Graphic Equalizer and Resonant Shelf Filter Design
This week's DSP Seminar is another double bill: Dave and I will review a couple filter design methods first presented a few years back at ICMC and AES. The first method is a graphic equalizer which interpolates prescribed band gains, and the second method produces resonant shelf filters closely matching the transfer function magnitudes of their analog counterparts. Abstracts follow. We will meet in the classroom at 2:15 PM.
Filter Design Using Second-Order Peaking and Shelving Sections
Jonathan S. Abel and David P. Berners
A method for designing audio ﬁlters is developed based on the observation that second-order peaking and shelving filters can be made nearly self-similar on a log magnitude scale with respect to peak and shelf gain changes. By cascading such second-order sections, ﬁlters are formed which may be ﬁt to dB magnitude characteristics via linear least-squares techniques. A graphic equalizer interpolating prescribed band gains is presented, along with a ﬁlter minimizing the Bark-weighted mean square dB difference between modeled and desired transfer function magnitudes. It is noted that using second-order sections parameterized by transition frequency and gain provides a natural mechanism for slewing and interpolation between tabulated designs.
Discrete-Time Shelf Filter Design for Analog Modeling
David P. Berners and Jonathan S. Abel
A method for the design of discrete-time second-order shelf filters is developed which allows the response of an analog shelf filter to be approximated in the digital domain. For filters whose features approach the Nyquist limit, the proposed method provides a closer approximation to the analog response than direct application of the bilinear transform. Three types of resonant shelf filter are discussed, and design examples are presented.