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You can apply a so-called all-pass transformation to a discrete-time low-pass prototype filter in order to convert it to other standard filters (such as high-pass, band-pass, and band-stop). This is accomplished by transforming the complex variable $z$ in the transfer function of the prototype filter by a function $G(z)$ which satisfies $|G(e^{j\omega})|=1$, ...


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However when I look at the closed loop transfer function, I would say that this system is unstable for 𝐺𝐻=βˆ’1. In this case the transfer function becomes infinity so a bounded input will result in a unbounded (=infinity) output. This depends on your definition of stability. $GH = -1$ is called marginally stable because depending on how you look at it, it ...


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There are a few things I can note about your question. As far as I have always learned, the nyquist stability criterion is taken over the openloop transfer function. if you take the closed loop transfer function, you should count the encirclements of 0 instead (if i recall correctly). The formal definition of stability, as expressed by the Lyapunov's ...


1

The "classic" way of estimating blurriness is (as far as I know) the difference of Gaussians approach: you filter your image with Gaussian blur filters of different variance. Then, you at which level of blurriness the most info is lost (i.e. where the largest difference between the last level of blurriness and the next level is). If your image ...


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