Discrete representation of signals on a logarithmic frequency scale

Logarithmic frequency representation plays an important role in many audio and acoustic signal processing applications. This article presents a methodology for frequency-warped signal processing where the frequency representation is logarithmic above a certain limit frequency. It is demonstrated how this approach can be used with FFT or linear prediction to perform non-parametric, or parametric constant-Q spectrum analysis, respectively. The benefits of the use of logarithmic frequency representation are demonstrated with harmonic signals. It is also discussed how linear filters can be designed and implemented directly on a logarithmic frequency scale.