Cyclic Correlation Module

This module provides functions to compute the cyclic cross-correlation between two 1D signals using either FFT-based or analytic methods, and to generate Zadoff-Chu sequences. It supports automatic input validation, optional zero-padding, and normalization.

Current version: 0.1.12

Features

• Input validation: Ensures signals are 1D and compatible in length.
• Flexible methods: Choose between "fft" (fast) and "analytic" (direct computation).
• Padding/truncation: Automatically pads or truncates signals to match lengths if needed.
• Normalization: Optionally normalizes the correlation output.
• Zadoff-Chu sequence generation: Generate ZC sequences for communication applications.

Functions

cyclic_corr(s1, s2, method="fft", wrt="short", normalized=True, ccwindow=0, shift=0)

Computes the cyclic cross-correlation between signals s1 and s2.

Parameters

• s1, s2: 1D lists or numpy arrays (input signals).
• method: "fft" (default) or "analytic".
• wrt: "short" (default) or "long"; specifies the correlation window reference.
• normalized: If True, normalizes the correlation output.
• ccwindow: If >0, sets the length of the correlation window (default 0, meaning full).
• shift: If >0, shifts the window start index.

Returns

• Z: Cyclic cross-correlation array.
• max_val: Maximum absolute value of the correlation.
• t_max: Index of the maximum correlation.
• min_val: Minimum absolute value of the correlation.

check_inputs_define_limits(s1, s2, method, wrt, normalized=True, ccwindow=0, shift=0)

Validates and prepares input signals for correlation computation.

ZC_sequence(r, q, N)

Generates a discrete Zadoff-Chu (ZC) sequence.

Parameters

• r (int): Root index of the ZC sequence. Must satisfy 1 <= r <= N.
• q (int): Cyclic shift of the sequence. Must satisfy q >= 0.
• N (int): Length of the sequence. Must satisfy N >= 1.

Returns

• numpy.ndarray: The generated Zadoff-Chu sequence of length N.

Example

from cyclic_correlation import ZC_sequence

zc = ZC_sequence(r=1, q=0, N=13)
print("Zadoff-Chu sequence:", zc)

Example

from cyclic_correlation import cyclic_corr

s1 = [1, 2, 3, 4]
s2 = [4, 3, 2, 1]
Z, max_val, t_max, min_val = cyclic_corr(s1, s2, method="fft", wrt="short", normalized=True)
print("Correlation:", Z)
print("Max value:", max_val)
print("Index of max:", t_max)
print("Min value:", min_val)

Requirements

• numpy

License

BSD-3-Clause