Transcript (ppt)

CONCEPTUAL
TOOLS
Fourier Theory
Neil E. Cotter
Associate Professor (Lecturer)
ECE Department
University of Utah
CONCEPTUAL
TOOLS
Fourier Theory
Any function of time = sum of sinusoids
CONCEPTUAL
TOOLS
Fourier Theory
• Example: create a square wave
• Use a graphing calculator to plot ƒ(t):
Use x range of -1 to 1
Plot the first term (sinusoid), then three terms
Observe how waveform becomes more square
CONCEPTUAL
TOOLS
Fourier Theory
• Function of time = sum of sinusoids
• Application:
Sound = air pressure changes versus time
Sound = function of time
Sound = sum of sinusoids
CONCEPTUAL
TOOLS
Fourier Theory
• 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