FFT (Fast Fourier transform)
|
This is a method to calculate the
discrete Fourier transform and its inverse. It breaks down a signal into
sinusoids of different frequencies transforms from time domain to frequency
domain.
|
Wavelet
transform
|
It is one of the methods of the
time-frequency-transformations. It decomposes the signals into different
frequency ranges and allows extraction of features relating to quality.
|
Table 1: The basic concepts of FFT and Wavelet transform
Next, we will show the main difference between FFT (Fast Fourier Transform) and wavelet transform in detail (Table 2). FFT and wavelet transform have different characteristic so that they are used to deal with different kinds of signals.
FFT
|
Fourier
Transform
|
|
Difference
|
In terms of trigonometric polynomial.
Convert time domain to the frequency domain.
Extract only frequency information, losing time information.
In whole time axis, cannot analyze at instant particular frequency
rises.
|
In terms of translations and dilation of mother wavelet.
Convert time domain to the time-frequency domain.
Extract both time evolution and frequency composition of a signal.
Provide more accurately localized temporal and frequency
information.
Has multiresolution capabilities.
|
Same
point
|
Deal with
expansion of functions in terms of a set of basic functions.
|
|
Application
|
Ø Long-lived, stationary signals.
Ø Suitable for time invariant signal.
|
Ø Transient, intermittent behavior.
Ø Suitable for time-varying phenomena.
Ø Can be used to analyze non-stationary signal.
|
