A CONSTRAINED NOTCH FOURIER-TRANSFORM

This paper presents a new sliding algorithm for estimating the amplitu de and phase of the Fourier coefficients of noise corrupted harmonic s ignals given a priori knowledge of the signal frequencies. The propose d method is similar in principle to the notch Fourier transform (NFT) technique suggested by Tadokoro et al. [6] except that it employs an i nfinite impulse response (IIR) rather than a finite impulse response ( FIR) notch filter parameterization. This modification provides bandwid th controlled bandpass (BP) filters whose center frequencies are equal ly spaced in the frequency spectrum. In this sense, the proposed techn ique can be regarded as a constrained notch Fourier transform (CNFT). Sliding algorithms have been derived for both the NFT and CNFT for the purpose of estimating the Fourier coefficients of the sinusoidal comp onents. The paper also proposes a similar algorithm to the CNFT for th e signals containing sinusoids at arbitrary known frequencies. The mai n feature of the modified CNFT is that it uses second-order IIR BP fil ters whose bandwidth and center frequency can be adjusted independentl y. The bandwidth control aspect provides the user with an efficient me ans of achieving the required resolution as web as reducing spectral l eakage. In general, the proposed approach leads to considerable reduct ion in terms of computational burden and memory storage.