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Questions and Answers
According to Fourier analysis, what is a composite signal composed of?
According to Fourier analysis, what is a composite signal composed of?
- 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)
What kind of frequency spectrum is produced when a periodic composite signal is decomposed using Fourier analysis?
What kind of frequency spectrum is produced when a periodic composite signal is decomposed using Fourier analysis?
- Band-limited spectrum
- Discrete spectrum (correct)
- Wideband spectrum
- Continuous spectrum
Which of the following best describes a nonperiodic composite signal?
Which of the following best describes a nonperiodic composite signal?
- 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
Why are single-frequency sine waves not typically used in data communications?
Why are single-frequency sine waves not typically used in data communications?
What is the primary benefit of decomposing a composite signal into its constituent sine waves?
What is the primary benefit of decomposing a composite signal into its constituent sine waves?
Which of the following is NOT a characteristic of a sine wave used in Fourier analysis?
Which of the following is NOT a characteristic of a sine wave used in Fourier analysis?
What does the bandwidth of a signal refer to?
What does the bandwidth of a signal refer to?
How would you describe the relationship between the time domain and frequency domain representations of a signal?
How would you describe the relationship between the time domain and frequency domain representations of a signal?
What is the fundamental frequency of a periodic signal?
What is the fundamental frequency of a periodic signal?
In the context of communication systems, why is it important to understand the frequency domain representation of a signal?
In the context of communication systems, why is it important to understand the frequency domain representation of a signal?
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Study Notes
Time and Frequency Domains of a Nonperiodic Signal
- The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.
Bandwidth of Periodic and Nonperiodic Composite Signals
- 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.
Examples of Nonperiodic Composite Signals
- 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
- 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.
Signals and Communication
- 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.
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