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Questions tagged [norm]

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On $H_\infty$ norm for transfer function

For a given scenario in the context of control system, I'm trying to investigate how the $H_\infty$ norm can be calculated for a transfer function as follows: $$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
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TV Norm - What Would Be the Formula?

I have a 2-D discrete signal in which each point can be represented as $(x, y)$. These points are varying with time $t$. Can we represent the TV-norm using the following formula? $$\sum_{t}|x_t - x_{...
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What is the meaning of $l_p$ norm in this model for sparse channel estimation?

The signal $y(n)$ can be modeled in the time-domain as $$y(n) = \sum_{i=0}^{L-1}h(i) x(n-i) + v(t) \tag{1}$$ where $\mathbf{h} = [h_1,h_2,\ldots,h_L]^T$ is the coefficient of length $L-1$, and $v(t)$...
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79 views

How to prove this norm inequality?

$$ \left( \sum |z_i|^a \right)^b \geq \left( \sum |z_i|^b \right)^a, \quad \forall a\in [1,2], b\in [2,+\infty) $$ Actually this is equivalent to $$ \|z\|_a \geq \|z\|_b \quad \forall a\leq b $$
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95 views

Derivative of $l_1$ norm

I want to compute the following derivative with respect to $n\times1$ vector $\mathbf x$. $$g = \left\lVert \mathbf x - A \mathbf x \right\rVert_1 $$ My work: $$g = \left\lVert \mathbf x - A \...