Fourier Series of Exponential Function

$latex \displaystyle x(t) = e^{t} &s=2 &bg=ffffff$  $latex \displaystyle - \pi <= t <= \pi &s=2 &bg=ffffff$ $latex \displaystyle T = 2\pi \rightarrow &s=2 &bg=ffffff$   $latex \omega_0 = 1 &s=2 &bg=ffffff$ $latex \displaystyle x(t) = a_0 + \sum_{n=1}^{\infty} \biggl[a_n cos(n\omega_0 t) + b_n sin(n \omega_0 t) \biggr] &s=3 &bg=ffffff$ $latex \displaystyle a_0 = \frac{1}{2\pi} \int_{-\pi}^{\pi} … Continue reading Fourier Series of Exponential Function

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Fourier Series, Pi and Zeta function

$latex x(t) = t^2 &s=2 &bg=ffffff$ and $latex - \pi <= t <= \pi &s=2 &bg=ffffff$ $latex \displaystyle x(t) = a_0 + \sum_{n=1}^{\infty} [a_n cos(n\omega_0 t) + b_n sin(n \omega_0 t)] &s=3 &bg=ffffff$ $latex T = 2\pi &s=2 &bg=ffffff$ $latex \omega_0 = 1 &s=2 &bg=ffffff$ $latex \displaystyle a_0 = \frac{1}{2 \pi} \int_{- \pi}^{\pi} t^2 dt … Continue reading Fourier Series, Pi and Zeta function

Basics of Fourier Series

$latex \Rightarrow &s=2 &bg=ffffff$   Fourier series is used for representing the Periodic power signals. $latex \Rightarrow &s=2 &bg=ffffff$   In Fourier series, a periodic signal is expanded in terms of its harmonics which are sinusoidal or complex exponential and orthogonal to each other. Types of Fourier Series Trigonometric Fourier Series $latex \displaystyle x(t) = a_0 + \sum_{n=1}^{\infty} [a_n cos(n … Continue reading Basics of Fourier Series

Fourier Series

Fourier series is used for representing the Periodic Power signal, the Periodic power signal is expanded in terms of its harmonics which are sinusoidal or complex exponential and orthogonal to each other. Fourier series for any sinusoidal signal is signal itself. Types of Fourier Series 1). Trigonometric Fourier Series:- 2). Complex Exponential Fourier Series:- Cn → Complex Exponential … Continue reading Fourier Series