Topic: Signals and Systems
A 33.33% duty cycle rectangular wave is fed to the input of an Spectrum Analyzer. What will be observed?
- A. $2^{nd}$, $5^{th}$, $8^{th}$... harmonics missing
- B. $3^{rd}$, $6^{th}$, $9^{th}$... harmonics missing
- C. $1^{st}$, $4^{th}$, $7^{th}$... harmonics missing
- D. All the harmonic present
Answer: B. $3^{rd}$, $6^{th}$, $9^{th}$... harmonics missing
Explanation: A rectangular wave with a duty cycle $d$ has Fourier series coefficients containing a $\text{sinc}(n\pi d)$ term. For $d = 1/3$ (33.33%), the harmonics are zero when $n\pi/3 = k\pi$, which means $n = 3k$. Therefore, the 3rd, 6th, 9th, etc., harmonics will be missing.