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