To prepare an array for fast fourier transforms, To use a fast fourier transform – HP 48g Graphing Calculator User Manual
Page 164
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13
To prepare an array
for fast
Fourier transforms:
1. Put the array of data on the stack.
2. If necessary, add zeros to the array so that all dimensions are equal
to an integral power of two. See chapter 14 for efficient ways to add
columns or rows of zeros to matrices.
To
use
a fast Fourier transform:
1. Enter the array of data to be transformed (or its name) onto
the stack. Make sure its dimensions are integral powers of 2 (see
above).
2. Press f
MTH 1 (NXT 1
FFT FFT to transform the data from the
time domain to the frequency domain.
or
Press
(i/ffFn
f
NXT
) FFT I FFT to transform the data from the
frequency domain to the time domain.
Example:
Using FFT and IFFT for forward and inverse fast Fourier
transforms. The example uses the elements of a random
vector to represent a sampled signal.
1. Create a 16-eIement random vector on the stack: enter - C 1 6 > RflNM.
2. Compute the one-dimensional discrete Fourier transform of this
signal: execute FFT. The elements of the resulting vector represent
the frequency components of the original signal.
3. Reconstruct the original signal by computing the one-dimensional
inverse discrete Fourier transform: execute I F F T . The result is the
same as the original signal, subject to small rounding errors.
You can compute two-dimensional Fourier transforms using matrices
as arguments. For instance, use a random 1 6 x 1 6 matrix in the above
example: {16 16> RFiNM.
13-8 Vectors and Transforms