## Low and High Shelving Filters

The analog transfer function for a*low shelf*is given by [103]

*transition frequency*dividing low and high frequency regions is . See Appendix E for a development of -plane analysis of analog (continuous-time) filters. A

*high shelf*is obtained from a low shelf by the conformal mapping , which interchanges high and low frequencies,

*i.e.*,

^{B.5}Low and high shelf filters are typically implemented in series, and are typically used to give a little boost or cut at the extreme low or high end (of the spectrum), respectively. To provide a boost or cut near other frequencies, it is necessary to go to (at least) a second-order section, often called a ``peaking equalizer,'' as described in §B.5 below.

#### Exercise

Perform the bilinear transform defined above and calculate the coefficients of a first-order*digital*low shelving filter. Find the pole and zero as a function of , , and . Set and verify that you get a gain of . Set and verify that you get a gain of 1 there.

**Next Section:**

Peaking Equalizers

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DC Blocker