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Yes repeated poles simply means there are more than one pole at the same location. Consider the simple case of a cascade of two integrators (in s) which is similar to the cascade of two accumulators (in z). The Laplace transform of an integrator Is $\frac{1}{s}$, which is one pole at the origin. Two integrators in cascade would be $\frac{1}{s^2}$ so has ...


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It's easy to show that the system defined by $$ y(t) = \int_{-\infty}^t x(\tau^2) d\tau $$ is Not Causal : it's because for for any value of $t$ the output $y(t)$ will always depend on future values of the input $x(t)$. Because while the dummy variable $\tau$ used in the integration ranges from $-\infty$ to $t$. The argument of the input function $x(t)$ ...


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