Implementing IIR/FIR Filters

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SECTION 1 Introduction SECTION 2 Second-Order Direct-Form IIR Digital Filter Sections SECTION 3 Single-Section Canonic Form (Direct Form II) SECTION 4 Single-Section Transpose Form SECTION 5 Cascaded Direct Form Table of Contents 1.1 Analog RCL Filter Types 1-4 1.2 Analog Lowpass Filter 1-5 1.3 Analog Highpass Filter 1-9 1.4 Analog Bandstop Filter 1-9 1.5 Analog Bandpass Filter 1-12 2.1 Digital Lowpass Filter 2-9 2.2 Digital Highpass Filter 2-11 2.3 Digital Bandstop Filter 2-18 2.4 Digital Bandpass Filter 2-18 2.5 Summary of Digital Coefficients 2-22 3.1 The Canonic-Form Difference Equation 3-1 3.2 Analysis of Internal Node Gain 3-5 3.3 Implementation on the DSP56001 3-10 4.1 Gain Evaluation of Internal Nodes 4-1 4.2 Implementation on the DSP56001 4-2 5.1 Butterworth Lowpass Filter 5-1 5.2 Cascaded Direct-Form Network 5-9 MOTOROLA iii
SECTION 6 Filter Design and Analysis System SECTION 7 FIR FILTERS Table of Contents 6.1 Canonic Implementation 6-2 6.2 Transpose Implementation (Direct Form I) 6-14 7.1 Linear-Phase FIR Filter Structure 7-2 7.2 Linear-Phase FIR Filter Design Using the Frequency Sampling Method 7-8 7.3 FIR Filter Design Using FDAS 7-22 7.4 FIR Implementation on the DSP56001 7-29 REFERENCES Reference-1 iv MOTOROLA
Page 1 and 2: Motorola’s High-Performance DSP T
Page 3: © Motorola Inc. 1993 Motorola rese
Page 7 and 8: Figure 2-3 Figure 2-4 Figure 2-5 Fi
Page 9 and 10: Figure 4-4 Figure 4-5 Figure 5-1 Fi
Page 11 and 12: Figure 7-9 Figure 7-10 Figure 7-11
Page 13 and 14: equivalent functions in the digital
Page 15 and 16: is taken to calculating the filter
Page 17 and 18: solving the differential equation i
Page 19 and 20: Gain Phase 1.5 1.0 0.5 0 -π/2 -π
Page 21 and 22: 1.3 Analog Highpass Filter The pass
Page 23 and 24: Gain Phase 1.5 1.0 0.5 π π/2 0 0
Page 25 and 26: V 0 R ----- = ---------------------
Page 27 and 28: V 0 R ----- = ---------------------
Page 29 and 30: 1-18 MOTOROLA
Page 31 and 32: In the digital domain, the continuo
Page 33 and 34: One mapping or transformation from
Page 35 and 36: Although this transformation was de
Page 37 and 38: property in particular as follows:
Page 39 and 40: Figure 2-10 are similar to the anal
Page 41 and 42: case but also in the code for the h
Page 43 and 44: Lowpass Gain Lowpass Phase 1.5 1.0
Page 45 and 46: Network Diagram Transfer Function G
Page 47 and 48: MPY MAC MAC MAC MAC Difference Equa
Page 49 and 50: Network Diagram x(n) Transfer Funct
Page 51 and 52: BANDSTOP GAIN BANDSTOP PHASE 1.5 1.
Page 53 and 54: Network Diagram x(n) Transfer Funct
Page 55 and 56:
BANDPASS GAIN BANDPASS PHASE 1.5 1.
Page 57 and 58:
Pole Equation of H(z) Zp = rcosθp
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x(n) b 0 + + Figure 3-24 The Second
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The last step uses the definition f
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where: θ p is the angle (see Figur
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Since this result does not depend o
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MPY MAC MACR MAC MACR Difference Eq
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3-12 MOTOROLA
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expression for the maximum gain at
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GAIN AT INTERNAL NODE, u(n) Transfe
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Gain Gain Gain 1.2 1.0 0.8 0.6 0.4
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4-8 MOTOROLA
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Hs ( ) damping factors, dk, of each
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Using , Eqn. 5-7 becomes: Hs ( ) N/
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α k = β k = γ k = tan 2 ( θ c /
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pass Butterworth filter (three seco
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Network Diagram x(n) α1 z -1 z -1
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5-12 MOTOROLA
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can be assembled by the DSP56001 as
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Phase (Radians) π π/2 0 -π/2 -π
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Seconds 6.3 E-03 4.7 E-03 3.1 E-03
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ZEROES OF TRANSFER FUNCTION Hd(z) R
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1 COEFF ident 1,0 2 include 'head2.
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77 P:0000 0C0040 jmp start ;jump to
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6.2 Transpose Implementation (Direc
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POLES OF TRANSFER FUNCTION Hd(z) Re
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1 C0EFF ident 1,0 2 include 'head1.
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75 76 P:0040 0003F8 ori #3,mr ;disa
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6-22 MOTOROLA
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7.19 Linear-Phase FIR Filter Struct
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G( θ) hi ()e jiθ - N- 1 = i = 0 E
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ut is twice the width of the origin
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Therefore, a nonrecursive filter (F
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sides of by e j2πkm/N and summing
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hi () 1 j πr πkN 1 --- Ak ( )e N
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given with AN ( ⁄ 2) = 0 and r= 1
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Likewise, the y component (imaginar
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h(n) 0.2 0.1 0 -0.1 0 16 31 Figure
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The continuous frequency gain and p
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Filter Gain, G(θ), (dB) Filter Gai
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7-24 MOTOROLA Figure 7-40 FDAS Outp
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If it is assumed that linear phase
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Reference 5). Basically, a guess is
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Figure 7-41 shows an example of an
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R0 x(n) b 0 X:(R0) x(n) x(n-1) x(n-
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7-34 MOTOROLA
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16. McClellan, J. H. and T. W. Park
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Implementing IIR/FIR Filters

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