Implementing IIR/FIR Filters

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Figure 6-5 Figure 6-6 Figure 6-7 Figure 6-8 Figure 6-9 Figure 6-10 Figure 7-1 Figure 7-2 Figure 7-3 Figure 7-4 Figure 7-5 Figure 7-6 Figure 7-7 Figure 7-8 Illustrations FDAS.OUT File of Example Filter for Cascaded Canonic Implementation 6-7 COEFF.OUT File of Example Filter Design – Scaled for Cascaded Canonic Implementation 6-9 COEFF.ASM File Generated by MGEN for Example Design and Cascaded Canonic Implementation 6-10 FDAS.OUT File of Example Filter for Cascaded Transpose – Form Implementation 6-15 COEFF.FLT File for Example Filer Design – Scaled for Cascaded Transpose Form 6-17 COEFF.ASM File Generated by MGEN for Example Design and Cascaded Transpose – Form Implementation 6-18 FIR Structure 7-3 Signal Data through a FIR Filter 7-5 Arbitrary Filter Example 7-14 Response Transformed from Polar Coordinates 7-16 FIR Coefficients from Eqn. 7-2 for Filter Example 7-17 Roots (Zeros) of Eqn. 7-21 for Filter Example 7-17 A 32-Point FIR Filter Example 7-18 Log Magnitude Response of Filter Example with Larger N Values 7-20 MOTOROLA ix
Figure 7-9 Figure 7-10 Figure 7-11 Figure 7-12 Illustrations Window Function Effects on Filter Example 7- 21 FDAS Output for FIR Bandpass Filter Example with a Kaiser Window 7-23 FDAS Output for FIR Bandpass Filter Example with Equiripple Design 7-28 FIR Filter Example 7-31 x MOTOROLA
Page 1 and 2: Motorola’s High-Performance DSP T
Page 3 and 4: © Motorola Inc. 1993 Motorola rese
Page 5 and 6: SECTION 6 Filter Design and Analysi
Page 7 and 8: Figure 2-3 Figure 2-4 Figure 2-5 Fi
Page 9: Figure 4-4 Figure 4-5 Figure 5-1 Fi
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
Page 59 and 60: x(n) b 0 + + Figure 3-24 The Second
Page 61 and 62:
The last step uses the definition f
Page 63 and 64:
where: θ p is the angle (see Figur
Page 65 and 66:
Since this result does not depend o
Page 67 and 68:
MPY MAC MACR MAC MACR Difference Eq
Page 69 and 70:
3-12 MOTOROLA
Page 71 and 72:
expression for the maximum gain at
Page 73 and 74:
GAIN AT INTERNAL NODE, u(n) Transfe
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Gain Gain Gain 1.2 1.0 0.8 0.6 0.4
Page 77 and 78:
4-8 MOTOROLA
Page 79 and 80:
Hs ( ) damping factors, dk, of each
Page 81 and 82:
Using , Eqn. 5-7 becomes: Hs ( ) N/
Page 83 and 84:
α k = β k = γ k = tan 2 ( θ c /
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pass Butterworth filter (three seco
Page 87 and 88:
Network Diagram x(n) α1 z -1 z -1
Page 89 and 90:
5-12 MOTOROLA
Page 91 and 92:
can be assembled by the DSP56001 as
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Phase (Radians) π π/2 0 -π/2 -π
Page 95 and 96:
Seconds 6.3 E-03 4.7 E-03 3.1 E-03
Page 97 and 98:
ZEROES OF TRANSFER FUNCTION Hd(z) R
Page 99 and 100:
1 COEFF ident 1,0 2 include 'head2.
Page 101 and 102:
77 P:0000 0C0040 jmp start ;jump to
Page 103 and 104:
6.2 Transpose Implementation (Direc
Page 105 and 106:
POLES OF TRANSFER FUNCTION Hd(z) Re
Page 107 and 108:
1 C0EFF ident 1,0 2 include 'head1.
Page 109 and 110:
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
Page 127 and 128:
Likewise, the y component (imaginar
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h(n) 0.2 0.1 0 -0.1 0 16 31 Figure
Page 131 and 132:
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
Page 147:
16. McClellan, J. H. and T. W. Park
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Implementing IIR/FIR Filters

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