pyffs.func¶
Methods for computing samples and Fourier Series coefficients of specific functions.
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dirichlet(x, T, T_c, N_FS)[source]¶ Return samples of a shifted Dirichlet kernel of period \(T\) and bandwidth \(N_{FS} = 2 N + 1\):
\[\phi(t) = \sum_{k = -N}^{N} \exp\left( j \frac{2 \pi}{T} k (t - T_{c}) \right) = \frac{\sin\left( N_{FS} \pi [t - T_{c}] / T \right)}{\sin\left( \pi [t - T_{c}] / T \right)}.\]- Parameters:
- Returns:
vals – Function values.
- Return type:
See also
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dirichlet_fs(N_FS, T, T_c, mod=None)[source]¶ Return Fourier Series coefficients of a shifted Dirichlet kernel of period \(T\) and bandwidth \(N_{FS} = 2 N + 1\).
- Parameters:
- Returns:
vals – Fourier Series coefficients in ascending order.
- Return type:
See also
dirichlet()(N_FS,) Fourier Series coefficients.
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dirichlet_2D(sample_points, T, T_c, N_FS)[source]¶ Return samples of a shifted 2D Dirichlet kernel of period \((T_x, T_y)\) and bandwidth \(N_{FS, x} = 2 N_x + 1, N_{FS, y} = 2 N_y + 1\):
\[\begin{split}\phi(x, y) &= \sum_{k_x = -N_x}^{N_x} \sum_{k_y = -N_y}^{N_y} \exp\left( j \frac{2 \pi}{T_x} k_x (x - T_{c,x}) \right) \exp\left( j \frac{2 \pi}{T_y} k_y (y - T_{c,y}) \right) \\ &= \frac{\sin\left( N_{FS, x} \pi [x - T_{c,x}] / T_x \right)}{\sin\left( \pi [x - T_{c, x}] / T_x \right)} \frac{\sin\left( N_{FS, y} \pi [y - T_{c,y}] / T_y \right)}{\sin\left( \pi [y - T_{c, y}] / T_y \right)}.\end{split}\]- Parameters:
- Returns:
vals – Function values at sample_points.
- Return type:
See also