Which statement best describes the relationship between line spectra and Fourier representations?

Which statement best describes the relationship between line spectra and Fourier representations?

• A. Line spectra plot amplitudes and phases of frequency components after Fourier representation.
• B. Line spectra plot time-domain samples of the signal.
• C. Line spectra show only the DC component.
• D. Line spectra require non-periodic signals.

Answer: (A)

Line spectra reveal the Fourier components of a signal by plotting the amplitudes and phases of those frequency components after performing the Fourier representation. For a periodic signal, the Fourier series breaks the signal into discrete sinusoids at harmonic frequencies, and the line spectrum shows each line at those frequencies with its height corresponding to the amplitude and its position (angle) to the phase. This is what lets you see the strength and timing of each frequency present in the signal.

Time-domain samples are not what a line spectrum represents, and a line spectrum typically contains more than just a DC component—there can be many lines at different harmonics. Also, line spectra arise from discrete-frequency components; non-periodic signals produce a continuous spectrum rather than a set of discrete lines.