Fourier Analysis

$\frac{{\partial}^2 \mu}{ \partial t^2 }=c^2 {\nabla}^2 \mu$

  • fourier series(Quadrant II) -> fourier transfom(Quadrant III): The period is infinite, so frequency domain becomes continuous.
  • fourier series(Quadrant II)-> discrete time fourier transform(Quadrant IV)
    • Time domain and frequency domain is symmetric.
    • Frequency domain becomes period if time domain is discrete.
    • The period is infinite, so frequency domain becomes continuous.
  • discrete time fourier transform(Quadrant IV) -> discrete fourier transform(Quadrant I): Frequency domain becomes discrete if time domain is periodic
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