UGC NET CSE | December 2014 | Part 3 | Question: 66

Question

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

• A. $\frac{1}{1+\left[\frac{D(u, v)}{D_{0}}\right]^{2n}}$
• B. $\frac{1}{1+\left[\frac{D(u, v)}{D_{0}}\right]^{n}}$
• C. $\frac{1}{1+\left[\frac{D_{0}}{D(u, v)}\right]^{2n}}$
• D. $\frac{1}{1+\left[\frac{D_{0}}{D(u, v)}\right]^{n}}$

Answer 1

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

^{so ans will be A}