## 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.*,

To convert these analog-filter transfer functions to digital form, we apply the bilinear transform:

^{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