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Suppose we have a two dimensional continuous linear shift invariant system has impulse response: $h(x,y)=\left\{ \begin{array}{ll} \frac{1}{2\pi a^2 b^2}, & \mbox{if } (\frac{x}{a_2})^2+(\frac{y}{b_2})^2 \leq 1 \\ 0 & elsewhere \end{array} \right.$

now I want to express the mentioned ellipse function in terms of circ function:

$circ(x,y)=\left\{ \begin{array}{ll} 1, & \mbox{if } (x^2)+(y^2) \leq 1 \\ 0 & elsewhere \end{array} \right.$

Your attention would be much appreciated.

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2 Answers 2

up vote 1 down vote accepted

$$h(x,y)=\frac1{2\pi a^2b^2}\cdot circ(\frac x{a_2},\frac y{b_2})$$

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$$h(x,y)=\frac1{2\pi a^2b^2}\operatorname{circ}\left(\frac x{a_2},\frac y{b_2}\right)$$

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