FEAT: Poisson process time of arrival and random reflection sign

[mberz]

Which issue(s) are closed by this pull request?

None

Changes proposed in this pull request:

• Add a function to sample times of arrival from a non homogeneous Poisson process
  • The non homogeneous Poisson process is mapped to a homogeneous equivalent for non iterative sampling
  • The cumulative density function is integrated numerically (instead of using the closed form solution from classic room acoustic theory) to support limiting the reflection rate to a fixed number.
• Add a function to sample the amplitude of the process from times of arrivals.
  • The amplitude can be sampled
    • from a binary sequence (-1, 1), effectively sampling the sign only
    • uniform or normal distributions which can be used to synthesize amplitude fine-structure

Dependencies

• This PR depends on PR ENH: Functions to calculate the average number of reflections and their density #174.

[Copilot]

Pull request overview

Adds new parametric utilities for simulating reflection arrival times via a (capped) non-homogeneous Poisson process and for converting arrival times into a ternary (-1/0/1) reflection sequence suitable for signal-based workflows in pyrato.

Changes:

• Added _start_time_of_arrival_poisson_process and time_of_arrival_poisson_process for sampling reflection arrival times (with optional reflection-rate limiting).
• Added ternary_reflection_sequence to map arrival times to discrete samples with random ±1 signs.
• Added unit tests covering start-time calculation, sampling reproducibility, bounds, rate limiting, and ternary sequence behavior.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 6 comments.

File	Description
pyrato/parametric.py	Introduces Poisson-process TOA sampling and ternary reflection sequence generation.
tests/test_parametric.py	Adds tests for the new TOA and ternary-sequence functionality.

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[Copilot]

Pull request overview

Copilot reviewed 3 out of 3 changed files in this pull request and generated 5 comments.