What technique shows that a square wave is made up of a sine wave and its odd harmonics?
The correct answer is A: Fourier analysis. Fourier analysis is the mathematical technique that shows a square wave is made up of a sine wave and its odd harmonics. Fourier analysis decomposes complex waveforms into their component sine waves.
According to Fourier analysis, a square wave consists of a fundamental sine wave at the square wave frequency, plus odd harmonics (3rd, 5th, 7th, etc.) at decreasing amplitudes. The fundamental has the largest amplitude, the 3rd harmonic has 1/3 the amplitude, the 5th harmonic has 1/5 the amplitude, and so on. This is why square waves have rich harmonic content and require wide bandwidth to transmit accurately. Fourier analysis is fundamental to understanding signal spectra and bandwidth requirements.
Exam Tip
Square wave harmonics = Fourier analysis. Remember: Fourier analysis shows that square waves consist of a fundamental sine wave plus odd harmonics. This is why square waves need wide bandwidth.
Memory Aid
"**S**quare **W**ave **H**armonics = **F**ourier **A**nalysis (think 'SWH = FA')"
Real-World Application
You're transmitting a square wave (like from a digital signal). Fourier analysis shows this square wave contains the fundamental frequency plus 3rd, 5th, 7th harmonics, etc. To transmit this accurately, you need bandwidth wide enough to include these harmonics. This is why digital signals often require more bandwidth than their fundamental frequency suggests.
FCC Part 97.3Key Concepts
Why Other Options Are Wrong
Option B: Incorrect. Vector analysis deals with magnitude and direction, not waveform decomposition into harmonics.
Option C: Incorrect. Numerical analysis is a general mathematical method, not specifically the technique that shows square waves are made of harmonics.
Option D: Incorrect. Differential analysis deals with rates of change, not waveform decomposition.
题目解析
The correct answer is A: Fourier analysis. Fourier analysis is the mathematical technique that shows a square wave is made up of a sine wave and its odd harmonics. Fourier analysis decomposes complex waveforms into their component sine waves. According to Fourier analysis, a square wave consists of a fundamental sine wave at the square wave frequency, plus odd harmonics (3rd, 5th, 7th, etc.) at decreasing amplitudes. The fundamental has the largest amplitude, the 3rd harmonic has 1/3 the amplitude, the 5th harmonic has 1/5 the amplitude, and so on. This is why square waves have rich harmonic content and require wide bandwidth to transmit accurately. Fourier analysis is fundamental to understanding signal spectra and bandwidth requirements.
考试技巧
Square wave harmonics = Fourier analysis. Remember: Fourier analysis shows that square waves consist of a fundamental sine wave plus odd harmonics. This is why square waves need wide bandwidth.
记忆口诀
**S**quare **W**ave **H**armonics = **F**ourier **A**nalysis (think 'SWH = FA')
实际应用示例
You're transmitting a square wave (like from a digital signal). Fourier analysis shows this square wave contains the fundamental frequency plus 3rd, 5th, 7th harmonics, etc. To transmit this accurately, you need bandwidth wide enough to include these harmonics. This is why digital signals often require more bandwidth than their fundamental frequency suggests.
错误选项分析
Option B: Incorrect. Vector analysis deals with magnitude and direction, not waveform decomposition into harmonics. Option C: Incorrect. Numerical analysis is a general mathematical method, not specifically the technique that shows square waves are made of harmonics. Option D: Incorrect. Differential analysis deals with rates of change, not waveform decomposition.
知识点
Fourier analysis, Square wave, Harmonics, Signal analysis
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.