Development and Performance Analysis of a Novel Single-bin FFT Algorithm

The Discrete Fourier Transform (DFT) plays an important role in digital signal processing. Fast Fourier Transform (FFT) is a set of algorithms for computing the DFT in short run-time. In many practical applications, DFT of only one frequency value is required rather than of all the frequency values. Algorithms for computing DFT of only one frequency are called Single-bin FFT algorithms. In this paper, we have developed a single-bin FFT algorithm based on the formulas for DFT of different frequency bins derived from the Radix-2 FFT algorithm. Finally, we have performed a comparative analysis of the developed algorithm with another available single-bin FFT algorithm, called the Goertzel algorithm.