# Audio Filtering

## 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

## 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