Time and Frequency Domains of a Nonperiodic Signal

Study Notes

The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.

Example 3.6: A periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz. Its bandwidth is 900 - 100 = 800 Hz.
Example 3.7: A periodic signal has a bandwidth of 20 Hz and the highest frequency is 60 Hz. The lowest frequency is 60 - 20 = 40 Hz.
Example 3.8: A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V. The lowest frequency is 140 - 100 = 40 kHz and the highest frequency is 140 + 100 = 240 kHz.

Example 3.9: An AM radio station in the United States has a 10-kHz bandwidth, with a total bandwidth dedicated to AM radio ranging from 530 to 1700 kHz.
Example 3.10: An FM radio station in the United States has a 200-kHz bandwidth, with a total bandwidth dedicated to FM radio ranging from 88 to 108 MHz.
Example 3.11: A nonperiodic composite signal is the signal received by an old-fashioned analog black-and-white TV, with a resolution of 525 × 700 pixels per screen and a scanning rate of 30 times per second.

Fourier analysis is a tool that changes a time domain signal to a frequency domain signal and vice versa.
Fourier series represents a composite periodic signal as a series of sine and cosine functions with integral harmonics of the fundamental frequency.

A single-frequency sine wave is not useful in data communications; instead, a composite signal made of many simple sine waves is used.
According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.
If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies. If the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.