Iterative autocorrelation calculation for streamed data using components

A computing system, the computing system comprising:

• one or more computing devices;
• each of the one or more computing devices comprising one or more processors;
• one or more storage media comprising a buffer for storing streamed data elements;
• 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 of a specified size of the buffer, including to:
• a. initialize a sum or a mean or both, and one or more other components of an autocorrelation at a specified lag l (l>0) for a pre-adjusted computation window of a specified size n (n>2*(l+1)) of the buffer, the pre-adjusted computation window containing n data elements from a data stream;
• b. generate an autocorrelation at lag l for the pre-adjusted computation window based on one or more of the initialized components;
• c. receive a data element to be added to the pre-adjusted computation window from the data stream;
• d. store the received data element in the buffer;
• e. adjust the pre-adjusted computation window, including to:
• remove a least recently received data element from the pre-adjusted computation window;
• and
• add the to-be-added data element to the pre-adjusted computation window;
• f. iteratively calculate a sum or a mean or both for the adjusted computation window;
• g. directly iteratively calculate one or more components of an autocorrelation at lag l for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l calculated for the pre-adjusted computation window, including to:
• access l data elements not including the removed data element and the added data element from each side of the adjusted computation window respectively, the removed data element and the added data element without accessing all data elements in the adjusted computation window to reduce data access latency thereby saving computing resources and reducing the computing system's power consumption;
• 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
• calculate each of the one or more accessed components by removing any contribution of the data element removed from the computation window from each of the accessed components and adding any contribution of the data element added to the computation window to each of the one or more accessed components based on the removed data element, 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
• h. generate the autocorrelation at lag l for the adjusted computation window based on one or more of the iteratively calculated components.

A computing system program product for use at a configured computing system comprising one or more computing devices and one or more storage media, each of the one or more computing devices comprising one or more processors, the computing system program product for implementing a method for generating an autocorrelation at a specified lag for data elements in 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 at least one of the one or more computing devices in the configured computation system, cause the configured computing system to perform the method, the method including steps to:

• initialize, by the configured computing system, a sum or a mean or both, and one or more other components of an autocorrelation at a specified lag l (l>0) for a pre-adjusted computation window of a specified size n (n>2*(l+1)) of the buffer, the pre-adjusted computation window containing n data elements from a data stream and the n data elements are 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;
• receive, by the configured computing system, a data element from the data stream to be added to the pre-adjusted computation window;
• store, by the configured computing system, the received data element in the buffer;
• adjust, by the configured computing system, the pre-adjusted computation window, including to:
• remove a least recent received data element from the pre-adjusted computation window;
• and
• add the received data element to the pre-adjusted computation window;
• iteratively calculate, by the configured computing system, a sum or a mean or both for the adjusted computation window;
• directly iteratively calculate, by the configured computing system, one or more components of an autocorrelation at lag l for the adjusted computation window based at least in part on the one or more components of the autocorrelation at lag l calculated for the pre-adjusted computation window, including to:
• access l data elements not including the removed data element and the added data element from each side of the adjusted computation window respectively, the removed data element and the added data element without accessing all data elements in the adjusted computation window to reduce data access latency thereby saving computing resources and reducing the configured computing system's power consumption;
• 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
• remove any contribution of the data element removed from the pre-adjusted computation window from each of the accessed components and add any contribution of the added data element to each of the accessed components based on the removed data element, 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 iteratively calculated components of the autocorrelation at lag l.