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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

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

Derivatives

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

Spinors

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) ?

Normalization

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

Exponentials

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?

Switchcap

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

FFT / DFT

20120711 Counter bitswapper

20120710 Inverse of 7 mod 2^32

Bitswapper

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

Navier-Stokes

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

LFSRs

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

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