D. Wulich

Synthesis of discrete time-varying null filters for frequency-varying signals using the time-warping technique

A synthesis of two second-order discrete time-varying filters (DTVF), capable of suppressing a sine signal with arbitrary frequency variation, is presented. These structures are obtained by using the time-warping concept. A noise analysis is carried out for these two DTVFs and their performance is compared. It is shown that for the particular application considered, the rule of time-dependence of the DTVF (the synchronization) may be effectively obtained by using a phase-locked loop (PLL) system. As an example, the DTVF-PLL system is used for synchronous phase estimation of a sine wave corrupted by closely spaced FM interference. Simulation results are provided to substantiate the analysis and demonstrate the efficiency of the proposed time-varying system. The main feature of the TLM method is its formulation and programming simplicity. The method also generates a large amount of information; not only is the impulse response of a structure obtained, yielding in turn its response to any excitation, but the characteristics of the dominant and higher order modes are also accessible in the frequency domain through the Fourier transform. >

PLL based discrete time varying filter for estimation of parameters of a sine signal corrupted by a closely spaced FM interference

A method for the estimation of the parameters of a sine signal corrupted by a strong FM interference is presented. The method consists of two stages. In the first stage, an FM interference is transformed into a harmonic wave with known frequency by using a special time-warping technique. This harmonic interference is then rejected in the transformed time domain by a time-invariant constrained notch filter. The time-warping is implemented using nonuniform sampling obtained by utilizing a phase locked loop (PLL) technique. It is shown that such processing results in a 0-dB signal-to-interference ratio at the output independently of the signal-to-interference ratio at the input (for negative values in decibels). The second stage involves parameter estimation, where a constrained adaptive notch filter is used for the enhancement of a signal under analysis.<<ETX>>

Constrained notch filtering of nonuniformly spaced samples for enhancement of an arbitrary signal corrupted by a strong FM interference

The proposed method is based on exploring the concept of constrained notch filtering (CNF) as applied to any given arbitrary signal with time varying parameters. First, it is shown that any signal with a constant envelope such as FM may be transformed to a discrete sinusoidal one by applying a nonuniform sampling strategy. Second, a signal buried under a strong FM interference is retrieved by applying CNF in the transformed time domain. The main assumption made is that there exists an auxiliary input which provides information about the instantaneous frequency of the interference. >

PLL synchronized time-varying constrained notch filter for retrieving a weak multiple sine signal jammed by FM interference

A method of retrieval of a multitone corrupted by a strong wideband FM interference is presented. The input mixture is transformed into a new time domain, resulting in a concentration of the FM interference around a chosen frequency; this inference is then rejected by a constrained notch filter with a fixed notch point. The time warping is implemented through nonequally spaced sampling. The method provides results superior to those of conventional adaptive processing, which fails to track the parameters of an FM interference with significantly large frequency deviations. >

Closed-loop self-synchronized signal controlled constrained notch filter with application for rejection of arbitrary frequency variation speed sinusoidal interference

The closed-loop self-synchronized constrained notch filter (CLSS-CNF) is proposed, and its ability for retrieval of narrowband signals corrupted by a strong FM interference is studied. Self-synchronization is achieved through the estimation of the instantaneous phase of the FM interference to control time-varying coefficients of SC-CNF by using a closed-loop structure. The CLSS-CNF can overcome the tracking capability threshold of a conventional constrained adaptive notch filter (CANF), and reject a sinusoidal interference with arbitrary speed of frequency variation. Based on this approach, two such filters are discussed, and their system performances compared. It is shown that the proposed filters are superior to both the conventional CANF as well as the recently proposed SC-CNF with open loop structure. Use of closed loop and the specially developed projection scheme for time-varying coefficients allow one to achieve a signal to the interference ratio (SIR/sub O/) of up to 20 dB compared to the input SIR/sub i/ of less than -20 dB.<<ETX>>

Discrete time-varying filter and PLL for synchronous estimation of parameters of a sine signal corrupted by a closely spaced FM interference

Abstract The concept of time-varying filters as applied to the problem of rejection of a sine signal with fast variations of frequency is explored. Using such filters, a method for synchronous (i.e., when frequency is known) estimation of phase and amplitude of a sine wave corrupted by closely spaced sinusoidal interference with fast frequency variations is proposed. It is shown that the coefficients of the time-varying filter can be effectively determined using a Phase Locked Loop. It is proved that the performance of the proposed estimator depends neither on the interference level nor on the speed of frequency variations. Comparison with an adaptive estimator based on a linear time invariant filter shows the superiority of the proposed one where the interference frequency changes rapidly over time.

Separation of close sinusoids by cross-coupled phase locked loop

A study is made of a cross-coupled phase-locked loop (CCPLL) used for separation of close sinusoids with slowly varying frequencies. It is assumed that the sinusoids have equal amplitudes, and it is shown that the CCPLL system can effectively separate two sine signals with an observation interval T<1/ Delta f. An analysis in the presence of noise is also given. It is shown that a satisfactory phase estimation can be achieved for SNR >or=15 dB. The result has application in fields such as ranging, symbol synchronization, and carrier recovery for coherent demodulation.<<ETX>>

Externally controlled time-varying constrained notch filter

An application of a constrained notch filter (CNF) for filtering a sine signal with arbitrary varying frequency is considered. It is shown that the concept of CNF can be easily extended to time-varying CNF (TVCNF) whose coefficients vary with time according to the rule of frequency variation of the considered FM signal. Such a TVCNF is able to reject the FM signal and at the same time remain transparent to any other signal. The main problem in TVCNF implementation is to provide a proper control (synchronization) of its coefficients. An application of the TVCNF for the enhancement of an arbitrary signal corrupted by a strong FM interference is investigated. It is shown that if the synchronization is based on the input mixture, then for any negative signal-to-interference ratio (SIR<<0 dB) at the input of the TVCNF, the SIR at its output reaches 0 dB.<<ETX>>

Self-synchronized signal controlled constrained notch filter for rejection of nonstationary interference

A novel signal controlled constrained notch filter (SC-CNF) structure with global feedback is presented. The SC-CNF is combined with an adaptive linear enhancer to retrieve a multitone signal corrupted by a strong nonstationary FM interference. Using a time-warping technique, the SC-CNF, by its nature time-varying, is transformed into a CNF which is time variant. Such transformation is implemented by nonequally spaced sampling (NESS) of the input mixture. A closed-loop system is proposed to improve the strategy of NESS. By exploiting the self-synchronization process, nearly complete rejection of FM interference is achieved. The condition for the occurrence of self-synchronization is obtained. The self-synchronized SC-CNF provides significant improvement (up to 30 dB) of the signal-to-interference ratio of the entire system output.<<ETX>>

An analysis of CCPLL behaviour in the presence of noise

This letter gives an analysis of a transparent CCPLL in the presence of noise. The analysis is based on geometrical considerations and is an extension of the well known geometric method for the analysis of FM signals in the presence of noise. The main result obtained here is that the phases of the separated (demodulated) FM signals are accompanied by a sequence of random «clicks». The level and rate of occurrence of these clicks depend on the «transparency» of the PLLs used in the CCPLL system