User`s guide
104
Figure 5 Fourier serious expansion of a periodic square wave (L=1). The number
of terms in the series varies from one, three, to seven and 25.
2.3.1.2 Introduction to Fast Fourier Transforms (FFT)
Fast Fourier transformation (FFT) is a technique used to rapidly convert data from time
domain to frequency domain. It decomposes a sequence of values into components of different
frequencies. The input to a FFT consists of a series of
data points sampled in time domain at a
constant sampling frequency (equally spaced intervals). The output consists of a series of
data points in frequency domain showing the contribution of each frequency to the overall signal.
The resolution of the FFT is given by
Sampling frequency
is determined by dividing the number of data points
by the time interval of sampling:
Higher the sampling frequency, higher the accuracy of the FFT. Below are the FFT
analysis of the function
, over the range of [0, 1] second. The function has a
frequency of 10 Hz. The input data and FFT analysis results are listed in Figure 26.
-2
-1
0
1
2
0 2 4 6 8
N=7
-2
-1
0
1
2
0 2 4 6 8
N=25
-2
0
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Data input when sampling frequency is 512Hz, and D=512 (N=9)
Eq.52
Eq.53