基于CSR8670的高精度IIR滤波器实现
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摘要
讨论了定点IIR滤波器在CSR8670平台上的高精度实现问题。定点DSP芯片由于低成本和低功耗等原因被广泛应用于消费类电子产品。IIR滤波器作为基本的信号处理模块,被广泛应用于各类数字信号处理芯片中。然而由于定点芯片字长有限,导致定点IIR滤波器的运算精度严重下降。本文从零极点分布及幅频响应的角度分析了定点IIR滤波器实现过程中存在的问题。为提高运算精度,提出一种双精度乘法,即利用24位乘法器实现48×48位乘法运算,仿真实验表明该方法可将计算精度提高4个数量级。
The problem of realization of high precision fixed-point IIR filter based on CSR8670 chip is discussed. Fixed-point DSP chips have been extensively used in consumer electronics products because of their low cost and low power consumption. IIR filter is widely used in various DSP chips as a fundamental signal processing module. However, the computation precision of fixed-point IIR filter decreases badly because of the limited word length of chips. The problem of decreased precision of fixed-point IIR filter is analyzed in terms of pole-zero positions and the amplitude frequency response. To improve the computation precision, this paper presents a double-precision method that 48×48-bit multiplication is realized with 24-bit multipliers, and experiments verify that the computation precision is improved by four orders of magnitude with the proposed method.
The problem of realization of high precision fixed-point IIR filter based on CSR8670 chip is discussed. Fixed-point DSP chips have been extensively used in consumer electronics products because of their low cost and low power consumption. IIR filter is widely used in various DSP chips as a fundamental signal processing module. However, the computation precision of fixed-point IIR filter decreases badly because of the limited word length of chips. The problem of decreased precision of fixed-point IIR filter is analyzed in terms of pole-zero positions and the amplitude frequency response. To improve the computation precision, this paper presents a double-precision method that 48×48-bit multiplication is realized with 24-bit multipliers, and experiments verify that the computation precision is improved by four orders of magnitude with the proposed method.
引文
[1] 刘卯国.DSP芯片技术及应用[M].北京:国防工业出版社,2007.7-8.
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[4] Barrett P.Implementing theRivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor[C]//Conference on the Theory and Application of Cryptographic Techniques.Springer Berlin Heidelberg,1986:311-323.
[5] Sloss A,Symes D,Wright C.ARM system developer’s guide:designing and optimizing system software[M].California,US:Morgan Kaufmann,2004.208-212.
[6] Brent R P.Fast multiple-precision evaluation of elementaryfunctions[J].Journal of the ACM (JACM),1976,23(2):242-251.
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[8] Shand M,Bertin P,Vuillemin J.Hardware speedups in long integer multiplication[J].ACM SIGARCH Computer Architecture News,1991,19(1):106-113.
[9] Hutter M,Wenger E.Fast multi-precision multiplication for public-key cryptography on embedded microprocessors[C]//International Workshop on Cryptographic Hardware and Embedded Systems.Springer Berlin Heidelberg,2011:459-474.
[10] Chang B C,Goi B M,Phan R C W,et al.Accelerating Multiple Precision Multiplication in GPU with Kepler Architecture[C]//High Performance Computing and Communications;IEEE 14th International Conference on Smart City;IEEE 2nd International Conference on Data Science and Systems (HPCC/SmartCity/DSS).IEEE,2016:844-851.
[11] 马旭.超高精度计算程序设计实例[J].计算机工程与应用,2017,53(14):51-55.
[12] 蒋松奇.基于CSR8670的蓝牙耳机设计与实现[D].南京:东南大学,2015.
[13] 张雄伟,邹霞,贾冲.DSP芯片原理与应用[M].北京:机械工业出版社,2005.12.
[14] 郑君里,应启珩,杨为理.信号与系统下册[M].第二版.北京:高等教育出版社,2000.220-223.
[15] Lang M C.Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radiusconstraint[J].IEEE Transactions on Signal Processing,2000,48(11):3109-3121.
[16] Menezes A J,VanOorschot P C,Vanstone S A.Handbook of applied cryptography[M].CRC press,1996.592-596.
[2] 马建仓,罗亚军,赵玉亭.蓝牙核心技术及应用[M].北京:科学出版社,2003.468-472.
[3] 程佩青.数字信号处理教程[M].第二版.北京:清华大学出版社,2001.387-388.
[4] Barrett P.Implementing theRivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor[C]//Conference on the Theory and Application of Cryptographic Techniques.Springer Berlin Heidelberg,1986:311-323.
[5] Sloss A,Symes D,Wright C.ARM system developer’s guide:designing and optimizing system software[M].California,US:Morgan Kaufmann,2004.208-212.
[6] Brent R P.Fast multiple-precision evaluation of elementaryfunctions[J].Journal of the ACM (JACM),1976,23(2):242-251.
[7] Brent R P.A Fortran multiple-precision arithmeticpackage[J].ACM Transactions on Mathematical Software (TOMS),1978,4(1):57-70.
[8] Shand M,Bertin P,Vuillemin J.Hardware speedups in long integer multiplication[J].ACM SIGARCH Computer Architecture News,1991,19(1):106-113.
[9] Hutter M,Wenger E.Fast multi-precision multiplication for public-key cryptography on embedded microprocessors[C]//International Workshop on Cryptographic Hardware and Embedded Systems.Springer Berlin Heidelberg,2011:459-474.
[10] Chang B C,Goi B M,Phan R C W,et al.Accelerating Multiple Precision Multiplication in GPU with Kepler Architecture[C]//High Performance Computing and Communications;IEEE 14th International Conference on Smart City;IEEE 2nd International Conference on Data Science and Systems (HPCC/SmartCity/DSS).IEEE,2016:844-851.
[11] 马旭.超高精度计算程序设计实例[J].计算机工程与应用,2017,53(14):51-55.
[12] 蒋松奇.基于CSR8670的蓝牙耳机设计与实现[D].南京:东南大学,2015.
[13] 张雄伟,邹霞,贾冲.DSP芯片原理与应用[M].北京:机械工业出版社,2005.12.
[14] 郑君里,应启珩,杨为理.信号与系统下册[M].第二版.北京:高等教育出版社,2000.220-223.
[15] Lang M C.Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radiusconstraint[J].IEEE Transactions on Signal Processing,2000,48(11):3109-3121.
[16] Menezes A J,VanOorschot P C,Vanstone S A.Handbook of applied cryptography[M].CRC press,1996.592-596.