EE Pro for TI-89, 92 Plus
Analysis - FFT
32
Chapter 8
Fourier Transforms
This section contains software computing discrete “Fast” Fourier transforms and its inverse.
v
FFT
v
Inverse FFT
8.1 FFT
A physical process can be monitored in two significantly different ways. First, the process can be monitored in
time domain in analog or digital form. Second, the data can be collected in the frequency domain in analog or
digital form. In a variety of measurement and digital storage devices, data is gathered at regular, discrete time
intervals. This data can be converted to its equivalent set in the frequency domain by the use of the so-called FFT
algorithm. This algorithm maps a data array of N items to the corresponding array in the frequency domain using
the following equation.
H
h
e
k
n
n 0
N 1
-2 j k n N
=
⋅
=
−
⋅ ⋅
∑
π
Eq. 8.1.1
The variable hn is the nth element in the time domain and Hk is the kth element in the frequency domain. The
FFT algorithm treats the data block provided as though it is one of a periodic sequence. If the underlying data is
not periodic, the resulting FFT-created wave is subject to substantial harmonic distortion. This section does not
pad the input array with 0’s when the number of data points is not a power of 2.
Field Descriptions
Time
: (Time Signal)
Enter an array or list of real or complex numbers.
Freq
: (Frequency Spectrum)
Returns spectral coefficients.
Example 8.1
Find spectral coefficients for the periodic time signal [1 2 3 4].
1. Enter [1 2 3 4] for
Time.
2. Press
„
to calculate and display results in the frequency domain
Freq.
3. The screen display of the output and the input are shown below.
←
Input Screen
Output of Computation
→