0.1 Background

The most natural way of analyzing the notes of an audio signal is through a time-frequency representation of it. This time-frequency representation is known as a spectrogram. However, this spectrogram has some resolution issues stemming from the windowing operation used on the signal in order to compute the STFT (Short-Time Fourier Transform) of it, putting it in the form we see: time vs. frequency. This windowing has an effect not unlike the Heisenberg Uncertainty Principle. A wide window improves the frequency resolution, and a narrow window improves the time resolution, thus we can never achieve a higher resolution in both the frequency and time domain (shown in figure below). However, we need to achieve a high resolution in both to analyze the notes with great precision.