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User:Zackron

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Welcome to my user page.

This page is mostly a sandbox page for me to test quick wiki code snippets.

Math Markup Samples

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Type Markup Result
DFT X(\omega_k) \equiv \sum_{n=0}^{N-1} x(t_n)e^{-j\omega_k t_n}, \qquad k=0,1,2,\ldots,N-1,
DFT X(k) \equiv \sum_{n=0}^{N-1} x(n)e^{-j2 \pi n k / N}, \qquad k=0,1,2,\ldots,N-1,
IDFT x(t_n) \equiv {1 \over N} \sum_{k=0}^{N-1} X(\omega_k)e^{j\omega_k t_n}, \qquad k=0,1,2,\ldots,N-1,
IDFT x(n) \equiv {1 \over N} \sum_{k=0}^{N-1} X(k)e^{j2 \pi n k / N}, \qquad k=0,1,2,\ldots,N-1,
Functions f: X \times Y \to \Bbb{R}

g: X \to Y

Series \{(x_1, y_1), ..., (x_N,\; y_N)\}
Function as Sum f(\mathbf{x}) = \sum_{j=1}^m w_j h_j(\mathbf{x})
Function as Sum E = \sum_{t=1}^T E(t) = \sum_{t=1}^T \sum_{i=1}^n(1/2)(\hat{Y}_i(t)-Y_i(t))^2
Function as Sum \frac {\partial^+ \text {TARGET}}{\partial z_i} = \frac {\partial \, \text{TARGET}}{\partial z_i} + \sum_{j>i} \frac {\partial^+ \text {TARGET}}{\partial z_j} * \frac {\partial z_j}{\partial z_i}
Function as Sum F\_z_i = \frac {\partial E}{\partial z_i} + \sum_{j>i} F\_z_i * \frac {\partial z_j}{\partial z_i}
Function as Sum F\_\hat{Y}(t) = \frac {\partial E}{\partial\hat{Y}_i(t)} = \hat{Y}_i(t) - Y_i(t),
Function as Sum \begin{align}F\_x_i(t) & = F\_\hat{Y}_{i - N}(t) + \sum_{j=i+1}^{N+n} W_{ji} * F\_\text{net}_j(t), \\ i & = N + n , \cdots , m + 1 \\ \end{align}
Function as Sum \begin{align}F\_\text{net}_i(t) & = s'(\text{net}_i) * F\_x_i(t), \\ i & = N + n , \cdots , m + 1 \\ \end{align}
Function as Sum F\_W_{ij} = \sum_{t=1}^T F\_\text{net}_i(t) * x_j(t)
Function as Sum \,s'(z) = s(z) * (1 - s(z)),

References

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