Constant-Q analysis using the chirp z-transform

Constant-Q spectral analysis can be performed by taking the Fourier transform of a windowed sequence where the window is a function of the product of time and frequency. If the window used is a decaying exponential whose argument is a constant times the product of time and frequency, the result is equivalent to evaluating the z-transform of the sequence along an outwardly going spiral in the complex z-plane. This analysis can thus be implemented using the chirp z-transform algorithm, and is discussed for the specific case of loudspeaker impulse-response measurements.