Incremental autocorrelation calculation for streamed data using components

A computing system, the computing system comprising:

• one or more computing devices;
• each computing device comprising one or more processors;
• one or more storage media comprising a buffer for storing data elements in a computation window of a data stream;
• a computation window size counter which indicates a quantity of data elements in the computation window;
• and
• one or more calculation modules that, when executed by at least one of the one or more computing devices, determine an autocorrelation at a specified lag for an adjusted computation window, wherein the determination of the autocorrelation includes to:
• a. initialize a lag l (l>0), a computation window size counter n (n>2*l+1), a sum or a mean, or both, and one or more components of an autocorrelation at lag l, other than a sum and a mean, for a pre-adjusted computation window containing n data elements of a data stream stored in the buffer;
• b. generate an autocorrelation at lag l for the pre-adjusted computation window based on one or more of the initialized components;
• c. access or receive a data element to be added to the pre-adjusted computation window;
• d. store the accessed or received data element to the buffer;
• e. adjust the pre-adjusted computation window by adding the accessed or received data element to the pre-adjusted computation window and adjusting the computation window size counter by adding its value by 1;
• f. incrementally calculate a sum or a mean or both for the adjusted computation window;
• g. directly incrementally calculate one or more components of an autocorrelation at lag l other than a sum and a mean for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l other than a sum and a mean for the pre-adjusted computation window, including to add a contribution of the data element added to the pre-adjusted computation window to each of the one or more components of the autocorrelation at lag l other than a sum and a mean respectively without accessing and using all data elements in the adjusted computation window to allow the computing system to use less memory and to result in faster computation time;
• and
• h. generate, based on one or more of the calculated components of the autocorrelation at lag l for the adjusted computation window, the autocorrelation at lag l for the adjusted computation window.

A computing system program product for use at a configured computing system that comprises one or more computing devices and one or more storage media, each computing device comprising one or more processors, the computing system program product for implementing a method for generating an autocorrelation at a specified lag for an adjusted computation window, the computing system program product comprising one or more non-transitory computing-device-readable storage media having stored thereon computing-device-executable instructions that, when executed by the configured computing system, cause the configured computing system to perform the method, the method including to:

• initialize, by the configured computing system, a lag l (l>0), a computation window size counter n (n>2*l+1), a sum or a mean or both, and one or more components of an autocorrelation at lag l other than a sum and a mean for a pre-adjusted computation window of the specified size n, wherein the pre-adjusted computation window contains n data elements from a data stream stored in a buffer on at least one of the one or more storage media;
• generate, by the configured computing system, an autocorrelation at lag l for the pre-adjusted computation window based on one or more of the initialized components;
• access or receive, by the configured computing system, a data element to be added to the pre-adjusted computation window;
• store, by the configured computing system, the accessed or received data element into the buffer;
• adjust, by the configured computing system, the pre-adjusted computation window, by adding the accessed or received data element to the pre-adjusted computation window and adjusting the computation window size counter;
• incrementally calculate, by the configured computing system, a sum or a mean or both for the adjusted computation window;
• directly incrementally calculate, by the configured computing system, one or more components of an autocorrelation at lag l other than a sum and a mean for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l other than a sum and a mean for the pre-adjusted computation window, including to:
• access or receive l data elements not including the added data element from each side of the adjusted computation window respectively without accessing or receiving all data elements in the adjusted computation window to allow the configured computing system to use less memory;
• access the one or more components of the autocorrelation at lag l other than a sum and a mean for the pre-adjusted computation window;
• and
• add a contribution of the data element added to the pre-adjusted computation window to each of the one or more accessed components based on the added data element and/or the l data elements from each side of the adjusted computation window without using all data elements in the adjusted computation window thereby resulting in faster computation time;
• and
• generate, by the configured computing system, the autocorrelation at lag l for the adjusted computation window based on one or more of the calculated components.