RcppWavelet: An R/C++ Implemententation of Continuous Wavelet Transform

Based on the work of Jules Françoise and Frederic Bevilacqua at IRCAM

Overview

The intent of the RcppWavelet package is to enable high performance wavelet analysis of time series data using R.

A short vignette, Using RcppWavelet, shows a simple use case.

Installation

System Requirements:

This has only been tested on Ubuntu 14.04, and currently fails to compile on my Windows PC

• Armadillo - C++ Linear Algebra Library
• Boost C++ Libraries
• OpenMP

library(devtools)
devtools::install_github("msummersgill/RcppWavelet")

Core Functionality

RcppWavelet::analyze() executes a continuous wavelet transform on an input numeric vector. Specifying cores > 1 uses openmp to enable multi-threading. Since the calculation of coefficients for each band can be executed independently, the processing time is substantially reduced for each additional core used.

Two wavelets are currently implemented: Morlet and Paul.

Input Parameters

• x: A zero-mean, normalized numeric vector with no NULL values
• bands_per_octave: Number of bands to calculate for each doubling of the frequency across the range
• frequency_min: Min Frequency
• frequency_max: Max Frequency
• samplerate_hz: Input signal sample rate (Hertz)
• mother_wavelet: Mother Wavelet, either "MORLET" or "PAUL"
• morlet_carrier: The carrier frequency for the Morlet Wavelet (not relevant for Paul wavelet)
• paul_order: The order of the Paul Wavelet to be used (not relevant for Morlet wavelet)
• cores: number of threads to be created using openMP

Wavelet <- RcppWavelet::analyze(x = signal_to_analyze,
                                bands_per_octave = 32,
                                frequency_min = 0.02,
                                frequency_max = 0.5,
                                samplerate_hz = 1,
                                mother_wavelet = "MORLET",
                                morlet_carrier = 30,
                                paul_order = 2,
                                cores = 6)

Output

The returned object is a list of five elements.

• signal: original input vector
• scalogram: a complex matrix representing the continuous wavelet transform of the input vector.
• frequencies: the periods of each band calculated
• periods: the corresponding periods for each band
• configuration: a summary of the wavelet's parameters

Helper functions

Signal Reconstruction

RcppWavelet::reconstruct()

Reconstructs signal based on wavelet transform.

Potential Further Development

• Helper functions for input de-trending, filtering, and normalization
• Implementation of FFTW in place of ARMA::FFT for improved speed