diff --git a/source/index.rst b/source/index.rst index 4578515..ebbcb45 100644 --- a/source/index.rst +++ b/source/index.rst @@ -20,6 +20,12 @@ Welcome to ScienceNotes's documentation! statistics/distributions/index.rst statistics/tests/index.rst +.. toctree:: + :maxdepth: 2 + :numbered: + :caption: Signal Processing + + signal_processing/fourier_tables.rst Indices and tables ================== diff --git a/source/signal_processing/fourier_tables.rst b/source/signal_processing/fourier_tables.rst new file mode 100644 index 0000000..a468844 --- /dev/null +++ b/source/signal_processing/fourier_tables.rst @@ -0,0 +1,39 @@ +Fourier Tables +-------------- + + +Table of pairs +============== + +.. csv-table:: + :header: Signal :math:`x(t)`, Fourier transform :math:`X(\\omega)` + :align: center + + :math:`\delta(t)`, :math:`1` + :math:`1`, :math:`2\pi\delta(\omega)` + :math:`\mathrm{rect}(\frac{t}{a})`, :math:`a\mathrm{sinc}(\frac{\omega a}{2})` + :math:`\frac{a}{\pi}\mathrm{sinc}(at)`, :math:`\mathrm{rect}(\frac{\omega}{2a})` + :math:`e^{-at}u(t)`, :math:`\frac{1}{j\omega + a}` + :math:`e^{j\omega_0t}`, :math:`2\pi\delta(\omega-\omega_0)` + :math:`\mathrm{cos}(\omega_0t)`, :math:`\pi[\delta(\omega-\omega_0)+\delta(\omega+\omega_0)]` + :math:`\mathrm{sin}(\omega_0t)`, :math:`\frac{\pi}{j}[\delta(\omega-\omega_0)+\delta(\omega+\omega_0)]` + + +Table of properties +=================== + +.. csv-table:: + :header: Signal :math:`x(t)`, Fourier transform :math:`X(\\omega)` + :align: center + + :math:`x(t)`, :math:`X(\omega)` + :math:`x(t-t_0)`, :math:`e^{-jwt_0}X(\omega)` + :math:`e^{jw_0t}x(t)`, :math:`X(\omega-\omega_0)` + :math:`x(at)`, :math:`\frac{1}{|a|}X(\frac{\omega}{a})` + :math:`\frac{d}{dt}x(t)`, :math:`j\omega X(\omega)` + :math:`tx(t)`, :math:`j\frac{d}{d\omega}X(\omega)` + :math:`x_1(t) \ast x_2(t)`, :math:`X_1(\omega) + X_2(\omega)` + :math:`x_1(t)x_2(t)`, :math:`\frac{1}{2\pi}X_1(\omega) \ast X_2(\omega)` + :math:`x(t)^*`, :math:`X^*(-\omega)` + :math:`X(t)`, :math:`2\pi x(-\omega)` + :math:`\int_{-\infty}^tx(\tau)d\tau`, :math:`\frac{X(\omega)}{j\omega}+\pi X(0) \delta(\omega)`