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Instantaneous Frequency Estimation

Any time-frequency representation of a signal contains crucial information on the characteristics of the signal. We deal with the estimation of the instantaneous frequency of signals corrupted by additive noise based on the use a time-frequency representation of the analyzed signal, followed by a morphological treatment of the image obtained. Any time-frequency representation of an acquired signal is concentrated around the instantaneous frequency law of its useful component (the projection of the ridges of the time-frequency representation on the time-frequency plane) and realizes the diffusion of its noise component. So, extracting the ridges of the time-frequency representation, the instantaneous frequency of its useful component can be estimated. Different time-frequency representations have different degrees of concentration around the instantaneous frequency law of the useful component. One of the best time-frequency representations in what concerns this concentration is the Wigner-Ville distribution. Unfortunately it contains interference terms. They can be reduced by the conjoint use of the Gabor and Wigner-Ville time-frequency representations of the same signal.

(a) Gabor representation of the useful component.
(b) Gabor representation of the acquired signal (useful component plus a train of white noise pulses).
(c) Result of the non-linear filtering of the previous result.

(d) Wigner-Ville representation of the acquired signal.
(e) The new time-frequency representation of the acquired signal obtained by the product of c) and d).

Using the image of this new time-frequency representation, its ridges can be extracted with the aid of some mathematical morphology operators. This is a ridges detection mechanism producing the projection on the time frequency plane. This projection represents the result of the proposed estimation method. The main advantage of the proposed method is the fact that the signals analyzed could have very low signal to noise ratios (SNRs).

(a) Ideal IF.
(b) Proposed method, for SNR=30dB.

Using the time-frequency based methods for instantaneous frequency estimation a frequency tracking filter was designed. An alternative approach for instantaneous frequency estimation is based on the utilization of Kalman filtering. Different applications in communications were conceived for the instantaneous frequency estimation based on Kalman filtering.

Selected Publications:

Alexandru Isar, Ioan Nafornita, "Time-Frequency Representations (in Romanian)", Ed. "Politehnica", 1998.

Cornelia Gordan, Marius Regep, Ioan Nafornita, "Estimating and Interpreting the Instantaneous Frequency of a Frequency Modulated Signal. Part 1: Fundamentals and Algorithms", Buletinul Stiintific al Universitatii "Politehnica" din Timisoara, tom. 43(57), 1998, fascicola 1, pp. 175-184.

Cornelia Gordan, Marius Regep, Ioan Nafornita, "Estimating and Interpreting the Instantaneous Frequency of a Frequency Modulated Signal. Part 2: Practical Results", Buletinul Stiintific al Universitatii "Politehnica" din Timisoara, tom. 43(57), 1998, fascicola 1, pp. 185-190.

Tibor Asztalos, Dorina Isar, Alexandru Isar, "Time-Frequency Filters", Proceedings of International Conference SCS-99, pp. 11-14, July ,5-7, 1999, Iasi.

Tibor Asztalos, Adrian Marina, Alexandru Isar, "A New Algorithm for the Estimation of the Instantaneous Frequency of a Signal Perturbed by Noise", Proceedings of the International Conference Mathematical Theory of Networks and Systems MTNS-2000, June, 17-25, 2000, proceedings on CD, Perpignan, France

Mirela Bianu, Cornelia Gordan, Ioan Nafornita, "A States Space Model of Nonstationary Signals with Phase Variation as a Polynomial", 4'th International Conference on Renewable Sources and Environmental Electro-Technologies, 6 - 9 iunie 2002, Oradea.

Janos Gal, Marius Salagean, Mirela Bianu, Ioan Nafornita, "The Instantaneous Frequency Determination for Signals with Polynomial Phase using Kalman Filtering", Buletinul Stiintific al Universitatii "POLITEHNICA" din Timisoara, Proceedings of the Symposium on Electronics and Telecommunications, Fifth edition, September 19-20, 2002, vol. I, pp. 186-189.

