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Fourier Transform

Fourier Transform
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2020-05-29 17:08
FunctionCalculusTransformation
This example demonstrates the process of Fourier Transform, a mathematical method that decomposes signals into different frequencies of sine waves. Using GeoGebra commands such as Circle, Vector, If, Segment, PolyLine, etc., the decomposition process is dynamically displayed. Suitable for university mathematics and signal processing courses.

GeoGebra Commands & Parameters

  1. Circle(A2, R3) → c3
  2. Vector(A1, P1) → v1
  3. Vector(A2, P1) → v2
  4. Vector(A3, P1) → v3
  5. If(n ≟ 1, v1, Vector[If[n ≟ 2, v2, v3]]) → v
  6. Circle((-4, -2.5), R1) → d1
  7. Circle((-4, -4.5), R2) → d2
  8. Circle((-4, -6.5), R3) → d3
  9. Segment(Center[d1], B1) → b1
  10. Segment(Center[d2], B2) → b2
  11. Segment(Center[d3], B3) → b3
  12. Vector(B1, (t, f1(t))) → u1
  13. Vector(B2, (t, f2(t))) → u2
  14. Vector(B3, (t, f3(t))) → u3
  15. Circle((x(A1), y(A1)), R2) → c2
  16. Circle((-4, -4.5), R1) → c1
  17. PolyLine((-4, -4.5), A1, A2, A3) → p
  18. Vector((-4, -4.5), ((-4, -4.5) * (1 - sep)) + (sep * A1)) → vs2
  19. Translate(d2, vs2) → c20
  20. Vector((-4, -6.5), ((-4, -6.5) * (1 - sep)) + (sep * A2)) → vs3
  21. Translate(d3, vs3) → c30
  22. Vector((-4, -2.5), (-4, (-4.5 * sep) + ((1 - sep) * (-2.5)))) → vs1
  23. Vector((-4, -2.5), (-4, (-4.5 * sep) + ((1 - sep) * (-2.5)))) → vs10
  24. Translate(f1, vs10) → ff1
  25. Vector((-4, -6.5), (-4, (-4.5 * sep) + ((1 - sep) * (-6.5)))) → vs30
  26. Translate(d1, vs1) → c10
  27. Translate(f3, vs30) → ff3