Singing signals are one of the input data that computer systems need to analyse, and singing is part of all the cultures in the world. However, although there have been several studies on audio signal processing during the last three decades, it is still an active research area because most of the available algorithms in the literature require improvement due to the complexity of audio/music signals. More efforts are needed for analysing sounds/music in a real-time environment since the algorithms should work only on the past data, while in an offline system, all the required data are available. In addition, the complexity of the data will be increased if the audio signals come from singing due to the unique features of singing signals (such as vocal system, vibration, pitch drift, and tuning approach) that make the signals different and more complicated than those from an instrument. This thesis is mainly focused on analysing singing signals and better understanding how trained- professional singers sing the pitch frequency and duration of the notes according to their position in a piece of music and the singing technique applied. To do this, it is discovered that by incorporating singing features, such as gender and BPM, a real-time pitch detection algorithm can be found to estimate fundamental frequencies with fewer errors. In addition, two novel algorithms were proposed, one for smoothing pitch contours and another for estimating onset, offset, and the transition between notes. These two algorithms showed better results as compared to several other state-of-the-art algorithms. Moreover, a new vocal dataset that included several annotations for 2688 singing files was published. Finally, this thesis presents two models for calculating pitches and the duration of notes according to their positions in a piece of music. In conclusion, optimizing results for pitch-oriented Music Information Retrieval (MIR) algorithms necessitates adapting/selecting them based on the unique characteristics of the signals. Achieving a universal algorithm that performs exceptionally well on all data types remains a formidable challenge given the current state of technology.