Final answer:
The question asks about the coefficients of the exponential Fourier series of periodic signals and comparing their spectra. Options a, b, and d are valid, while option c is incorrect.
Step-by-step explanation:
The question is asking about the coefficients of the exponential Fourier series of periodic signals, and specifically about sketching the amplitude and phase spectra of each. It then asks to compare the spectra and discuss the results. Let's go through each option:
- a) Coefficients involving complex integrals that require numerical methods. Complex integrals are used to calculate the coefficients when the waveforms are not simple trigonometric functions. This requires numerical methods such as numerical integration techniques to approximate the values.
- b) Coefficients that can be calculated using trigonometric functions. Trigonometric functions can be used to calculate the coefficients when the waveform is a simple periodic function such as a sine or cosine wave. In this case, the coefficients can be directly determined using the Fourier series formulas.
- c) Fourier series is not applicable for periodic signals. This statement is incorrect. Fourier series is specifically designed to analyze and represent periodic signals using a series of harmonic components.
- d) Comparing the amplitude and phase spectra. Comparing the amplitude and phase spectra is a common practice to examine the frequency content and phase characteristics of a periodic signal. This comparison can provide insights into the composition and behavior of the signal.
Based on this analysis, options a, b, and d are valid in the context of the question, while option c is incorrect.