Square Wave

signal-synthesis · 37 views
signal-synthesisperiodic

What It Is

Square wave --- binary oscillation (±1), maximal harmonic content with 1/n odd-harmonic Fourier series

Interpretation

Standard analysis sees: bounded / light-tailed; few distinct values; long-range memory (persistent); strongly periodic; low-complexity (predictable, not noise-like); multifractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on E8 Lattice:coset_transition (+6.6z) — beyond what the standard bank predicts for it. It sits beside Morse Code in the atlas (standard-bank rank 26) — a neighbor conventional features miss.

What standard analysis sees
tail heaviness0.02
asymmetry0.56
occupancy0.07
short-range corr0.76
long-range memory0.89
spectral colour0.40
periodicity0.92
complexity0.00
time-irreversibility0.51
volatility clustering0.81
multifractality0.99
dimensionality0.45
nonstationarity0.06
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
E8 Lattice:coset_transition+6.6zbank-miss 1.0σ
Wavelet Cascade:coarse_scale_kurtosis_slope-3.4zbank-miss 1.2σ
Mostow Rigidity:margulis_ratio+3.3zbank-miss 2.0σ
Spherical S²:angular_spread+3.1zbank-miss 2.0σ
Visibility Graph:avg_clustering_coeff-3.0zbank-miss 2.2σ
Mostow Rigidity:volume_entropy-3.0zbank-miss 1.5σ
Fisher Information:velocity_spectral_gini+2.4zbank-miss 1.1σ
Bispectrum:bicoherence_gini-2.3zbank-miss 1.3σ

Composition

dtypefloat64
range[-1, 1]
unique values2 / 16384
mean ± std-0.00598 ± 1

Binary sequence — two distinct symbols.

Render Gallery

Atlas Position

Nearest neighborDistance
Pulse-Width Modulation3.81
Morse Code4.75
μ-law Sine4.84

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:valuation_transition_predictabilityrank 3/3060.9882
2-adic › 2-adic:multiscale_markov_predictabilityrank 4/3060.9900
D4 Triality › D4 Triality:edge_ortho_polarityrank 305/3060.0074
E8 Lattice › E8 Lattice:coset_transitionrank 2/3060.3659
Fisher Information › Fisher Information:velocity_spectral_ginirank 4/3060.7793
G2 Root System › G2 Root System:pair_angle_kurtosisrank 2/306286.3648
G2 Root System › G2 Root System:short_long_ratiorank 2/3060.9979
Higher-Order Statistics › Higher-Order Statistics:perm_entropyrank 305/3060.0120
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structurerank 302/3061.9677
Information Theory › Information Theory:compression_ratiorank 305/3060.0023
Klein Bottle › Klein Bottle:rank_deficitrank 3/3060.9642
Klein Bottle › Klein Bottle:rank_deficit_maxrank 4/3060.9761
Laplacian › Laplacian:poisson_recovery_errorrank 305/3060.0020
Mostow Rigidity › Mostow Rigidity:margulis_ratiorank 2/3060.9801
Mostow Rigidity › Mostow Rigidity:mean_turn_anglerank 2/3060.9893
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_stdrank 1/3060.1674
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 2/3060.1483
Ordinal Partition › Ordinal Partition:forbidden_transitionsrank 1/3060.8800
Projective ℙ² › Projective ℙ²:cross_ratio_stdrank 304/3060.0000
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentrationrank 302/3060.0063
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