Filters and Superposition Neil E. Cotter Associate Professor (Lecturer) ECE Department University of Utah CONCEPT U AL TOOLS

Filter Filter = change sinusoids, depending on frequency Result = change in waveform Example: remove low frequency from square wave Waveform now has sharp edges (more high frequencies) Application: emphasize or attenuate notes in music Equalizer = set of filters Treble and bass controls = filters CONCEPT U AL TOOLS

Filter Filter input = waveform (function of time) Filter output = modified waveform CONCEPT U AL TOOLS Filter InputOutput

Fourier Theory Filter input = sum of sinusoids Example: square wave = sum of sinusoids CONCEPT U AL TOOLS Filter InputOutput

Superposition Pass one sinusoid at a time through filter Input = sinusoid => output is sinusoid of same frequency CONCEPT U AL TOOLS Filter InputOutput

Superposition Sum output sinusoids = Fourier series for output waveform CONCEPT U AL TOOLS Filter InputOutput

Sinusoids Filter analysis = understanding what happens to sinusoids as they go through filter CONCEPT U AL TOOLS Filter InputOutput

Filter Circuit Filter = Electronic circuit Input = Voltage waveform from mp3 player Output = Voltage waveform to drive earbuds CONCEPT U AL TOOLS Filter (Circuit) Input (Voltage Waveform) Output (Voltage Waveform)