# Whale Whistles

## Problem

We would like to represent a signal as a sum of chirplets. Chirplets
are Gaussians that are parameterized by their location in time,
location in frequency, chirp rate, and duration. We proposed to
do this by estimating the chirplet parameters with maximum likelihood
estimation. Here we present two examples with whale whistles.
## Example One

Below, we have the time-series (bottom), log spectrum (left), and
spectrogram of a whale whistle. It is number 14 from the NUWC data
set and the dynamic range in the spectrogram is 50 dB.
Listen.

We now take this whistle and represent it as a sum of chirplets.
Below is the approximation with 7 chirplets. The approximation
sounds like the original with the noise removed.
Listen.

## Example Two

We show another example with number 61 from the NUWC data set.
Listen.

This is the approximation with 8 chirplets.
Listen.

Jeffrey C. O'Neill (jco8 at cornell.edu)