time series

Typically an audio signal, denoted by y, and represented as a one-dimensional numpy.ndarray of floating-point values. y[t] corresponds to amplitude of the waveform at sample t.

sampling rate

The number of samples per second of a time series. This is denoted by a positive number sr.


A short slice of a time series used for analysis purposes. This usually corresponds to a single column of a spectrogram matrix.


A vector or function used to weight samples within a frame when computing a spectrogram.

frame length

The (positive integer) number of samples in an analysis window (or frame). This is denoted by an integer variable n_fft.

hop length

The number of samples between successive frames, e.g., the columns of a spectrogram. This is denoted as a positive integer hop_length.

window length

The length (width) of the window function (e.g., Hann window). Note that this can be smaller than the frame length used in a short-time Fourier transform. Typically denoted as a positive integer variable win_length.


A matrix S where the rows index frequency bins, and the columns index frames (time). Spectrograms can be either real-valued or complex-valued. By convention, real-valued spectrograms are denoted as numpy.ndarrays S, while complex-valued STFT matrices are denoted as D.

onset (strength) envelope

An onset envelope onset_env[t] measures the strength of note onsets at frame t. Typically stored as a one-dimensional numpy.ndarray of floating-point values onset_envelope.


Also known as pitch class profile (PCP). Chroma representations measure the amount of relative energy in each pitch class (e.g., the 12 notes in the chromatic scale) at a given frame/time.