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}(c_1g(t) + c_2h(t) = \int_{-\infty}^\infty c_1g(t) dt + \int_{-\infty}^\infty c_2h(t) dt $ $ =c_1\int_{-\infty}^\infty g(t)e^{i2\pi ft} dt + c_2 \int_{-\infty}^\infty g(t)e^{i2\pi ft} dt $ |
| Time Shifting | $ \mathfrak{F}(g(t - a)) = e^{-i2\pi fa}*G(f) $ | $ \int_{-\infty}^\infty g(t-a)e^{-2\pi ft}dt $ $ \int_{-\infty}^\infty g(u)e^{-i2\pi f(u+a)} du $ |
