Carnegie Mellon University
Browse
The Short Time Fourier Transform and Local Signals.pdf (500.55 kB)

The Short Time Fourier Transform and Local Signals

Download (500.55 kB)
thesis
posted on 2011-06-01, 00:00 authored by Shuhei Okamura

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT’s modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross- covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

History

Date

2011-06-01

Degree Type

  • Dissertation

Department

  • Statistics

Degree Name

  • Doctor of Philosophy (PhD)

Advisor(s)

William Eddy,Jelena Kovacevic,Chad Schafer,Howard Seltman

Usage metrics

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC