Filtering & Aliasing - week 5

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  • Filtering and Aliasing
    • Filters
      • The ideal anti-aliasing filter is a brick wall low-pass at the Nyquist frequency
      • Filter should be applied before sampling
      • Characteristics
        • The region of minimal attenuation is called a pass-band (unity)
        • Half-power point is at -3dB
        • The steepness of a filter is called the roll-off rate
          • 20 x n dB per decade
          • 6 x n dB per octave
        • The region of unwanted signal is called a stop-band
        • The order determines the roll off
          • Order = roll-off (octave) / 6
          • Order = roll-off (decade) / 20
        • Transfer functions
          • Butterworth
          • Bessel
          • Chebyshev
        • Ripple (gain) in stop- or pass-band
      • Types
        • Band pass (BP) attenuates frequencies in the stop-band above and below certain cut offs
        • Low pass (LP) attenuates frequencies above the cut off
        • High pass (HP) attenuates frequencies below cut off
        • Band stop (BS) attenuates frequencies in the stop-band between certain cut offs
    • Aliasing
      • Also called frequency fold-back
      • Oversampling can be used to reduce aliasing
      • Key considerations
        • Amount of attenuation in pass-band
        • No phase distortion in pass-band
        • Desired filter roll-off in stop-band
        • Steepness in transition region
          • Note how this affects different frequencies and the ripple


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