US007831645B1 (12) United States Patent (10) Patent No.: US 7,831,645 B1 Berners et al. (45) Date of Patent: Nov. 9, 2010 (54) DIGITAL RESONANT SHELF FILTER OTHER PUBLICATIONS (75)75 Inventors: E.id P. s "E. S. R. SEGs) Azizi.Parametric Seyed-Ali. and Graphic “A New Equalizer Concept Banks'.of Interference Audio CompensationEngineering Soc., for Onanan S. ADel, Menlo Park, Convention Paper 5482, Sep. 21-24, 2001, New York, NY. pp. 1-8. (73) Assignee: Kind of Loud Technologies, LLC, Azizi,E.R.E. Seyed-Ali, “A New C t of Interf C tion f Santa Cruz, CA (US) Convention Paper 5629, May 10-13, 2002, Munich, Germany, pp. 1-8. (*) Notice: Subject to any disclaimer, the term of this Berners, David P. et al., “Discrete-Time Shelf Filter Design for patent is extended or adjusted under 35 Analog Modeling”. Audio Engineering Soc., Convention Paper, Oct. U.S.C. 154(b) by 1274 days. 11-13, 2003, New York, NY. pp. 1-5. Blesser, Barry A., et al., “Audio Dynamic Range Compression for (21) Appl. No.: 11/249,162 Minimum Perceived Distortion', IEEE Transactions on Audio and Electroacoustics, vol. AU-17, No. 1, Mar. 1969, pp. 22-32. (22) Filed: Oct. 11, 2005 (Continued) Primary Examiner Tan V Mai Related U.S. Application Data (74) Attorney, Agent, or Firm Pillsbury Winthrop Shaw (60) Provisional application No. 60/617,343, filed on Oct. Pittman LLP 8, 2004. s (57) ABSTRACT (51) Int. Cl. A method and system for designing a discrete-time filter G06 L/00 (2006.01) having a transfer function which approximates that of an G06F 7/10 (2006.01) - 0 52) U.S. C 708/3: 708/300 analog shelf filter is disclosed. Prior art methods include (52) U.Oa - - - - - - - - - - - - O- - A- - - - - - -O - - - - - - - - - - - - - - - - - - - - - - - - - - s apolV1ngpplying the bilib11 near tranSIOrmf to thehe analog filter,filter. Whichwhich hhas (58) Field of Classification Search .....................708/8O1 3OO 708/3, 322 the drawback of warpingrping high-frequencynig quency features of the desired transfer function. In an embodiment of the present See application file for complete search history. invention, an analog filter is designed which anticipates the (56) References Cited warping imposed by the bilinear transform. For filters whose features approach the Nyquist limit, the inventive method U.S. PATENT DOCUMENTS provides a closer approximation to the analog response than 5,287,511 A * 2/1994 Robinson et al. ............ 717/106 direct application of the bilinear transform. 6,581,080 B1* 6/2003 Richards ..................... TO8,320 2004/0042625 A1 3f2004 Brown ........................ 381 (103 20 Claims, 8 Drawing Sheets 301 Sampling rate, f, 3OO analog filter, Ho(s) prewarping bilinear transformation input, r(t) filtering US 7831645 B1 Page 2 OTHER PUBLICATIONS Mapes-Riordan, Dan, “A Worst-Case Analysis for Analog Quality (Alias Free) Digital Dynamics Processing'. J. Audio Eng. Soc., vol. Bohn, Dennis A., “Constant-Q Graphic Equalizers”. Audio Engi 47, No. 11, Nov. 1999, pp. 948-952. neering Soc., Convention Paper 2265-D-15. Oct. 12-16, 1985, New McGrath, David, et al., “Raised Cosine Equalization Utilizing Log York, NY. pp. 1-42. Scale Filter Synthesis'. Audio Engineering Soc., Convention Paper 6257. Oct. 28-31, 2004, San Francisco, CA, pp. 1-16. Deczky, Andrew G., “Unispherical Windows'. IEEE, 2001, pp. Olveira, A.J., “A Feed forward Side Chain Limiter/Compressor/De II-85-II-88. esser with Improved Flexibility”. J. Audio Eng. Soc., vol. 37, No. 4. Floru, Fred, “Attack and Release Time Constraints in RMS-Based Apr. 1999, pp. 226-240. Feedback Compressors”. J. Audio Eng. Soc., vol. 47, No. 10, Oct. Orfanidis, S. J., “Digital Parametric Equalizer Design with Pre 1999, pp. 788-804. scribed Nyquist Frequency Gain'. J. Audio Eng. Soc., vol. 45, No. 6, Kraght, Paul, “Aliasing in Digital Clippers and Compressors'. J. Jun. 1997, pp. 444-455. Audio Eng. Soc., vol. 48, No. 11, Nov. 2000, pp. 1060-1065. Tarczynski, A., et al., “A WISE Method for Designing IIR Filters'. Lang, Mathias C., "Least-Squares Design of IIR Filters with Pre IEEE Trans. On Signal Proc., 2001, vol. 49, No. 7, Jul. 2001, pp. scribed Magnitude and Phase Responses and a Pole Radius Con 1421-1432. straint', IEEE, 2000, pp. 3109-3121. * cited by examiner U.S. Patent Nov. 9, 2010 Sheet 1 of 8 US 7831645 B1 101 Sampling rate,f 105 analog filter,o H(s) 1 OO bilinear transformation input, x(t) 107 H(z) 109 M filtering FG. 1 (PRIOR ART) upSampledO p Samplingpling rate, nfsn: 2O5 2OO analog filter, H(s) bilinear transformation input, x(t) 212 Output, y(t) We 21 O 213 -W- upsampling filtering downsampling FIG. 2 (PRIOR ART) U.S. Patent Nov. 9, 2010 Sheet 2 of 8 US 7831645 B1 3O1 Sampling rate, f, 3O2 305 3OO analog filter, Ho(s) H(s) prewarping bilinear transformation input, x(t) 308 Output, y(t) N A? 307 M filtering FIG. 3 U.S. Patent Nov. 9, 2010 