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XAPIIR.f
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1256 lines (1248 loc) · 93.1 KB
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C
C FORTRAN code for XAPIIR routines (Harris, 1990)
C
C
C StG comment out below here
c parameter(nx=1,nt=6100,dt=0.0055,fc1=0.25,fc2=0.5)
c common//x(nt)
c character*80 namei(30),nameo(30)
c open(23,file='dynamic_50',form='formatted')
c open(24,file='dynamic_5005hz')
c do 5 k=1,nt
c read(23,*) x(k)
c 5 continue
c CALL XAPIIR( x, nt, 'BU', 0.0, 0.0, 4,
c +'LP', fc1, fc2, dt, 1 )
c
c do 20 k=1,nt
c write(24,10) x(k)
c 10 format(8e16.8)
c 20 continue
c end
C StG comment out above here
C
C XAPIIR -- SUBROUTINE: IIR FILTER DESIGN AND IMPLEMENTATION
C
C AUTHOR: Dave Harris
C
C LAST MODIFIED: September 12, 1990
C
C ARGUMENTS:
C ----------
C
C DATA REAL ARRAY CONTAINING SEQUENCE TO BE FILTERED
C ORIGINAL DATA DESTROYED, REPLACED BY FILTERED DATA
C
C NSAMPS NUMBER OF SAMPLES IN DATA
C
C
C APROTO CHARACTER*8 VARIABLE, CONTAINS TYPE OF ANALOG
C PROTOTYPE FILTER
C '(BU)TTER ' -- BUTTERWORTH FILTER
C '(BE)SSEL ' -- BESSEL FILTER
C 'C1 ' -- CHEBYSHEV TYPE I
C 'C2 ' -- CHEBYSHEV TYPE II
C
C TRBNDW TRANSITION BANDWIDTH AS FRACTION OF LOWPASS
C PROTOTYPE FILTER CUTOFF FREQUENCY. USED
C ONLY BY CHEBYSHEV FILTERS.
C
C A ATTENUATION FACTOR. EQUALS AMPLITUDE
C REACHED AT STOPBAND EDGE. USED ONLY BY
C CHEBYSHEV FILTERS.
C
C IORD ORDER (#POLES) OF ANALOG PROTOTYPE
C NOT TO EXCEED 10 IN THIS CONFIGURATION. 4 - 5
C SHOULD BE AMPLE.
C
C TYPE CHARACTER*8 VARIABLE CONTAINING FILTER TYPE
C 'LP' -- LOW PASS
C 'HP' -- HIGH PASS
C 'BP' -- BAND PASS
C 'BR' -- BAND REJECT
C
C FLO LOW FREQUENCY CUTOFF OF FILTER (HERTZ)
C IGNORED IF TYPE = 'LP'
C
C FHI HIGH FREQUENCY CUTOFF OF FILTER (HERTZ)
C IGNORED IF TYPE = 'HP'
C
C TS SAMPLING INTERVAL (SECONDS)
C
C PASSES INTEGER VARIABLE CONTAINING THE NUMBER OF PASSES
C 1 -- FORWARD FILTERING ONLY
C 2 -- FORWARD AND REVERSE (I.E. ZERO PHASE) FILTERING
C
C
C SUBPROGRAMS REFERENCED: BILIN2, BUROOTS, WARP, CUTOFFS, LPTHP, LPTBP,
C LP, LPTBR, BEROOTS, C1ROOTS, C2ROOTS, CHEBPARM, DESIGN, APPLY
C
SUBROUTINE XAPIIR( DATA, NSAMPS, APROTO, TRBNDW, A, IORD,
+ TYPE, FLO, FHI, TS, PASSES )
C
DIMENSION DATA(1)
CHARACTER*8 TYPE, APROTO
INTEGER NSAMPS, PASSES, IORD
REAL*4 TRBNDW, A, FLO, FHI, TS, SN(30), SD(30)
LOGICAL ZP
C
C Filter designed
C
CALL DESIGN( IORD, TYPE(1:2), APROTO(1:2), A, TRBNDW,
& FLO, FHI, TS, SN, SD, NSECTS )
C
C Filter data
C
IF ( PASSES .EQ. 1 ) THEN
ZP = .FALSE.
ELSE
ZP = .TRUE.
END IF
CALL APPLY( DATA, NSAMPS, ZP, SN, SD, NSECTS )
C
RETURN
END
C APPLY
C Subroutine to apply an iir filter to a data sequence.
C The filter is assumed to be stored as second order sections.
C Filtering is in-place.
C Zero-phase (forward and reverse) is an option.
C
C Input Arguments:
C ----------------
C
C DATA Array containing data
C
C NSAMPS Number of data samples
C
C ZP Logical variable, true for
C zero phase filtering, false
C for single pass filtering
C
C SN Numerator polynomials for second
C order sections.
C
C SD Denominator polynomials for second
C order sections.
