Accuracy Improvement of Instantaneous Frequency Estimation by Finite Order FIR Hilbert Transformer Using Notch Filter

Abstract

Frequency estimation is used in a wide range of areas such as radar, telecommunications, voice analysis and weight measurement using tuning fork sensor. This paper describes an instantaneous frequency (IF) estimation method. The original signal combined with the Hilbert transform form a complex analytic signal. The phase of the analytic signal is defined as the instantaneous phase and the time derivative of its phase IF. However, the amplitude of the signal obtained by phase-shifting the input signal by 90 degrees is different from that of the input signal because a ripple is generated in the frequency characteristics of the finite-order finite impulse response (FIR) Hilbert transformer (HT). As a result, errors are contained in the IF. In this paper, we propose a highly accurate IF estimation method using a notch filter. It is shown analytically that a harmonic frequency component is included in the IF obtained by using a finite-order FIR HT. Then, it is shown that the accurate instantaneous frequency can be obtained by removing the harmonic frequency component using an infinite impulse response (IIR) notch filter. Finally, the effectiveness of the proposed method is shown in simulations.