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1、Chapter13Solutions13.1TheADSP-2181uses16bitsforbothsignedandunsignedformats.(a)0000100110110011(b)0000100110110011Forpositiveintegers,thereisnodifferencebetweenthesignedandunsignedformats.13.2(a)(i)The1.15representationisgivenbytruncate(0.93207x215+0.5)=3054210=0x774E=01110111010011102.(
2、ii)The6.10representationisgivenbytruncate(0.93207x210+0.5)=95410=0x03BA=00000011101110102.(iii)The12.4representationisgivenbytruncate(0.93207x24+0.5)=1510=0x000F=00000000000011112.(b)(i)Thequantizedvalueis0.93206787109375,foraquantizationerrorof–0.00000212890625.(ii)Thequantizedvalueis0.
3、931640625,foranerrorof–0.000429375.(iii)Thequantizedvalueis0.9375,givingaquantizationerrorof0.00543.13.3(a)Thelargestvalueis011111.11111111112,or31.9990234375,andthesmallestvalueis100000.0000000000,or–32,sotherangeis63.9990234375.Thesmallestresolvabledifferenceis2–10.Thus,thedynamicrange
4、is20log(fullscalerange/smallestresolvabledifference)=96.33dB.(b)Thelargestvalueis011111111111.11112,or2047.9375,andthesmallestvalueis100000000000.0000,or–2048,sotherangeis4095.9375.Thesmallestresolvabledifferenceis2–4.Thus,thedynamicrangeis20log(fullscalerange/smallestresolvabledifferenc
5、e)=96.33dB.(c)Thelargestvalueis01111111111111112,or32767,andthesmallestvalueis1000000000000000,or–32768,sotherangeis65535.Thesmallestresolvabledifferenceis1.Thus,thedynamicrangeis20log(fullscalerange/smallestresolvabledifference)=96.33dB.Notethatallthreefixedpointformatshavethesamedynami
6、crange.13.4(a)In1.3format,0.61310=0.1012.Therefore,thequantizedvalueis0.625.In2.2format,1.8510=01.112,sothequantizedvalueis1.75.(b)Theproductofthequantizednumbersis(0.625)(1.75)=1.0937510=01.00011000000000.Aminimum2.5formatisneededtorepresentthisproductexactly.Notethataformat1.3numbermul
7、tipliedbya2.2numberwillgiveatworstanumberin(1+2).(3+2)=3.5format.(c)Thetrueproductis(0.613)(1.85)=1.13405,0.0403(or3.55%)greaterthanthequantizedproduct.13.5Thecoefficientsforthefilterare[5,1,5].Touse1.15format,thecoefficientsmustbescaleddownbyafactorof8,or23,whichgivessca
