I/O delays in Digital Control
20081006 FFT window design for sinusoidal synthesis
motor control
20081001 AR - ARMA
20080713 Toroid plots
implementing RLE
20080712 Accellerating the inner accumulator loop
Inner loop over angle/tangent
Toroidal Hough Transform
20080711 Hough over 0->pi/2
20080705 LFSR: roundup
20080703 Generalized Pitch Detection
20080701 simplified HT for direction estimation
20080630 2D direction estimation (confused)
20080628 Lens correction
symmetric 2D LFSR
20080627 LFSR resolving linear orientation ambiguity
reverse LFSR
20080626 Snowcrash encoding
Discretized integral transforms: domain / codomain loop order
The Hough Transform
20071216 Chaos and Clipping
20071121 Chaotic Oscillators
20070505 Splines
20070111 LED lights on a circle
20061009 Dither, PWM, Sigma-Delta, Bresenham
20060620 Combining Splitting Fields
20060617 Poles with multiplicity > 1
20060522 Subspaces
20060520 Finite differences
20060505 Dither
20051017 The number e
20051016 Entropy
20030804 Killing Chipmunks with Parametric Dynamic Wavetable Synthesis