Prony Decomposition Routines

prony is a python package that provides numerical routines for Prony decomposition of discrete signals.

What is Prony decomposition?

The Prony method is a way to obtain the damped-sinusoidal components constituiting a signal. In other words, it expresses the signal as a linear combination of damped sinusoids.

This damped-sinusoid representation is in fact equivalent to all-pole models encountered in signal processing (filter design and system identification). It may also be considered a special case of Padé approximant technique.

The damped-sinusoid a.k.a all-pole representation is particularly useful to describe infinite-impulse-response (IIR) filters in a parsimonious manner. As a consequence, many physical systems with resonant modes - speakers, rooms, waveguides etc. - are modelled this way.

The Prony algorithms implemented in this package can, given a recorded discrete impulse response, estimate the coefficients, frequencies, and damping factors of its constituents.

For a mathematical description, scroll down

Installation and Developing

Please use uv for the love of God.

1. Clone the repo

git clone https://github.com/enceladus2000/prony --branch main

2. Initialize a virtual environment.

cd prony
uv venv
source .venv/bin/activate

3. Run uv sync

uv sync

See this notebook for an example.

Algorithm Details

The signal model is as follows:

$$ s[n] = \sum_{k=1}^K a_i 2^{-n/d_i} \cos(2\pi n / T_i + \phi_i) $$

where $a_i$, $T_i$ is the time period and $\phi_i$ is the phase offset of the component. $d_i$ is the decay factor - in this formulation, it is the number of samples it takes for the component to decay (in amplitude) to half the original.