1. Associate Professor (Lecturer)
CONCEPTUAL
TOOLS
Fourier Theory
Neil E. Cotter
Associate Professor (Lecturer)
ECE Department
University of Utah

2. Fourier Theory Any function of time = sum of sinusoids CONCEPTUAL
TOOLS
Fourier Theory
Any function of time = sum of sinusoids

3. Fourier Theory Example: create a square wave
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

4. Fourier Theory Function of time = sum of sinusoids Application:
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

5. Fourier Theory Filter = change sinusoids, depending on frequency
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