Implementing IIR/FIR Filters

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Filter Type Low Pass Analog Filter Type Butterworth Passband Ripple In -dB -.5000 Stopband Ripple In -dB -20.0000 Passband Cutoff Frequency 200.000 Hertz Stopband Cutoff Frequency 300.000 Hertz Sampling Frequency 1000.00 Hertz Filter Order: 6 Filter Design Method: Bilinear Transformation Coefficients of Hd(z) are Quantized to 24 bits Quantization Type: Fixed Point Fractional Coefficients Scaled For Cascade Form II NORMALIZED ANALOG TRANSFER FUNCTION T(s) Numerator Coefficients Denominator Coefficients ***************************************** ********************************** S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM .000000E+00 .000000E+00 .100000E+01 .100000E+01.193185E+01 .100000E+01 .000000E+00 .000000E+00 .100000E+01 .100000E+01.141421E+01 .100000E+01 .000000E+00 .000000E+00 .100000E+01 .100000E+01.517638E+01 .100000E+01 INITIAL GAIN 1.00000000 UNNORMALIZED ANALOG TRANSFER FUNCTION T(s) Numerator Coefficients Denominator Coefficients ***************************************** ********************************** S**2 TERM S TERM CONST TERM S**2 TERM S TERM CONST TERM .000000E+00 .000000E+00 .299809E+07 .100000E+01.334500E+04 .299809E+07 .000000E+00 .000000E+00 .299809E+07 .100000E+01.244871E+04 .299809E+07 .000000E+00 .000000E+00 .299809E+07 .100000E+01.896290E+03 .299809E+07 INITIAL GAIN 1.00000000 DIGITAL TRANSFER FUNCTION Hd(z) Numerator Coefficients Denominator Coefficients ***************************************** ********************************** Z**2 Z TERM CONST TERM Z**2 Z TERM CONST TERM .2520353794 .5040707588 .252035379 1.00000 -.1463916302 .0225079060 .2364231348 .4728463888 .236423134 1.00000 -.1684520245 .1765935421 .3606387377 .7212774754 .360638737 1.00000 -.2279487848 .5921629667 INITIAL GAIN .876116210 Figure 6-10 FDAS.OUT File of Example Filter for Cascaded Canonic Implementation (sheet 1 of 2) MOTOROLA 6-7
ZEROES OF TRANSFER FUNCTION Hd(z) Real Part Imaginary Part Real Part Imaginary Part Radius -.100000000E+01 .00000000E+00 -.100000000E+01 .00000000E+00 .100000000E+01 -.999290168E+00 .00000000E+00 -.100071034E+01 .00000000E+00 .999290168E+00 -.100000000E+01 .00000000E+00 -.100000000E+01 .00000000E+00 .100000000E+01 POLES OF TRANSFER FUNCTION Hd(z) Real Part Imaginary Part Real Part Imaginary Part Radius .731958151E-01 .130959072E+00 .731958151E-01 -.130959072E+00 .150026351E+00 .842260122E-01 .411703195E+00 .842260122E-01 -.411703195E+00 .420230344E+00 .113974392E+00 .761034036E+00 .113974392E+00 -.761034036E+00 .769521258E+00 NUMERATOR COEFFICIENTS - HIGHEST ORDER <strong>FIR</strong>ST (in z) .214893785E-01 .128936282E+00 .322340720E+00 .429787634E+00 .322340720E+00 .128936282E+00 .214893785E-01 DENOMINATOR COEFFICIENTS - HIGHEST ORDER <strong>FIR</strong>ST (in z) .100000000E+01 -.542792439E+00 .887692610E+00 .267088214E+00 .143235132E+0 -.184597152E-01 .235370025E-02 IMPULSE RESPONSE MIN = -.179722E+00, MAX = .452734E+00 Figure 6-5 FDAS.OUT File of Example Filter for Cascaded Canonic Implementation (sheet 2 of 2) 6-8 MOTOROLA
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Motorola’s High-Performance DSP T
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© Motorola Inc. 1993 Motorola rese
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SECTION 6 Filter Design and Analysi
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Figure 2-3 Figure 2-4 Figure 2-5 Fi
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Figure 4-4 Figure 4-5 Figure 5-1 Fi
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Figure 7-9 Figure 7-10 Figure 7-11
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equivalent functions in the digital
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is taken to calculating the filter
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solving the differential equation i
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Gain Phase 1.5 1.0 0.5 0 -π/2 -π
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1.3 Analog Highpass Filter The pass
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Gain Phase 1.5 1.0 0.5 π π/2 0 0
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V 0 R ----- = ---------------------
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V 0 R ----- = ---------------------
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1-18 MOTOROLA
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In the digital domain, the continuo
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One mapping or transformation from
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Although this transformation was de
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property in particular as follows:
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Figure 2-10 are similar to the anal
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case but also in the code for the h
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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
Page 75 and 76: Gain Gain Gain 1.2 1.0 0.8 0.6 0.4
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 /
Page 85 and 86: pass Butterworth filter (three seco
Page 87 and 88: Network Diagram x(n) α1 z -1 z -1
Page 91 and 92: can be assembled by the DSP56001 as
Page 93 and 94: Phase (Radians) π π/2 0 -π/2 -π
Page 95: Seconds 6.3 E-03 4.7 E-03 3.1 E-03
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
Page 113 and 114: 7.19 Linear-Phase FIR Filter Struct
Page 115 and 116: G( θ) hi ()e jiθ - N- 1 = i = 0 E
Page 117 and 118: ut is twice the width of the origin
Page 119 and 120: Therefore, a nonrecursive filter (F
Page 121 and 122: sides of by e j2πkm/N and summing
Page 123 and 124: hi () 1 j πr πkN 1 --- Ak ( )e N
Page 125 and 126: given with AN ( ⁄ 2) = 0 and r= 1
Page 127 and 128: Likewise, the y component (imaginar
Page 129 and 130: h(n) 0.2 0.1 0 -0.1 0 16 31 Figure
Page 131 and 132: The continuous frequency gain and p
Page 133 and 134: Filter Gain, G(θ), (dB) Filter Gai
Page 135 and 136: 7-24 MOTOROLA Figure 7-40 FDAS Outp
Page 137 and 138: If it is assumed that linear phase
Page 139 and 140: Reference 5). Basically, a guess is
Page 141 and 142: Figure 7-41 shows an example of an
Page 143 and 144: R0 x(n) b 0 X:(R0) x(n) x(n-1) x(n-
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16. McClellan, J. H. and T. W. Park
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Implementing IIR/FIR Filters

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