Table of CT Fourier Series Coefficients and Properties
Fourier series Coefficients
| Function | Fourier Series | Coefficients |
|---|---|---|
Properties of CT Fourier systems
| Property Name | Property | Proof |
|---|---|---|
| Linearity | $ \mathfrak{F}{(c_1g(t) + c_2h(t)} = c_1G(f) + c_2H(f) $ | $ \mathfrak{F}(ax_{1}[n] + bx_{2}[n]) = \sum_{n=-\infty}^{\infty}[ax_{1}[n] + bx_{2}[n]]e^{-j\omega n} $ $ \sum_{n=-\infty}^{\infty}ax_{1}[n]e^{-j\omega n} + \sum_{n=-\infty}^{\infty}bx_{2}[n]e^{-j\omega n} $ |
