Spectrum Representation
Chapter 3
This Lecture:
 Chapter 3, Section 3-1,3-2, 3-3
 Other Reading:
Appendix A: Complex Numbers
Phasor and a spectrum!
 It is a compact representation of the frequency content of a signal that is composed of
sinusoids
 The phasors can simplify the addition of sinusoids of the same frequency
 the spectrum is simply the collection of amplitude, phase, and frequency
information that allows us to express the signal in the form
the complex amplitude (i.e., phasor) for the complex
exponential of frequency fk
Review of Euler Formula
SPECTRUM Interpretation
Example
SPECTRUM of SINE
Example
Example
DC component
The spectrum of this signal is the set of five rotating phasors represented by
two-sided spectrum
The Spectrum of a Sum of Sinusoids
Recall
DC component
The spectrum of this signal is the set of five rotating phasors represented by
Spectrum set
Beat
 Beat sound of the same amplitude but different frequency
 multiply two sinusoids having different frequencies
Example spectrum of Product
Beat Note Waveform
The two frequencies can be expressed as
f1 = fc-f
and
f2=fc+f
where we have defined
a center frequency fc = ½(f1+f2 )
and
a deviation frequency
f = ½(f1-f2 )
which we assume is much smaller than fc .
The spectrum of this beat signal is plotted
Recall