## 1 Introduction
Frequency domain algorithms are based on Fourier domain or cepstral analysis, with the Harmonic Product Spectrum (HPS) [14] as a notable example: it computes the product of the power spectra of a signal and its downsampled versions to emphasize harmonic components. The fundamental frequency is then estimated by identifying peaks in the resulting spectrum. In recent years, the research trend was predominantly based on Deep Learning methods based on Convolutional Neural Networks (CNN) [15], which offer the advantages of being able to control the size of the computational net and also to specifically train on suitable data, since the problem of pitch detection is data-dependent [16]. However, CNN-based methods are not easily generalizable, and require data and especially time for training time before they are usable in their \"inference\" form--which usually brings high accuracies but slightly less optimal speed [17]. The prior definition of the latency/complexity of a pitch detection algorithm is hard to determine, since each algorithm and performance inherently depends on the acoustic and digital nature of the data--such as the number of bits for quantization. Theoretically, HPS-based methodologies yield a complexity of O(NlogN), and straightforward autocorrelation is at O(N\({}^{2}\)), whereas FFT-based autocorrelation is O(NlogN) yet again, being comparable to HPS. The Fast Fourier Transform (FFT) algorithm is used to speed up the computation of autocorrelation. By leveraging the symmetry properties in the autocorrelation function, the complexity of FFT-based autocorrelation is reduced. The process involves padding the input signal to the nearest power of 2, computing the FFT of the padded signal, squaring the magnitude of each frequency bin to obtain the power spectrum, computing the inverse FFT of the power spectrum and normalizing the result by dividing it by the length of the input signal. After a rough estimate of F0, many algorithms have to rely on some corrective heuristics to fine-tune the result and/or avoid octave errors. Common signal processing solutionsmay be employed for this purpose as well, with notable results such as the work by [PERSON] et al. [18] employing HPS and Euclidean summation. However, although this results in improved accuracy, it is an inherently computationally expensive mean, and real-time pitch detectors might choose to avoid relying on correctors--this is also the approach that we chose in the present paper. Due to the inherent harmonic nature of most real-world sound signals, especially when dealing with speech or music analysis, octave errors are a common criticality among pitch detection algorithms, being triggered by the eventual presence of strong first- or second-order harmonics and, partially, by aliasing. Two of the most widely used algorithms, SWIPE [19] and YIN [20], which will be detailed later in Section 2, are based on autocorrelation. More algorithms are listed in the works by [PERSON] and [PERSON] [19] and [PERSON] et al. [1]. Attempts at fast pitch detectors are based on the simplification of the transformation procedures, such as the work by [PERSON] et al. [21], which leverages the constant-Q Gabor transform for a threshold-based approach within a four-dimensional logarithmic harmonic spectrum shift. A work by [PERSON] et al. [22] aims to avoid short-time analysis and thus the underlying approximations about local stationarity by employing the Hilbert transform to derive \"instantaneous\" frequency components to contour F0: the performances might be comparable to YIN or SWIPE, but no indication on speed is given. In general, the problem of real-time, high-speed pitch detection has to be faced with the development of a computationally light algorithm that still retains a relative error suitable for the required application (mainly professional audio and live performances).