## 1 Introduction  
A signal is defined as periodic when the same sequence of values re-occurs after a fixed amount of time, defined as a period, whose inverse is the frequency. By [PERSON]'s principles, a real-world signal can be described as a sum of sinusoids (or \"pure tones\") that only carry one frequency [1]. The fundamental frequency, or F0, is defined as the lowest frequency describing a periodic component of a signal. In the audio domain, F0 is defined as the pitch, which in music is translated to a specific note. Detecting the F0 of a signal is a crucial application in many fields, with audio, music, and speech processing being heavily reliant on pitch-detection-based technologies, as well as other fields such as fault detection of moving parts, which are related to their resonance frequency [2], or sonar systems for target detection, classification and localization [3]. Moreover, pitch detection can also be employed in the characterization of accurate sinusoidal voltages, as described by [PERSON] et al. [4]. The problem of pitch detection is crucial in all the applications that rely on knowing the fundamental frequency in order to perform periodicity-related computations, such as acoustic feature extraction relying on prosodic metrics such as HNR, jitter or shimmer that evaluate \"cycle-to-cycle\" variations [5]. Moreover, professional audio relies on pitch detection to build tuners for real instruments, or for real-time pitch re-adjusting applicationsespecially directed toward vocal tuning. Real-time detectors are thus necessary to enable performers to monitor pitch accuracy and trigger events in real time, especially related to MIDI applications [6]. Additionally, fast, real-time pitch detection is valuable in interactive audio applications, such as games and virtual reality, where it enables dynamic audio synthesis and effects as well as responsive processing. The two main characteristics of pitch detection algorithms are speed and accuracy, which often imply a trade-off depending on the specific application--for example, posterior analyses do not need real-time F0 estimation, as opposed to live music [6]. With the diffusion of technologies such as \"Autotune\" for real-time pitch correction in singers [7], and with the widespread use of MIDI instruments and/or live MIDI transformers to digitalize acoustic instruments, real-time pitch detection sees a crucial application in the music industry. Especially for MIDI purposes where a sound needs to be translated into a discrete note, speed is favored over accuracy due to the need for low-latency live solutions, and thanks to the fact that the detected frequency is discretized into a note of the tempered system allowing for a certain range for errors. The problem of detecting the fundamental frequency in real time is crucial whenever live performances are involved, as even minuscule latencies of a few milliseconds can be perceived by the musician or operator. In speech analysis, F0 carries a crucial role as a biometric feature for characterizing voice impairment, up to singlehandedly being used for pre-diagnostic purposes, where F0-related features and their variations are used for the detection of respiratory [8], phonatory [9; 10] or neurodegenerative diseases [11; 12; 13]. Given the multifaceted applications and different industry needs, the state of the art of pitch detection depends on the application. From the mathematical point of view, although an ever-growing plethora of algorithms are being developed, the vast majority can be generally categorized into three approaches: time-based, frequency or Cepstrum-based, full heuristic. Time domain approaches are generally based on the mathematical principles behind autocorrelation, which inherently has peaks every time a signal repeats (maximum correlation with itself): the problem of pitch detection is thus translated into the problem of finding the maximum of the autocorrelation function.