Recovery of transit times and frequencies of multiple pulses via the Short-Time Fourier Transform

Authors

  • Jesus Manzanares-Martinez Departamento de Investigacion en Fisica Universidad de Sonora Blvd. Luis Encinas y Rosales, CP 83000 Hermosillo, Sonora, Mexico http://orcid.org/0000-0003-0586-234X
  • Carlos Ivan Ham-Rodriguez
  • Betsabe Manzanares-Martinez

DOI:

https://doi.org/10.31349/RevMexFis.64.296

Keywords:

Short Time Fourer Transform, pulses, time-of-flight

Abstract

In this work, we present a study to determine the transit times and frequencies of pulses by using
the Short-Time Fourier Transform (STFT). We consider the case of an acoustic signal composed of
five Gaussian pulses which have a high overlapping in time but oscillate at different frequencies. We
proceeded in three steps. First, we illustrate how the STFT calculated through a sliding window
produces a spectrogram where transit time is on one axis and frequency on the other. Second, we
derive an exact analytical solution of the STFT to develop an intuitive vision of the mathematical
technique. Finally, in a third step, we present an experiment to demonstrate that the STFT is a
useful technique to characterize a complex acoustical signal.

Author Biography

Jesus Manzanares-Martinez, Departamento de Investigacion en Fisica Universidad de Sonora Blvd. Luis Encinas y Rosales, CP 83000 Hermosillo, Sonora, Mexico

Investigador de tiempo completo

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Published

2018-04-30

How to Cite

[1]
J. Manzanares-Martinez, C. I. Ham-Rodriguez, and B. Manzanares-Martinez, “Recovery of transit times and frequencies of multiple pulses via the Short-Time Fourier Transform”, Rev. Mex. Fís., vol. 64, no. 3 May-Jun, pp. 296–301, Apr. 2018.

Issue

Vol. 64 No. 3 May-Jun (2018): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.