Lecture 7: Spectral Representation Signals and Systems Lecture 7: Spectral Representation
Example 3-5: Amplitude Modulation Find the spectral components of x(t) x(t)= [5 + 4cos(40πt)] cos(400πt)
Figure 3.7: Spectrum of AM signal x(t)= cos (2π(20)t) cos (2π(200)t)
Periodic Signals f0 = gcd (fk)
Harmonic Signal Spectrum
Define Fundamental Frequency
Harmonic Signal (3 frequencies)
Periodic Signals
Period of Complex Exponential
Harmonic Signal (3 frequencies)
Another Spectrum
Examples Harmonic Signal xh(t)= 2cos (20πt) – 2/3 cos (20π(3)t) + 2/5 cos (20π(5)t) Non-Harmonic Signal x2(t)= 2cos (20πt)– 2/3 cos (20π(8)1/2t) + 2/5cos (20π(27) 1/2t)
Irrational Spectrum
xh(t)= 2cos (20 πt) – 2/3 cos (20π(3)t) + 2/5 cos (20π(5)t) Harmonic Signal
Non-Harmonic Signal x2(t)= 2cos (20πt)– 2/3 cos (20π(8)1/2t) + 2/5cos (20π(27) 1/2t)
Example: Synthetic Vowel
Spectrum of a Vowel
Spectrum of a Vowel
Vowel Waveform