Goertzel Algorithm Generalized to Non-integer Multiples of Fundamental Frequency

Abstract

The paper deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the paper providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.

The paper deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the paper providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.