The JM-Filter to Detect Specific Frequency in Monitored Signal

The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing inside a digital signal processor. It has been widely known and argued in relevant literature that the Fast Fourier Transform (FFT) is useless in detecting specific frequencies in a monitored signal of length N because most of the computed results are ignored. In this paper, we present an efficient FFT-based method to detect specific frequencies in a monitored signal, which will then be compared to the most frequently used method which is the recursive Goertzel algorithm that detects and analyses one selectable frequency component from a discrete signal. The proposed JM-Filter algorithm presents a reduction of iterations compared to the first and second order Goertzel algorithm by a factor of r, where r represents the radix of the JM-Filter. The obtained results are significant in terms of computational reduction and accuracy in fixed-point implementation. Gains of 15 dB and 19 dB in signal to quantization noise ratio (SQNR) were respectively observed for the proposed first and second order radix-8 JM-Filter in comparison to Goertzel algorithm.

Automated summary

The paper presents an FFT-based method to efficiently detect specific frequencies in a monitored signal, showing significant improvements in computational reduction and accuracy in fixed-point implementation compared to the Goertzel algorithm. Gains of 15 dB and 19 dB in signal to quantization noise ratio (SQNR) were observed for the proposed first and second order radix-8 JM-Filter in comparison to Goertzel algorithm.