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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

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

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