Transcript (ppt)

CONCEPTUAL
TOOLS
Filters and
Superposition
Neil E. Cotter
Associate Professor (Lecturer)
ECE Department
University of Utah
CONCEPTUAL
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
CONCEPTUAL
TOOLS
Filter
• Filter input = waveform (function of time)
• Filter output = modified waveform
Filter
Input
Output
CONCEPTUAL
TOOLS
Fourier Theory
• Filter input = sum of sinusoids
• Example: square wave = sum of sinusoids
Filter
Input
Output
CONCEPTUAL
TOOLS
Superposition
• Pass one sinusoid at a time through filter
• Input = sinusoid => output is sinusoid of
same frequency
Filter
Input
Output
CONCEPTUAL
TOOLS
Superposition
• Sum output sinusoids = Fourier series for
output waveform
Filter
Input
Output
CONCEPTUAL
TOOLS
Sinusoids
• Filter analysis = understanding what happens
to sinusoids as they go through filter
Filter
Input
Output
CONCEPTUAL
TOOLS
Filter Circuit
• Filter = Electronic circuit
• Input = Voltage waveform from mp3 player
• Output = Voltage waveform to drive earbuds
Filter
(Circuit)
Input
Output
(Voltage Waveform)
(Voltage Waveform)