33383bdd-964e-4f82-955c-0c67cc24d3a7 50 4 5 false false 0 0 decimal

Hilbert Transform

X HilbertT m X rows : ε m 2 log Floor 1 + : m m m 2 ε^/ 12 / ≡ (- eval : y X Re X UnitsOf / vectorize m fft : n M n 1 matrix eval 11 line : h 121 m 1 - 2 / trunc M + (* 11 m 2 m 2 / trunc * - (- M + m 1 - 2 / trunc M stack eval : y h * vectorize m ifft 71 line :

a b n pR a b a - n / 0 n range * + 11 line :

Application: Envelope Detection

Discerte time domain

T 0 s * 10 s * 1000 pR :

Signal

S 21 Hz * T * sin + (12 Hz * T * sin * vectorize :

Hilbert transform

H S HilbertT :

Signal envelope

T S augment T H abs vectorize augment 2 1 sys

Signal phase

T H arg vectorize augment 1 1 sys

Alvaro