sineCW60 Edge Shape Functions
Author: Thomas MARTIN, DF7TV
Revision date: June 1, 2025
Reference: https://www.qsl.net/df7tv/morse-code-processing.html

All functions are defined for x in [0, 1].

GS1 (1.56):
y(x) = [exp(-0.5 * ((x - 1)/0.436)^2) - exp(-0.5 * (1/0.436)^2)] /
       [1 - exp(-0.5 * (1/0.436)^2)]                                 (1)

RC (1.57):
y(x) = 0.5 - 0.5 * cos(pi * x)                                       (2)

CF (1.58):
y(x) = 0.46620824
     - 0.49597453 * cos(pi * x)
     + 0.03379176 * cos(2 * pi * x)
     - 0.00402547 * cos(3 * pi * x)                                  (3)

AP1 (1.60):
y(x) = 1.0
     - 3.05937423 * (x - 1)^2
     + 3.93982779 * (x - 1)^4
     - 2.83450610 * (x - 1)^6
     + 1.18652517 * (x - 1)^8
     - 0.23247263 * (x - 1)^10                                      (4)

AP2 (1.61):
y(x) = 1.0
     - 3.08953423 * (x - 1)^2
     + 4.02519021 * (x - 1)^4
     - 2.93077271 * (x - 1)^6
     + 1.24004322 * (x - 1)^8
     - 0.24492649 * (x - 1)^10                                      (5)

AP3 (1.62):
y(x) = 1.0
     - 3.13487054 * (x - 1)^2
     + 4.15502848 * (x - 1)^4
     - 3.07919687 * (x - 1)^6
     + 1.32362225 * (x - 1)^8
     - 0.26458332 * (x - 1)^10                                      (6)

CK (1.64):
y(x) = 0.46096
     - 0.5 * cos(pi * x)
     + 0.03904 * cos(2 * pi * x)                                    (7)

GS2 (1.65):
y(x) = [exp(-0.5 * ((x - 1)/0.379)^2) - exp(-0.5 * (1/0.379)^2)] /
       [1 - exp(-0.5 * (1/0.379)^2)]                                (8)

BM (1.82):
y(x) = (1 - |x - 1|) * cos(pi * |x - 1|)
       + (1/pi) * sin(pi * |x - 1|)                                 (9)

CP (2.09):
y(x) = 0.36334998
     - 0.48935168 * cos(pi * x)
     + 0.13665002 * cos(2 * pi * x)
     - 0.01064832 * cos(3 * pi * x)                                (10)


Note: For its application in SynthEdit Waveshaper2B module,
      equation (9) of function  BM (1.82) has been simplified to:
      y(x) = x * cos(pi * (1 - x)) + (1/pi) * sin(pi * (1 - x))
      All other functions are implemented exactly as shown above.


License:
This work, sineCW60 Edge Shape Functions
Copyright 2024-2025 by Thomas MARTIN, DF7TV,
is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
See: https://creativecommons.org/licenses/by-sa/4.0/