Introduction to the RFB

The Ramanujan Filter Bank is a new filter-bank structure for estimating and tracking periodicities in data. This filter-bank is inspired from the recently proposed period estimation techniques based on dictionary representations of periodic signals (click here). Apart from inheriting the numerous advantages that the dictionary techniques offered over conventional period-estimation methods (such as those using the DFT), the filter-banks proposed here expand the domain of problems that can be addressed to a much richer set. For instance, we can now produce instantaneous period vs time plots (using simple integer computations) for signals whose periodic nature changes with time. This includes signals that are periodic only for a short duration and signals such as chirps.

The RFB is introduced in these papers. We are currently developing applications of the RFB in finding microsatellites in DNA, identifying protein repeats, and in detecting epipleptic seizures. Our papers outlining these applications are under preparation. We are making our code implementing the RFB available below.

Matlab Code

The following code is only relevant to the application of finding DNA microsatellites using the Ramanujan Filter Bank. The following paper was recently presented at ISCAS 2016.

• Tenneti S.V. and Vaidyanathan P.P., "Detecting Tandem Repeats in DNA using Ramanujan Filter Bank,'' (under review) IEEE Int. Conf. on Circuits and Systems, Montreal, May 2016.

1. RFB_DNA.m . Description: Main function implementing the RFB. Please type help RFB_DNA in the Matlab Command Window for usage details. Please note: This code uses 24 iterations, one for each way of assiging the numbers 1, 2, 3 and 4 to the base pairs A, T, C and G. In practice, we expect that much fewer iterations should suffice. The optimal assignment of numbers to the base pairs is currently being explored by us.


2. Some sample input files in .txt format containing FASTA:
   
   
   • AC010136.txt To view this sequence on Genbank, click here.
   
   
   • U43748.txt To view this sequence on Genbank, click here.

Our Papers on the RFB

• Tenneti S.V. and Vaidyanathan P.P., "Ramanujan filter banks for estimation and tracking of periodicity,'' Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Brisbane, April 2015.


• P. P. Vaidyanathan and Tenneti S. V., "Properties of Ramanujan Filter Banks", Proc. European Signal Processing Conference, France, August 2015.

Related Work

Journal Papers

• Vaidyanathan P.P., "Ramanujan sums in the context of signal processing: Part I: fundamentals," IEEE Trans. on Signal Proc., vol. 62, no. 16, pp. 4145--4157, Aug., 2014.


• Vaidyanathan P.P., "Ramanujan sums in the context of signal processing: Part II: FIR representations and applications," IEEE Trans. on Signal Proc., vol. 62, no. 16, pp. 4158--4172, Aug., 2014.


• Tenneti S.V., Vaidyanathan P.P., "Nested Periodic Matrices and Dictionaries: New Signal Representations for Period Estimation," IEEE Transactions on Signal Processing, vol.63, no.14, pp.3736,3750, July 15, 2015.


• Tenneti S.V. and Vaidyanathan P.P., "Arbitrarily Shaped Periods in Multi-Dimensional Discrete Time Periodicity," IEEE Signal Processing Letters, vol.22, no.10, pp.1748--1751, Oct. 2015.

Conference Papers

• Vaidyanathan P.P., "Ramanujan-sum expansions for finite duration (FIR) sequences," Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Florence, Italy, May 2014.


• Vaidyanathan P.P. and Pal P., "The Farey dictionary for sparse representation of periodic signals," Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Florence, Italy, May 2014.


• Tenneti S.V. and Vaidyanathan P.P., "Dictionary approaches for identifying periodicities in data," Proc. Asil. Conf. Sig., Sys., and Comp., Monterey, CA, Nov. 2014.


• Vaidyanathan P.P. and Tenneti S.V., "Ramanujan subspaces and digital signal processing,'' Proc. Asil. Conf. Sig., Sys., and Comp., Monterey, CA, Nov. 2014.


• Tenneti S.V. and Vaidyanathan P.P., "Ramanujan filter banks for estimation and tracking of periodicity properties,'' Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Brisbane, April 2015.


• Vaidyanathan P.P., "Multidimensional Ramanujan-sum expansions on nonseparable lattices,'' Proc. IEEE Int. Conf. Acoust. Speech, and Signal Proc., Brisbane, April 2015.


• P. P. Vaidyanathan and Tenneti S. V., "Properties of Ramanujan Filter Banks", Proc. European Signal Processing Conference, France, August 2015.


• Tenneti S. V. and Vaidyanthan P. P., "Minimal Dictionaries for Spanning Periodic Signals", (to appear in) Proc. Asilomar Conference on Signals, Systems, and Computers, Monterey, CA, Nov. 2015.


• Tenneti S. V. and Vaidyanthan P. P., "Period Estimation and Tracking: Filter Bank Design using Truth Tables of Logic", (to appear in) Proc. Asilomar Conference on Signals, Systems, and Computers, Monterey, CA, Nov. 2015.

People

P.P. Vaidyanathan
Professor
Caltech
Email: ppvnath[at]systems[dot]caltech[dot]edu

Srikanth V. Tenneti
Graduate Student
Caltech
Email: stenneti[at]caltech[dot]edu