# Sine Wave Generation Using an Unstable IIR Filter

Sine Wave Generation Using an Unstable IIR Filter

An unstable infinite impulse response (IIR) filter can be used as a sine wave generator. This little-known trick is useful when generating a pure tone with a microcontroller platform such as the Arduino or a computer such as the Raspberry Pi. Since the IIR filter is unstable, an input is not required to produce an output. Given appropriate initial conditions, an unstable recursive equation will produce an oscillating output for an indefinite length of time.