konstantQtransform

KonstantQTransform, commonly called the constant-Q transform (CQT), is a time-frequency representation designed to provide geometrically spaced frequency bins that align with musical pitch perception. It analyzes an audio signal by mapping it to a spectrum where each bin corresponds to a musical note or pitch class.

A defining feature is that the Q factor, defined as Q = f_k / Δf_k, is kept approximately constant across all bins. This yields finer frequency resolution at low frequencies and coarser resolution at high frequencies, matching how humans perceive pitch. The frequency bins are typically spaced by a fixed ratio per octave, such as 2^(1/bins_per_octave).

Computationally, the transform computes Y[k] as a convolution-like sum of the signal with a complex-valued kernel h_k centered at f_k and with bandwidth proportional to f_k. In practice, implementations use precomputed kernels or FFT-based methods to speed up computation, enabling real-time or near-real-time analysis for suitable parameter choices.

Compared with the short-time Fourier transform, the CQT provides logarithmic frequency spacing, which is advantageous for music-related tasks. It is not strictly orthogonal, and energy is not exactly preserved, but it offers a compact, perceptually relevant representation that emphasizes musical pitch content. Design choices, such as windowing and kernel construction, influence spectral leakage and bias.

Applications of the KonstantQTransform include music information retrieval, pitch detection, chord recognition, transcription, and audio analysis. Numerous libraries implement CQT or KonstantQTransform in Python, MATLAB, and C++, making it a common tool in audio signal processing. See also Constant-Q transform, Short-Time Fourier Transform, and Wavelet Transform.