These files describe Matlab codes to run two analyses described in our publication. The Period Analysis directory contains the Matlab scripts to run Period Estimate Assisted by Learning (PEAL), a Fast Fourier Transform method with a learning algorithm to estimate circadian period from the non-sinusoidal waveforms. Further information is found in the README.TXT there are 4 main files for period identification of circadian transcripts measured with microarray technology. 1)'periodEstimateMARepWT' is used when no pseudo-sinusoidal waves are required and two replicates are available for each transcript time series 2)'periodEstimateMAWT' is used when no pseudo-sinusoidal waves are required and only one replicate is available for each transcript time series 3)'periodEstimateMARep' is used when pseudo-sinusoidal waves are required and two replicates are available for each transcript time series 4)'periodEstimateMA' is used when pseudo-sinusoidal waves are required and only one replicate is available for each transcript time series The Systems Identification and Nu gap analysis folder provides the Matlab codes to run system identification and nu-gap analysis. Information is provided in readme.txt.