Analysis of a set of points from an array

I have an array that contain N=100 points with "double" values. The points in the array represent a curve (see picture ) blue line is the curve. I need an analysis component that will answer the following questions: - What is the behavior of the curve ( constant growing , constant falling, just fluctuations around a value ) - What is the fluctuation (deviation from the mean) - Is fluctuations relatively periodic? - what is the average period? - what is the deviation from average period? - are there many fluctuations? - a measure of fluctuation sizes (is it 1% of the value or 50% of the value?) - what is the intrinsic(expected) value at a particular point The task is to develop and describe the algorithms with explanations. Apparently, to do this task effectively, the person needs to have some math knowledge. ## Deliverables 1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. 2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables): a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment. b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request. 3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement). ## Platform VS2005, .NET , Windows XP,