Sequences¶

Symbol-mapping sequences¶

sdr.binary_code(degree: int) → NDArray[int_]

Generates a binary code of length \(n = 2^m\).

sdr.gray_code(degree: int) → NDArray[int_]

Generates a Gray code of length \(n = 2^m\).

Correlation sequences¶

sdr.barker_code(length: int, ...) → ndarray[Any, dtype[int64]]

sdr.barker_code(length: int, output: 'field') → FieldArray

sdr.barker_code(length: int, output) → ndarray[Any, dtype[float64]]

Generates the Barker code/sequence of length \(n\).

sdr.hadamard_code(length: int, ...) → ndarray[Any, dtype[int64]]

sdr.hadamard_code(length: int, index: int, output) → FieldArray

sdr.hadamard_code(length: int, ...) → ndarray[Any, dtype[float64]]

Generates the Hadamard code/sequence of length \(n = 2^m\).

sdr.walsh_code(length: int, ...) → ndarray[Any, dtype[int64]]

sdr.walsh_code(length: int, index: int, output) → FieldArray

sdr.walsh_code(length: int, ...) → ndarray[Any, dtype[float64]]

Generates the Walsh code/sequence of length \(n = 2^m\).

sdr.gold_code(length: int, ...) → ndarray[Any, dtype[int64]]

sdr.gold_code(length: int, index: int = 0, ...) → FieldArray

sdr.gold_code(length: int, ...) → ndarray[Any, dtype[float64]]

Generates the Gold code/sequence of length \(n = 2^m - 1\).

sdr.kasami_code(length: int, ...) → ndarray[Any, dtype[int64]]

sdr.kasami_code(length: int, ...) → FieldArray

sdr.kasami_code(length: int, ...) → ndarray[Any, dtype[float64]]

Generates the Kasami code/sequence of length \(n = 2^m - 1\).

sdr.zadoff_chu_sequence(length: int, ...) → NDArray[complex128]

Generates the root-\(u\) Zadoff-Chu sequence of length \(N\).

Linear recurrent sequences¶

class sdr.FLFSR

Implements a Fibonacci linear-feedback shift register (LFSR).

class sdr.GLFSR

Implements a Galois linear-feedback shift register (LFSR).

sdr.berlekamp_massey(sequence: FieldArray, ...) → Poly

sdr.berlekamp_massey(sequence: FieldArray, output) → FLFSR

sdr.berlekamp_massey(sequence: FieldArray, output) → GLFSR

Finds the minimal polynomial \(c(x)\) that produces the linear recurrent sequence \(y\).

Maximum-length sequences¶

sdr.m_sequence(degree: int, ...) → ndarray[Any, dtype[int64]]

sdr.m_sequence(degree: int, ...) → FieldArray

sdr.m_sequence(degree: int, ...) → ndarray[Any, dtype[float64]]

Generates a maximum-length sequence (\(m\)-sequence) from a Fibonacci linear feedback shift register (LFSR).

sdr.preferred_pairs(degree: int, ...) → Iterator[tuple[Poly, Poly]]

Generates primitive polynomials of degree \(m\) that produce preferred pair \(m\)-sequences.

sdr.is_preferred_pair(poly1: PolyLike, poly2: PolyLike) → bool

Determines if two primitive polynomials generate preferred pair \(m\)-sequences.