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数字信号处理英文课件Chapter8.pdf

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Chapter8:FIRFilterDesignTechniques CHAPTER8FIRFILTERDESIGN1IdealFrequency-SelectiveFilters TECHNIQUES()ω() •LetHdjandhdnbethefrequencyandimpulseresponses, respectively,ofadesired(ideal)filter. •TheyarerelatedbytheFouriertransform: •Thischaptercoversthefollowing. ∞ ()ω()–jωn Hdj=∑hdne(2.1) 1.IdealFrequencySelectiveFilters............................................2n=–∞ 2.DesignofFIRFiltersUsingWindows....................................6π ()1()ωjωnω 3.FrequencySamplingMethod.................................................22hdn=------π∫Hdjed(2.2) 2–π 4.OptimalFIRFilterDesign......................................................26 ()ω •SinceHdjisperiodic,Eq.(2.1)isaFourierseries. 5.DifferentiatorsandHilbertTransformers...............................40 •Therefore,h()nrepresentstheFouriercoefficients. 6.DesignofFIRfiltersusingMatlab.........................................47d A.Bouzerdoum Page2of52 Chapter8:FIRFilterDesignTechniquesChapter8:FIRFilterDesignTechniques ◆Ideal-LowPassFilter◆IdealFilterCharacteristics ,ωω≤ ⎧1c H()jω=⎨H()jωH()jω d,ω<ωπ≤dd ⎩0c ω11 cjωn–jωnω 1ec–ecsincnωω h()n===------∫ejωndω-------------------------------------------------- d2πj2πnπnπωωππωωπ ω–––– –ccccc IdealLowpassIdealHighpass ()ω 1Hdj ω ()ωH()jω πωωπHdjd ––cc 1 ()–ππ hdnωω ωωωωπωωωωπ –2–112––2–112 n 0IdealBandpassIdealBandstop A.BouzerdoumA.Bouzerdoum Page3of52Page4of52 Chapter8:FIRFilterDesignTechniquesChapter8:FIRFilterDesignTechniques ◆CharacteristicsofIdealFilters2DesignofFIRFiltersUsingWindows •Thesimplestwaytoobtainalinear-phaseFIRfilteristotruncatethe Filter FrequencyResponseImpulseResponseh()0 Typedimpulseresponseofanidealfilter. N ⎧1,ωω≤ωω1 Lowcsincnc()ω≈()ω()–jωn H()jω=⎨h()n=-----------------------HdjHj=∑hdne(2.3) passd⎩0,ω<ωπ≤dπnπ cnN=–1 ,ω≤≤ωπ()≤≤ ⎧1csinωnω⎧hdn,if–N1nN1 HighH()jω=⎨()δ()cchn()⎨(2.4) passd,ωω<hdn=1n–-----------------π–------π= ⎩0cn⎩0,otherwise ,ω≤≤ωωωωωω()()⋅() Band⎧112sin2n–sin1n2–hn=hdnwn(2.5) H()jω=⎨h()n=----------------------------------------------