ECE 101 Signals and Systems
Spring 2006
Fourier Analysis
Requirements for Fourier Analysis:
1. Understand the essence of Fourier Analysis (what? why? how?)
2. Memorize the definitions (Fourier Series for continuous/discrete time signals, Fourier
transform for continuous/discrete time signals)
3. Understand the useful properties (linearity, time shifting, time reversal,differentiation,
integration, amplitude shifting)
4. Be able to transform signals from the time domain to the frequency domain and vice
versa (using definitions and properties).
Understanding Fourier Analysis
What is Fourier Analysis about?
•
Representing and analyzing signals and systems in the
frequency domain
. Time
domain presentation and frequencydomain presentation are like two sides of a coin:
they are about the same thing but revealing different views.
•
Two technical parts:
Fourier Series
and
Fourier Transform
.
–
Fourier series are applicable only to periodic signals (or signals have a finite time
interval). It is found that a periodic continuoustime (respectively discretetime)
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 Spring '08
 Li
 Fourier Series

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