```python
from sympy import symbols, fourier_transform, sinc, pi,\
                  DiracDelta, Heaviside, exp, sin, cos

w, t = symbols('omega t')
a, b, W, T = symbols('a b W T', positive=True)

fourier_transform(DiracDelta(t), t, w)
```




$\displaystyle 1$




```python
fourier_transform(Heaviside(t + T/2) - Heaviside(t - T/2), t, w)
```




$\displaystyle \frac{\sin{\left(\pi T \omega \right)}}{\pi \omega}$




```python
fourier_transform(sinc(2*pi*W*t), t, w)
```




$\displaystyle \begin{cases} \frac{1}{2 W} & \text{for}\: \frac{W^{2}}{\left|{\omega^{2}}\right|} > 1 \\0 & \text{otherwise} \end{cases}$




```python
fourier_transform(exp(-a**2*t**2), t, w)
```




$\displaystyle \frac{\sqrt{\pi} e^{- \frac{\pi^{2} \omega^{2}}{a^{2}}}}{a}$



8927a5b29d49c80a8fefe11b71d44443685a9926
ipynb
Jupyter Notebook
Fourier transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-07T09:36:36.000Z
2021-09-07T09:36:36.000Z
Fourier transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
Fourier transform.ipynb
mfkiwl/GMPE340
3602b8ba859a2c7db2cab96862472597dc1ac793
MIT
2021-09-20T18:48:20.000Z
2021-09-20T18:48:20.000Z
Qwen/Qwen-72B
1. YES
2. YES