Low Pass Filtering

  • Review general concept of low-pass filtering.
  • 1D Ideal Lowpass filter.
  • Generalization to 2D Ideal Lowpass filter.
  • 2D Butterworth Lowpass filter.
  • 2D Gaussian Lowpass filter.
  • All filters presented with the assumption the signal is modulated at the Nyquist frequency in the time domain before and after being filtered in the frequency domain. Their mathematical representations make this assumption and are greatly simplified as a result.

 

High Pass Filtering

  • Review general concept of high-pass filtering.
  • 1D Ideal Highpass filter
  • Generalization to 2D Ideal Highpass filter.
  • 2D Butterworth Highpass filter.
  • 2D Gaussian Highpass filter.
  • Laplacian filtering, and its formulation as a frequency domain filter.