Fourier series formulas

Table of Fourier transform S.No F(t) F(ω) 1 \( e^{-at}u(t) \) \( \frac {1}{a+j\omega}, \ a\gt 0 \) 2 \( e^{at}u(-t) \) \( \frac {1}{a-j\omega}, \ a\gt 0 \) 3…

Fourier Transform Properties 1. Linearity $$ ax(t)+bv(t) \longleftrightarrow aX(\omega)+bV(\omega) $$ 2. Time Shift $$ x(t-c) \longleftrightarrow e^{-j\omega c} X(\omega ) $$ 3. Time Scaling $$ x(at) \longleftrightarrow \frac 1a X…

Fourier series A Fourier series is nothing but the expansion of a periodic function f(x) with the terms of an infinite sum of sins and cosine values. It decomposes any…