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 G2 Root System:pair_angle_kurtosis (+10.4z) — beyond what the standard bank predicts for it. It sits beside Morse Code in the atlas (standard-bank rank 31) — a neighbor conventional features miss.

What standard analysis sees
tail heaviness0.01
asymmetry0.51
occupancy0.06
short-range corr0.80
long-range memory0.97
spectral colour0.39
periodicity0.95
complexity0.00
time-irreversibility0.48
volatility clustering0.82
multifractality0.99
dimensionality0.40
nonstationarity0.08
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
G2 Root System:pair_angle_kurtosis+10.4zbank-miss 1.4σ
E8 Lattice:coset_transition+6.5zbank-miss 1.4σ
Mostow Rigidity:margulis_ratio+3.5zbank-miss 2.0σ
Spherical S²:angular_spread+3.4zbank-miss 1.9σ
Wavelet Cascade:intermittency_slope-3.4zbank-miss 1.0σ
Visibility Graph:avg_clustering_coeff-3.0zbank-miss 1.8σ
Mostow Rigidity:volume_entropy-3.0zbank-miss 1.1σ
Mostow Rigidity:mean_turn_angle+2.9zbank-miss 1.2σ

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 Modulation3.82
Morse Code4.75
μ-law Sine4.84

Open in Atlas →

Which Geometries Light Up

2-adic2-adic:valuation_transition_predictabilityrank 3/3070.9882
2-adic2-adic:multiscale_markov_predictabilityrank 4/3070.9900
D4 TrialityD4 Triality:edge_ortho_polarityrank 306/3070.0074
E8 LatticeE8 Lattice:coset_transitionrank 2/3070.3659
Fisher InformationFisher Information:velocity_spectral_ginirank 4/3070.7793
G2 Root SystemG2 Root System:pair_angle_kurtosisrank 2/307286.3648
G2 Root SystemG2 Root System:short_long_ratiorank 2/3070.9979
Higher-Order StatisticsHigher-Order Statistics:perm_entropyrank 306/3070.0120
Hyperbolic (Poincaré)Hyperbolic (Poincaré):curvature_structurerank 303/3071.9677
Information TheoryInformation Theory:compression_ratiorank 306/3070.0023
Klein BottleKlein Bottle:rank_deficitrank 4/3070.9642
Klein BottleKlein Bottle:rank_deficit_maxrank 5/3070.9761
LaplacianLaplacian:poisson_recovery_errorrank 306/3070.0020
Mostow RigidityMostow Rigidity:margulis_ratiorank 2/3070.9801
Mostow RigidityMostow Rigidity:mean_turn_anglerank 2/3070.9893
Multi-Scale WassersteinMulti-Scale Wasserstein:w_stdrank 1/3070.1674
Multi-Scale WassersteinMulti-Scale Wasserstein:w_meanrank 2/3070.1483
Ordinal PartitionOrdinal Partition:forbidden_transitionsrank 1/3070.8800
Projective ℙ²Projective ℙ²:cross_ratio_stdrank 305/3070.0000
S² × ℝ (Thurston)S² × ℝ (Thurston):sphere_concentrationrank 303/3070.0063
in continuous-flows
alphabetical
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