HP (Hewlett-Packard) 50g ユーザーズマニュアル
Page 16-48
the number of operations using the FFT is reduced by a factor of 10000/664
≈
15.
The FFT operates on the sequence {x
j
} by partitioning it into a number of shorter
sequences. The DFT’s of the shorter sequences are calculated and later
combined together in a highly efficient manner. For details on the algorithm
refer, for example, to Chapter 12 in Newland, D.E., 1993, “An Introduction to
Random Vibrations, Spectral & Wavelet Analysis – Third Edition,” Longman
Scientific and Technical, New York.
combined together in a highly efficient manner. For details on the algorithm
refer, for example, to Chapter 12 in Newland, D.E., 1993, “An Introduction to
Random Vibrations, Spectral & Wavelet Analysis – Third Edition,” Longman
Scientific and Technical, New York.
The only requirement for the application of the FFT is that the number n be a
power of 2, i.e., select your data so that it contains 2, 4, 8, 16, 32, 62, etc.,
points.
power of 2, i.e., select your data so that it contains 2, 4, 8, 16, 32, 62, etc.,
points.
Examples of FFT applications
FFT applications usually involve data discretized from a time-dependent signal.
The calculator can be fed that data, say from a computer or a data logger, for
processing. Or, you can generate your own data by programming a function
and adding a few random numbers to it.
The calculator can be fed that data, say from a computer or a data logger, for
processing. Or, you can generate your own data by programming a function
and adding a few random numbers to it.
Example 1 – Define the function f(x) = 2 sin (3x) + 5 cos(5x) + 0.5*RAND,
where RAND is the uniform random number generator provided by the
calculator. Generate 128 data points by using values of x in the interval
(0,12.8). Store those values in an array, and perform a FFT on the array.
where RAND is the uniform random number generator provided by the
calculator. Generate 128 data points by using values of x in the interval
(0,12.8). Store those values in an array, and perform a FFT on the array.
First, we define the function f(x) as a RPN program:
<<
x ‘2*SIN(3*x) + 5*COS(5*x)’ EVAL RAND 5 * + NUM >>
and store this program in variable
@@@@f@@@. Next, type the following program to
generate 2
m
data values between a and b. The program will take the values of
m, a, and b:
<<
m a b << ‘2^m’ EVAL n << ‘(b-a)/(n+1)’ EVAL Dx << 1 n FOR j
‘a+(j-1)*Dx’ EVAL f NEXT n
ARRY >> >> >> >>
Store this program under the name GDATA (Generate DATA). Then, run the
program for the values, m = 5, a = 0, b = 100. In RPN mode, use:
program for the values, m = 5, a = 0, b = 100. In RPN mode, use:
5#0#100@GDATA!