Abstract: Methods and Systems to analyze data from multiple periodic processes and deinterleave those periods including providing process data for analysis from at least one periodic generator; identify underlying different periodic processes; providing a Modified Euclidean Algorithm (MEA) to extract a fundamental period from a set of sparse and noisy observations of a periodic process; relying on the probabilistic interpretation of an equidistributed MEA (EQUIMEA) to deinterleave processes with multiple periods; and outputting the deinterleaved data to be applied to desired applications and analyses. The method may converge to the exact value of the period with as few as ten data samples.

Abstract: The present embodiments include methods of time-frequency analyzing signals. Some embodiments provide methods of processing signals comprising: adaptively partitioning at least a portion of a signal in a time domain into a plurality of segments of the signal; and transforming each of the segments of the signal producing respective expansions in a frequency domain and obtaining respective samples of the windows of signal in the frequency domain.

Abstract: The present embodiments include methods of time-frequency analyzing signals. Some embodiments provide methods of processing signals comprising: adaptively partitioning at least a portion of a signal in a time domain into a plurality of segments of the signal; and transforming each of the segments of the signal producing respective expansions in a frequency domain and obtaining respective samples of the windows of signal in the frequency domain.

Abstract: The present embodiments include methods of time-frequency analyzing signals. Some embodiments provide methods of processing signals comprising: receiving a communication signal; adaptively partitioning the signal in a time domain into a plurality of windows of the signal; transforming each of the windows of the signal producing respective expansions in a frequency domain and obtaining respective samples of the windows of signal in the frequency domain; and mapping the samples in the frequency domain back into the time domain.

Abstract: The present embodiments include methods of time-frequency analyzing signals. Some embodiments provide methods of processing signals comprising: receiving a communication signal; adaptively partitioning the signal in a time domain into a plurality of windows of the signal; transforming each of the windows of the signal producing respective expansions in a frequency domain and obtaining respective samples of the windows of signal in the frequency domain; and mapping the samples in the frequency domain back into the time domain.