Comparing Signals
The DDMA team was posed the problem by a customer of comparing measurements of strain over time on engineered part from an experiment with the results of their simulations. We proposed these methods for extracting and comparing the relevant characteristics of signals.
The first algorithm is geomeasures2, from the IDA code suite. This algorithm takes as input a coordinate description of a simple closed curve, and a vector of scales. The result is a family of eight geometric quantities, each computed for both each point of the curve and each provided scale. This can be interpreted as being eight scalar-valued function of two variables. Each gives a multiscale description of geometric characteristics of the curve, and be thought of as a particular shape signature of the curve. The second algorithm computes the Monge-Kantorovich (MK) distance between two functions. This is also known as the earth-mover’s distance, or the optimal transport distance. It can be thought of as a warping distance, as it is measured in terms of an optimal warping mapping.
Tom Asaki - Signal Energy Measures and Metrics
Several measures and metrics based on the cummulative energy content of time signals. Similarity, in this case, is not based directly on geometric comparisons but on signal energy transfer.
Gilad Lerman - Envelopes of Signals via Medmax
Our goal is to find the envelope of a signal. We suggest the Medmax algorithm for this purpose. The algorithm is an elaboration of the median filter, however it allows different order statistics.
Matt Sottile - Spectrogram warping distance
This metric is based on computing the similarity of short time Fourier rep- resentations of the signal at well defined windows. It also provides a metric of similarity for the evolution of a particular frequency component over these windows in time.
Kevin Vixie & Selim Esedoglu - Variational Tools for Signal Similarity Analysis
This collection of eight routines, and their associated subroutines, implement a number of metrics for quantifying the differences between signals from experiments and simulations. Our approach has been informed by the intuitive process by which experts judge the similarity and differences between two given signals (typically, one signal from experiments, and the other from simulation).
The code and documentation for all of the above.