Fourier Analysis

Fourier Analysis#

Overview#

This section covers Fourier analysis functions from NCL:

Functions#

cfftf#

NCL’s cfftf calculates an unnormalized forward complex discrete Fourier transform of a real periodic sequence

Grab and Go#

import numpy as np

example_data = [
    1002,
    1017,
    1018,
    1020,
    1018,
    1027,
    1028,
    1030,
    1012,
    1012,
    982,
    1012,
    1001,
    996,
    995,
    1011,
    1027,
    1025,
    1030,
    1016,
    996,
    1006,
    1002,
    982,
]

cfftf = np.fft.fft(example_data)

print(cfftf.real)

[ 2.42650000e+04  1.60612517e+01 -1.61808312e+02  2.60000000e+01
  3.95000000e+01 -6.47808940e+01  1.00000000e+00 -3.26972907e+01
  3.25000000e+01  2.60000000e+01 -4.19168826e+00  3.54169330e+01
 -4.30000000e+01  3.54169330e+01 -4.19168826e+00  2.60000000e+01
  3.25000000e+01 -3.26972907e+01  1.00000000e+00 -6.47808940e+01
  3.95000000e+01  2.60000000e+01 -1.61808312e+02  1.60612517e+01]

cfftb#

NCL’s cfftb calculates a backward complex discrete Fourier transform

Grab and Go#

import numpy as np

example_data = [
    1002,
    1017,
    1018,
    1020,
    1018,
    1027,
    1028,
    1030,
    1012,
    1012,
    982,
    1012,
    1001,
    996,
    995,
    1011,
    1027,
    1025,
    1030,
    1016,
    996,
    1006,
    1002,
    982,
]

cfftb = np.fft.ifft(example_data)

print(cfftb.real)

[ 1.01104167e+03  6.69218822e-01 -6.74201299e+00  1.08333333e+00
  1.64583333e+00 -2.69920392e+00  4.16666667e-02 -1.36238711e+00
  1.35416667e+00  1.08333333e+00 -1.74653677e-01  1.47570554e+00
 -1.79166667e+00  1.47570554e+00 -1.74653677e-01  1.08333333e+00
  1.35416667e+00 -1.36238711e+00  4.16666667e-02 -2.69920392e+00
  1.64583333e+00  1.08333333e+00 -6.74201299e+00  6.69218822e-01]

Inverse Fourier transformation of the forward Fourier transform returns input data

import numpy as np

example_data = [
    1002,
    1017,
    1018,
    1020,
    1018,
    1027,
    1028,
    1030,
    1012,
    1012,
    982,
    1012,
    1001,
    996,
    995,
    1011,
    1027,
    1025,
    1030,
    1016,
    996,
    1006,
    1002,
    982,
]

cfftf = np.fft.fft(example_data)
cfftb = np.fft.ifft(cfftf)

print(cfftb.real)

[1002. 1017. 1018. 1020. 1018. 1027. 1028. 1030. 1012. 1012.  982. 1012.
 1001.  996.  995. 1011. 1027. 1025. 1030. 1016.  996. 1006. 1002.  982.]

Python Resources#