Q. Show Spectral Analysis and Signal Bandwidth?

Spectral analysis is based on the fact that a sinusoidal waveform is completely characterized by three quantities: amplitude, phase, and frequency. By plotting amplitude and phase as a function of frequency f(= ω/2π = 1/T), the frequency-domain picture conveys all the information, including the signal's bandwidth and other significant properties about the signal that consists entirely of sinusoids. The two plots together (amplitude versus frequency and phase versus frequency) constitute the line spectrum of the signal x(t).

If x(t) happens to be a periodic signal whose Fourier coefficients are known, Equation can be rewritten as

The phase angles are referenced to the cosine function, in agreement with our phasor notation. The corresponding phasor diagram of Fourier coefficients is shown in Figure. Equation reveals that the spectrum of a periodic signal contains lines at frequencies of 0, f,2f, and all higher harmonics of f, although some harmonics may be missing in particular cases. The zero-frequency or dc component represents the average value a0, the components corresponding to the first few harmonics represent relatively slow time variations, and the higher harmonics represent more rapid time variations.