Detection and Extraction of Weak Signals Buried in Noise using the Autoregressive Model
Jingnan Cai, Keagan Callis
Abstract
A program was built which exploits correlation in stationary noise to predict future values of the noise, allowing for detection and extraction of the shape of weak signals which enter the noise at some unknown onset time. In computer simulations, we determined the exact onset time of a signal which we introduced to stationary and correlated noise at data point 4000, and when plotting the extracted signal versus the actual signal we obtained an R2 value of 0.94 and the root mean square from the original signal 0.1523, indicating our program successfully extracted the shape of the signal. An application of our program to audio signals allowed us to successfully extract the shape of a signal buried within audio noise from a speaker and determine its onset time with the same R2 value of 0.82.
Introduction
Advanced methods of detecting signals with much lower amplitudes than the noise are incredibly useful and usually vital to a variety of different applications. In this experiment, we used the Autoregressive Model to recognize patterns in stationary and correlated noise in order to predict future values of that noise, since correlated noise is common in nature anyway[1]. By subtracting the prediction from the actual noise-corrupted signal, we can then extract the desired signal. A possible application of this type of model would be to filter out unwanted noise obtained from performing a type of MRI on a person – i.e. to filter out signals from tissue that is not desired to be inspected. This statistical model is also applied broadly to the field of finance and marketing and data mining as a tool of pattern recognition and prediction.
In this project, we applied our method to various computer simulations to extract synthetic signals introduced into the stationary and correlated noise. After seeing that it was working as intended, we applied our program to extract an audio signal which we buried in correlated noise and played out of a speaker, and were able to successfully extract that audio signal.