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A Butterworth lowpass filter of order $n$, with a cutoff frequency at distance $D_{0}$ from the origin, has the transfer function $H(u, v)$ given by

1. $\frac{1}{1+\left[\frac{D(u, v)}{D_{0}}\right]^{2n}}$
2. $\frac{1}{1+\left[\frac{D(u, v)}{D_{0}}\right]^{n}}$
3. $\frac{1}{1+\left[\frac{D_{0}}{D(u, v)}\right]^{2n}}$
4. $\frac{1}{1+\left[\frac{D_{0}}{D(u, v)}\right]^{n}}$

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The transfer function of a Butterworth lowpass filter of order n with cutoff frequency

at distance D0 from the origin is defined as:

H(u,v) =  1/1+(D(u,v)/D0)2n