Mirela Bianu, Alexandru Isar, "The Reduction of Interference Terms in the Time-Frequency Plane", Proceedings of International Symposium SCS'2003, Iasi, July, 10-11, 2003, pp. 461-464

Monica Borda, Ioan Nafornita, Alexandru Isar, "A new instantaneous frequency estimation method based on the use of image processing techniques", Proceedings of IS&T/SPIE's Annual Symposium Electronic Imaging, 20-24 January, 2003, Santa Clara, California, USA

Marius Salagean, Mirela Bianu, Cornelia Gordan, "Instantaneous Frequency and its Determination", Buletinul stiintific al UPT tom 48 (62) Electronica si Telecomunicatii, fascicula 1-2, 2003

Alexandru Isar, Dorina Isar, Mirela Bianu, "A Statistical Analysis of Two Classes of Time-Frequency Representations", Facta Universitatis, vol. 16, no. 1, April, 2003, pp. 115-134.

Borda, M., Nafornita, I., Isar, D., Isar, A., "New instantaneous frequency estimation method based on image processing techniques", Journal of Electronic Imaging, April-June 2005, volume 14, Issue 2, 023013-1-11.

Gal, J., Campeanu, A., Nafornita, I., "Estimation of Noisy Sinusoids Instantaneous Frequency by Kalman Filtering", Scientific Bulletin of the Politehnica University of Timisoara, Transactions on ELECTRONICS and COMMUNICATIONS, vol. 51(65), no.2, pp.69-72, ISSN 1583-3380

Salagean, M., Nafornita, I., "The estimation of the instantaneous frequency using time-frequency methods", Scientific Bulletin of the Politehnica University of Timisoara, Transactions on ELECTRONICS and COMMUNICATIONS, vol. 51(65), no. 2, pp. 195-198, 2006, ISSN 1583-3380

Marius Salagean, Ioan Nafornita, " Time-frequency methods for multicomponents signals", International Symposium on Signal, Circuits and Systems, ISSCS 2007, Iasi, Romania, 12-13 July 2007.

J. Gal, A. Campeanu, I. Nafornita, " Estimation of chirp signals in gaussian noise by Kalman filtering", International Symposium on Signal, Circuits and Systems, ISSCS 2007, Iasi, Romania, 12-13 July 2007.

Janos Gal, Andrei Campeanu, Ioan Nafornita, Identification of Polynomial Phase Signals by Extended Kalman Filtering, EUSIPCO 2008, Switzerland

D. Isar, A. Isar, A New Time-Frequency Adaptive Filter, Scientific Bulletin of Politehnica Univ. of Timisoara, Trans. on Electronics and Telecommunications, tom 53(67), fasc.1, pp. 115-118, ISSN 1583-3380, Int. Symposium of Electronics and Telecommunications, Sept. 25-26, 2008, Timisoara, Romania

Janos Gal, Andrei Campeanu, Ioan Nafornita, "Kalman Noncoherent Detection of CPFSK Signal", The 8th International Conference on Communications COMM 2010, 10-12 June 2010, Bucuresti, vol I., pp. 65-68.

Janos Gal, Andrei Campeanu, Ioan Nafornita, "Noncoherent Demodulation of Continouos Phase Modulation Signals using Extended Kalman Filtering", OPTIM 2010 -12th International Conference on Optimization of Electrical and Electronic Equipment, Brasov, 20-22 mai 2010, pag. IACM.4.1.09

A.Campeanu, J. Gal, I. Nafornita, 64-QAM Carrier Synchronization by an Extended Kalman Filtering Algorithm, Proceedings of the First International Conference on Wireless and Mobile Networks, Paris, October, 23-24, 2011

Gal, J.; Campeanu, A.; Nafornita, I.; The estimation of chirp signals parameters by an extended Kalman filtering algorithm, Signals, Circuits and Systems (ISSCS), 2011 10th International Symposium on, June 30 2011-July 1 2011, pp: 1 - 4 , ISBN: 978-1-61284-944-7

Isar, A; Isar, D, Analog Frequency Tracking Filter, ADVANCES IN ELECTRICAL AND COMPUTER ENGINEERING, UNIV SUCEAVA, FAC ELECTRICAL ENG, Suceava, Romania, ISSN 1582-7445, 17, 22, 6 pag., 2013, 10.4316/AECE.2013.02003, WOS:000322179400003.