Sheet 3 of 8 US 7,831,645 B1 4. O 1 accept analog filter H0(s), Sampling ratef 4. O 2 select preserved filter features 4 O 3 determine bilinear warping Constant Td 404 fix shelf gain Yi 405 Compute Q1, Op I 406 apply bilinear transform to produce H(z) FIG. 4 U.S. Patent Nov. 9, 2010 Sheet 4 of 8 US 7831645 B1 O III II 504 HH 24. IILM|||||1|| II II -1H III || || || || || || ||108 ||1 frequency - Hz FIG. 5 502 U.S. Patent Nov. 9, 2010 Sheet 5 of 8 US 7831645 B1 HillIIASU - HW1 IAWHE H-1B|ISSM IIIIII III || || ||O FIG. 6 U.S. Patent Nov. 9, 2010 Sheet 6 of 8 US 7831645 B1 *NC) frequency HZ FIG. 7 U.S. Patent Nov. 9, 2010 Sheet 7 of 8 US 7831645 B1 10 frequency - Hz FIG. 8 U.S. Patent Nov. 9, 2010 Sheet 8 of 8 US 7831645 B1 nvention - - - - - Prior Art Analog - 10 1 o' 10 Frequency, Hz FIG. 9 US 7,831,645 B1 1. 2 DIGITAL RESONANT SHIELF FILTER Because of its increased warping at higher frequencies, the bilinear transform is a poor choice for discrete-time modeling CROSS-REFERENCE TO RELATED of filters with features near the Nyquist limit. APPLICATIONS Another prior art approach is to process the input signal at a high sampling rate, as shown in FIG. 2. By using a suffi The present application is based on, and claims priority ciently large oversampling factor, the Nyquist limit may be from, U.S. Provisional Applin. No. 60/617,343, filed Oct. 8, moved much higher than the relevant filter features, and the 2004, commonly owned by the present assignee, the contents warping of those features by the bilinear transform will be of which are incorporated herein by reference. This applica minimized. However, this approach has the drawback of addi tion is also related to commonly-owned and concurrently 10 tional computational cost, and also introduces artifacts due to filed U.S. application Ser. No. 1 1/249,159, the contents the upsampling process. thereof also being incorporated herein by reference. In a prior art method applicable to parametric sections, and described in S. J. Orfanidis, “Digital Parametric Equalizer FIELD OF THE INVENTION Design with Prescribed Nyquist-Frequency Gain”,Journal of 15 the Audio Engineering Society, Vol. 45, no. 6, pp. 444, June This invention pertains to the field of digital signal process 1997, Orfanidis developed formulas which translate filter ing, and in particular to equalization and filtering, especially center frequency, gain and bandwidth into the coefficients of of audio signals. a second-order digital filter having a transfer function which interpolated the levels of the analog parametric filter at DC, BACKGROUND OF THE INVENTION the center frequency, and the Nyquist limit. This approach does not suffer from warping of the frequency axis as do the In the recording, production and playback of audio, one prior art methods based on the bilinear transform, and has the important and widely used tool is equalization, the manipu benefit that it is order preserving, and as Such, the resulting lation of signal level and phase as a function of frequency. filter is efficient to implement. Equalization may be used to correct problems in a recorded 25 No such method is available for analog shelf filters. There signal, for instance to eliminate unwanted resonances in a remains a need in the art, therefore, to develop an efficient, drum track by Suppressing energy in selected frequency order-preserving method for designing a digital filter having bands, or to reduce a singer's lisp by enhancing certain high a transfer function which approximates that of an analog shelf frequencies. Equalization is also often used for artistic pur filter. poses to give each instrument its own space in the audio band, 30 or to create a certain feel—different genres of music, for instance, typically have different characteristic power spec SUMMARY OF THE INVENTION tra. A method and system for designing a discrete-time filter In mixing and mastering, probably the most commonly having a transfer function which approximates that of an used equalizers are parametric sections and shelf filters. Para 35 analog shelf filter is disclosed. According to one aspect of the metric sections enhance or suppress a selected band of fre present invention, an intermediate analog filter is designed quencies, whereas shelf filters apply again to all frequencies which anticipates the warping imposed by the bilinear trans either above or below a prescribed frequency. Both first-order form. When the bilinear transform is applied to the interme and second-order shelf filters are used, with the second-order diate analog filter, a discrete-time filter is obtained that more or so-called resonant shelf filters sometimes having a reso 40 nant peak on one side or the other of the transition between its closely matches the desired characteristics of the analog filter low-frequency and high-frequency gains.