Washington University School of Engineering and Applied Science Power Consumption of Customized Numerical Representations for Audio Signal Processing Roger Chamberlain, Yen Hsiang Chew, Varuna DeAlwis, Eric Hemmeter,John Lockwood, Robert Morley, Ed Richter, Jason White, and Huakai Zhang This research is supported by the NIH under grant 1R4-3DC04028-02. HPEC 2002 1
Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 24 SEP 2002 2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Power Consumption of Customized Numerical Representations for Audio Signal Processing 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Washington University School of Engineering and Applied Science 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release, distribution unlimited 13. SUPPLEMENTARY NOTES Also see ADM001473, The original document contains color images. 14. ABSTRACT 15. SUBJECT TERMS 11. SPONSOR/MONITOR S REPORT NUMBER(S) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified 18. NUMBER OF PAGES 21 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
Outline Audio Signal Requirements Customized Numerical Representations SNR and Dynamic Range Design of Computation Structures Power Consumption Results Summary and Conclusions HPEC 2002 2
Audio Signal Applications Music MP3 players Speech communications equipment hearing aids (our target application) Signal requirements to understand speech ~30 db SNR over entire dynamic range ~100 db dynamic range Power consumption critical for all of above HPEC 2002 3
Customized Numerical Representations 16-bit integer is traditional for audio 90 db dynamic range, SNR from 0 to 90 db Logarithmic representation more closely mimics human perception Loudness response is highly non-linear SNR is relatively constant across dynamic range Floating point representations are partially logarithmic and partially linear 32-bit IEEE standard is more than is needed Tailor choice for number of bits in exponent and mantissa to needs of application HPEC 2002 4
SNR and Dynamic Range SNR (db) = 20 log 10 2 V i V + 1 i 2 V 12 i Dynamic Range (db) = 20 log 10 V V max min HPEC 2002 5
16-bit Integer SNR SNR (db) 100 90 80 70 60 50 40 30 20 10 0 0.00001 0.0001 0.001 0.01 0.1 1 Input Value (Vi) HPEC 2002 6
9-bit Logarithmic SNR 60 50 40 SNR (db) 30 20 10 0 1E-07 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 Input Value (Vi) HPEC 2002 7
Floating Point SNR 5-bit exponent 4, 5, and 6-bit mantissa SNR (db) 60 50 40 30 20 10 0 1E-10 0.00000001 0.000001 0.0001 0.01 1 Input Value (Vi) FP 5-6 FP 5-5 FP 5-4 HPEC 2002 8
400 6-bit exp. Dynamic Range 350 300 Range (db) 250 200 150 100 5-bit exp. log. 4-bit exp. int. 50 0 6-6 FP 6-5 FP 6-4 FP 5-6 FP 5-5 FP 5-4 FP 9-bit Log 4-6 FP 4-5 FP 4-4 FP 16-bit Integer Representation HPEC 2002 9
Hearing Aid Architecture Most of the computations the hearing aid performs are multiply-accumulates. HPEC 2002 10
Floating Point MAC Design Traditional structure for floating point hardware computations Perl script generates synthesizable VHDL code for specific exponent and mantissa size Small size of mantissa implies lower power multiplier hardware HPEC 2002 11
Floating Point MAC Xi_j/Cj(4 downto 0) Yi(4 downto 0) Xi_j Mant * Mant Normalize Shifter Acc Mant S Mant Normalize Register Yi Cj Xi_j/Cj(9 downto 5) Exp + Exp Normalize Exp Sub Yi(10) Exp Normalize Yi(9 downto 5) S Xi_j/Cj(10) S Clk Latch Enable HPEC 2002 12 Reset
Logarithmic MAC Design Multiply function provided by an adder: log( A B) = log( A) + log( B) Addition function exploits the following relationship: log ( A + B) = log( A) + log 1+ Last term implemented via a lookup table B A HPEC 2002 13
9-bit Logarithmic MAC Xi_j Cj Xi_j/Cj(8 downto 0) * Multiplied Result Look-up Table Add Result or Pass-through Register Yi Xi_j/Cj (9) s s Comparator Clk Latch Reset Enable HPEC 2002 14
Verification Via FPX Platform Audio Data FPX Fieldprogrammable Port Extender Audio Data HPEC 2002 15
FPX Platform HPEC 2002 16
Layout AMI 0.5 ìm process ADK library from Mentor Graphics HEP 5-5 floating point MAC is shown HPEC 2002 17
Power Estimation via Simulation Simulate using Mentor Graphics MACH-PA Spice-level simulation tool Driven by extracted layout Focus on Multiply-Accumulate units Random input vectors Simulation provides current usage P = IV provides power results HPEC 2002 18
Power Consumption Average Power (mw) 80 60 40 20 0 70.5 16-bit Integer 10.9 9.6 10.15 8.5 2.7 1-5-5 1-5-4 1-4-5 1-4-4 9-bit Log Numerical Representation HPEC 2002 19
Summary and Conclusions Customizing a numerical representation to the specific needs of an application can have tangible benefits Several 9 or 10-bit representations have improved SNR and dynamic range for audio speech applications relative to traditional 16- bit integers Both customized floating point and logarithmic representations have been considered Power savings are significant HPEC 2002 20
For Further Information http://www.ccrc.wustl.edu/hearingaid or hearingaid@ccrc.wustl.edu HPEC 2002 21