Topic: Continuous-time Signals
Which of the following statements is true?
- A. Trigonometric Fourier series of an even function of time contains only DC term and sine terms
- B. Trigonometric Fourier series of an odd function of time contains only cosine terms
- C. Trigonometric Fourier series of an odd function of time contains only DC term and sine terms
- D. Trigonometric Fourier series of an even function of time contains only DC term and cosine terms
Answer: D. Trigonometric Fourier series of an even function of time contains only DC term and cosine terms
Explanation: By the properties of Fourier series, an even function of time is symmetric around the y-axis and therefore its Fourier series representation contains only the DC component ($a_0$) and cosine terms ($a_n$). Sine terms ($b_n$) are zero.