| Type
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Markup
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Result
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| DFT
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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,
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| DFT
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X(k) \equiv \sum_{n=0}^{N-1} x(n)e^{-j2 \pi n k / N}, \qquad k=0,1,2,\ldots,N-1,
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| IDFT
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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,
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| IDFT
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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,
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| Functions
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f: X \times Y \to \Bbb{R}
g: X \to Y
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| Series
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\{(x_1, y_1), ..., (x_N,\; y_N)\}
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| Function as Sum
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f(\mathbf{x}) = \sum_{j=1}^m w_j h_j(\mathbf{x})
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| Function as Sum
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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
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| Function as Sum
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\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}
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| Function as Sum
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F\_z_i = \frac {\partial E}{\partial z_i} + \sum_{j>i} F\_z_i * \frac {\partial z_j}{\partial z_i}
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| Function as Sum
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F\_\hat{Y}(t) = \frac {\partial E}{\partial\hat{Y}_i(t)} = \hat{Y}_i(t) - Y_i(t),
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| Function as Sum
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\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}
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| Function as Sum
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\begin{align}F\_\text{net}_i(t) & = s'(\text{net}_i) * F\_x_i(t), \\ i & = N + n , \cdots , m + 1 \\ \end{align}
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| Function as Sum
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F\_W_{ij} = \sum_{t=1}^T F\_\text{net}_i(t) * x_j(t)
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| Function as Sum
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\,s'(z) = s(z) * (1 - s(z)),
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