## 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

• 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