Howtosignalprocessing
- What is the Fourier transform of a periodic function?
- What is Fourier series for periodic signals?
- Is Fourier series only for periodic functions?
- How the Fourier transform is useful in analysis of periodic signals?
What is the Fourier transform of a periodic function?
Key concept: Fourier Transform of Fourier Series Representation of xT(t) If we write a periodic function. xT(t)=+∞∑n=−∞cnejnω0t. then its Fourier Transform is. XT(ω)=2π+∞∑n=−∞cnδ(ω−nω0)
What is Fourier series for periodic signals?
The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals. This lesson shows you how to compute the Fourier series coefficients, or weights, from the signal.
Is Fourier series only for periodic functions?
The Fourier series is always a periodic function, even if original function s(x) wasn't.
How the Fourier transform is useful in analysis of periodic signals?
6.4.
The Fourier transform (FT) provides a way to characterize the overall regularity as well as the related concept of the frequency scale of a periodic signal. An important feature of FT is the orthogonality of the basic functions, which allows for a unique decomposition of signals.
