Simple binwise methods

Combination methods based on simple binwise operations are designed to be simple and very fast to compute, though they may not provide the best results in terms of time-frequency resolution. The table below lists the simple binwise methods available in the package, as well as the function they compute for each entry X_{k, m}.

Description of simple binwise methods

Method key

Binwise function

Description

mean

\frac{1}{P}\sum_{p = 1}^P X_{k, m}[p]

Arithmetic mean

hmean

\left(\prod_{p = 1}^P X_{k, m}[p]\right)^{\frac{1}{P}}

Harmonic mean

gmean

\left(\frac{1}{P}\sum_{p = 1}^P \frac{1}{X_{k, m}[p]} \right)^{-1}

Geometric mean

min

\min_{p = 1, 2, \hdots, P} X_{k, m}[p]

Minimum

Further reading

  • Package release article: To be added.

  • D.Sc. thesis on combination methods: M. do V. M. da Costa, Novel time-frequency representations for music information retrieval, D.Sc., Federal University of Rio de Janeiro, Rio de Janeiro, Brasil (2020 Apr.).

  • Reference paper 1: C. Detka, P. Loughlin, and A. El-Jaroudi, “On combining evolutionary spectral estimates,” in IEEE Seventh SP Workshop on Statistical Signal and Array Processing, Jun. 1994, pp. 243–246.

  • Reference paper 2 (min and gmean): P. Loughlin, J. Pitton, and B. Hannaford, “Approximating time-frequency density functions via optimal combinations of spectrograms,” IEEE Signal Processing Letters, vol. 1, no. 12, pp. 199–202, Dec. 1994.

Calling signature

ctfr.methods.mean(signal, sr, *, <shared parameters>)
ctfr.methods.hmean(signal, sr, *, <shared parameters>)
ctfr.methods.gmean(signal, sr, *, <shared parameters>)
ctfr.methods.min(signal, sr, *, <shared parameters>)
ctfr.methods.mean_from_specs(specs, *, <shared parameters>)
ctfr.methods.hmean_from_specs(specs, *, <shared parameters>)
ctfr.methods.gmean_from_specs(specs, *, <shared parameters>)
ctfr.methods.min_from_specs(specs, *, <shared parameters>)

Note

As with all combination methods, you can also use ctfr.ctfr() or ctfr.ctfr_from_specs().

See ctfr.ctfr() and ctfr.ctfr_from_specs() for more details on the shared parameters for computing CTFRs with this package.