Frequency estimation from short pulses of sinusoidal signals

Joint time delay and frequency estimation via state-space realization

“…Following the framework of the Viberg-Stoica method [17], we construct a future output vector (8) which is a -vector with . Using (6), is expressed as (9) where (10) and (11) It is required that must have full-column rank of , and a necessary condition for it is . If , a sufficient condition is that has full-column rank.…”

“…Recently, the problem of joint time delay and frequency estimation of sinusoidal signals has also attracted considerable attention. Application examples for this work include speech enhancement and pitch estimation using a microphone array [5], [6], synchronization in code division multiple access (CDMA) systems [7], analysis of thalamocortical seizure pathways [8] and fequency-shift keying (FSK) demodulation using multiple segments [9].…”

Joint time-delay and frequency estimation using parallel factor analysis

“…In this paper, we consider that the source signal is a sinusoidal signal and the objective is to find the time-delay and frequency parameters from the received sensor outputs [2]- [3]. The joint time-delay and frequency estimation problem has applications such as analysis of thalamocortical seizure pathways [4], frequency-shift keying demodulation using multiple data segments [5] and speaker localization [6]. Without loss of generality, we consider two sensor outputs which are modeled as: r 1 (n) = s(n) + q 1 (n) r 2 (n) = s(n − D) + q 2 (n), n = 0, 1, · · · , N − 1 (1) where s(n) = P m=1 α m exp(jω m n) consists of P complex sinusoids.…”