Comparison and Application of Time-Frequency Analysis Methods for Nonstationary Signal Processing - Advanced Research on Computer Education, Simulation and Modeling - page 287

nonstationary signals, the time-frequency techniques are introduced. Figure 1 shows
three descriptions of a chirp signal: (a) is the description in time domain which loses the
frequency information, (b) is the description in frequency domain which loses the time
information, and (c) is the time-frequency representation which shows the signal
energy flowing in a time and frequency plane.
The basic idea of time-frequency analysis is to design a joint function, which can
describe the characteristics of signals on a time-frequency plane [1]. Studies of the
time-frequency analysis have become an important research field; and many
time-frequency representation methods are presented. In this paper, five time-frequency
techniques, i.e., the short-time Fourier transform (STFT), wavelet transform (WT),
Wigner-Ville distribution (WVD), pseudo-WVD (PWVD) and Hilbert-Huang
transform (HHT) are investigated and compared.

Fig. 1. Three description methods of a chirp signal in (a) time, (b) frequency and (c)
time-frequency domains

2 Theory Background

2.1 Short-Time Fourier Transform

The short-time Fourier transform (STFT) presented by Gabor in 1946 is to intercept
the signals by using a window function. The section in the window which can be
regarded as stationary signal is processed by the Fourier transform to find its
frequency components. The entire frequency information over time can be obtained
by moving the window function along the time axis [2]. The STFT of a signal x(t) can
be described as:

− j 2 πτ f

∫

+∞
−∞

*

STFT (, ) t f = x ( ) τ g ( τ − t e ) d τ

(3)

.

x