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Robo-Voice Synthesizer

Power-line Interference

  • Filter: Notch (Bandstop)
  • Type: Butterworth
  • Order: 2nd
  • Centre (fo): 60 Hz
  • Transfer Function: H(s) ≐ (s^2 + 142122.3)/(s^2 + 533.1s + 142122.3)

Since we are removing a highly specific frequency, namely the 60 Hz hum from AC power sources, without affecting the passband, a Butterworth notch filter is the ideal choice. This is owing to its ability to precisely and sharply attenuate frequency-specific noise. Additionally, a Q-factor of 60 is chosen to maintain a bandwidth of 1.0 Hz, as per the equation: Q = fo/BW.

Background Noise

  • Filter: Bandpass
  • Type: Butterworth
  • Order: 2nd
  • Cut-off: fl = 0.1 Hz, fh = 450 Hz
  • Transfer Function: H(s) ≐ 45/(s^2 + 0.015s + 45)

Since we are preserving a specific range of frequencies, i.e., 0.1 Hz to 450 Hz (as specified), a bandpass filter is a solid option. A Butterworth configuration has been chosen to provide a maximally flat frequency response that ensures the passband is undisturbed.