Time and Frequency Domains of a Nonperiodic Signal

Questions and Answers

A single sine wave with a specific frequency

A series of square waves with varying duty cycles

A combination of triangular waves with varying slopes

A combination of simple sine waves with different frequencies, amplitudes, and phases (correct)

Band-limited spectrum

Discrete spectrum (correct)

Wideband spectrum

Continuous spectrum

A signal that does not repeat with a consistent pattern and frequency (correct)

A signal that changes abruptly and unpredictably

A signal that has a limited bandwidth and frequency range

A signal that repeats with a consistent pattern and frequency

They carry very little information and are not suitable for transmitting data. Signup and view all the answers

It simplifies the analysis of the signal and makes it easier to understand its properties. Signup and view all the answers

Duty cycle Signup and view all the answers

The range of frequencies present in the signal Signup and view all the answers

They are complementary and provide different but related perspectives of the signal. Signup and view all the answers

The frequency at which the signal repeats itself Signup and view all the answers

To filter and amplify specific frequencies within the signal Signup and view all the answers

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.