Filters

  • Change amplitude / phase of frequencies of sound

  • Many applications

    • "Tone" control, "Equalizer"

    • Effects, e.g. "wah" example

    • Band limiting for antialiasing, resampling, etc

    • Etc etc

Common Ideal Filter Shapes

  • Usually 0-1 with Passband, Stopband: goal is to block some range of frequencies while leaving others alone9QAWP-6RRDW-39TP4

  • Low Pass

  • High Pass, Bandpass, Band Notch

Units and Normalization

  • Common to leave out sampling rate and gain in DSP

    • In time domain, samples are just numbered

    • In frequency domain, frequencies range from 0..1 where 1 is the Nyquist limit

    • Amplitude is normalized to -1..1 in time domain, 0..1 in frequency domain

  • We have already talked about dB

    • There are several dB scales floating around

    • Most common is \( 20~ log_{10}(A) \) where A may be RMS (normal), peak, or peak-to-peak

Filter "Quality" Measures

  • The ideal low pass filter is a "brick wall":

    • Gain in passband is exactly 1 for all frequencies

    • Gain in stopband is exactly 0 for all frequencies

    • Transition is instantaneous (vertical) at corner frequency

  • Sadly, this is unachievable in practice.

  • The "Q factor" of a filter is a sort of measure of this

Analog Filters

  • Made of electricity: resistors, capacitors, inductors, op-amps, etc.

  • Analog filters are simple, of necessity

  • Analog filters are kind of meh: typically use as few of them as possible when digital is available

  • Obvious example: anti-aliasing and DC removal "blocking" (typically a blocking capacitor)for DAC and ADC

Aside: Linear Time-Invariant Systems

  • Normal filter definition / requirement

  • Output signal is a linear function of input signal ("no distortion")

    • Preserves frequencies of input waves

  • Output signal does not depend on input time

    • Signals are notionally infinite, so this is a hard constraint

  • Analog filters are LTI

Last modified: Sunday, 12 April 2020, 3:39 PM