Zryn said:What do you mean by "digital or discrete spectrum" ? The '(t)' in x(t) designates a continuous time dependent signal.
Anyway, are you familiar with the 3 co-efficients (a0, an, & bn), the way the Fourier series will be represented after you find them, how to calculate each one, and any shortcuts (like an odd or even function) that may hasten the process?
A Fourier Series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It can be used to describe a wide range of periodic phenomena, such as sound, light, and electrical signals.
Finding Fourier Series coefficients allows us to accurately represent a periodic function and analyze its properties. It also allows us to approximate non-periodic functions by using a finite sum of Fourier Series terms.
There are various methods for calculating Fourier Series coefficients, such as the Euler-Fourier formula, the complex form of Fourier Series, and the trigonometric form of Fourier Series. Each method involves integrating the given function over one period and solving for the coefficients.
Fourier Series has many applications in science, engineering, and mathematics. It is used in signal processing, image analysis, data compression, and solving differential equations. It is also used to study the behavior of waves, vibrations, and other periodic phenomena.
Yes, Fourier Series can be used to approximate non-periodic functions by using a finite number of terms. However, the accuracy of the approximation depends on the smoothness of the function and the number of terms used.