C
C NSECTS Number of second-order sections
C
C Output Arguments:
C -----------------
C
C DATA Data array (same as input)
C
C
SUBROUTINE APPLY( DATA, NSAMPS, ZP, SN, SD, NSECTS )
C
REAL*4 SN(1), SD(1), DATA(1)
REAL*4 OUTPUT
LOGICAL ZP
C
JPTR = 1
DO 1 J = 1, NSECTS
C
X1 = 0.0
X2 = 0.0
Y1 = 0.0
Y2 = 0.0
B0 = SN(JPTR)
B1 = SN(JPTR+1)
B2 = SN(JPTR+2)
A1 = SD(JPTR+1)
A2 = SD(JPTR+2)
C
DO 2 I = 1, NSAMPS
C
OUTPUT = B0*DATA(I) + B1*X1 + B2*X2
OUTPUT = OUTPUT - ( A1*Y1 + A2*Y2 )
Y2 = Y1
Y1 = OUTPUT
X2 = X1
X1 = DATA(I)
DATA(I) = OUTPUT
C
2 CONTINUE
C
JPTR = JPTR + 3
C
1 CONTINUE
C
IF ( ZP ) THEN
C
JPTR = 1
DO 3 J = 1, NSECTS
C
X1 = 0.0
X2 = 0.0
Y1 = 0.0
Y2 = 0.0
B0 = SN(JPTR)
B1 = SN(JPTR+1)
B2 = SN(JPTR+2)
A1 = SD(JPTR+1)
A2 = SD(JPTR+2)
C
DO 4 I = NSAMPS, 1, -1
C
OUTPUT = B0*DATA(I) + B1*X1 + B2*X2
OUTPUT = OUTPUT - ( A1*Y1 + A2*Y2 )
Y2 = Y1
Y1 = OUTPUT
X2 = X1
X1 = DATA(I)
DATA(I) = OUTPUT
C
4 CONTINUE
C
JPTR = JPTR + 3
C
3 CONTINUE
C
END IF
C
RETURN
END
C
C DESIGN -- Subroutine to design IIR digital filters from analog
C prototypes.
C
C Input Arguments:
C ----------------
C
C IORD Filter order (10 MAXIMUM)
C
C TYPE Character*2 variable containing filter type
C LOWPASS (LP)
C HIGHPASS (HP)
C BANDPASS (BP)
C BANDREJECT (BR)
C
C APROTO Character*2 variable designating analog prototype
C Butterworth (BU)
C Bessel (BE)
C Chebyshev Type I (C1)
C Chebyshev Type II (C2)
C
C A Chebyshev stopband attenuation factor
C
C TRBNDW Chebyshev transition bandwidth (fraction of
C lowpass prototype passband width)
C
C FL Low-frequency cutoff
C
C FH High-frequency cutoff
C
C TS Sampling interval (in seconds)
C
C Output Arguments:
C -----------------
C
C SN Array containing numerator coefficients of
C second-order sections packed head-to-tail.
C
C SD Array containing denominator coefficients
C of second-order sections packed head-to-tail.
C
C NSECTS Number of second-order sections.
C
C
SUBROUTINE DESIGN( IORD, TYPE, APROTO, A, TRBNDW,
& FL, FH, TS, SN, SD, NSECTS )
C
COMPLEX P(10), Z(10)
CHARACTER*2 TYPE, APROTO
CHARACTER*3 STYPE(10)
REAL*4 SN(1), SD(1)
C
C Analog prototype selection
C
IF ( APROTO .EQ. 'BU' ) THEN
C
CALL BUROOTS( P, STYPE, DCVALUE, NSECTS, IORD )
C
ELSE IF ( APROTO .EQ. 'BE' ) THEN
C
CALL BEROOTS( P, STYPE, DCVALUE, NSECTS, IORD )
C
ELSE IF ( APROTO .EQ. 'C1' ) THEN
C
CALL CHEBPARM( A, TRBNDW, IORD, EPS, RIPPLE )
CALL C1ROOTS( P, STYPE, DCVALUE, NSECTS, IORD, EPS )
C
ELSE IF ( APROTO .EQ. 'C2' ) THEN
C
OMEGAR = 1. + TRBNDW
CALL C2ROOTS( P, Z, STYPE, DCVALUE, NSECTS, IORD, A, OMEGAR )
C
END IF
C
C Analog mapping selection
C
IF ( TYPE .EQ. 'BP' ) THEN
C
FLW = WARP( FL*TS/2., 2. )
FHW = WARP( FH*TS/2., 2. )
CALL LPTBP( P, Z, STYPE, DCVALUE, NSECTS, FLW, FHW, SN, SD )
C
ELSE IF ( TYPE .EQ. 'BR' ) THEN
C
FLW = WARP( FL*TS/2., 2. )
FHW = WARP( FH*TS/2., 2. )
CALL LPTBR( P, Z, STYPE, DCVALUE, NSECTS, FLW, FHW, SN, SD )
C
ELSE IF ( TYPE .EQ. 'LP' ) THEN
C
FHW = WARP( FH*TS/2., 2. )
CALL LP( P, Z, STYPE, DCVALUE, NSECTS, SN, SD )
CALL CUTOFFS( SN, SD, NSECTS, FHW )
C
ELSE IF ( TYPE .EQ. 'HP' ) THEN
C
FLW = WARP( FL*TS/2., 2. )
CALL LPTHP( P, Z, STYPE, DCVALUE, NSECTS, SN, SD )
CALL CUTOFFS( SN, SD, NSECTS, FLW )
C
END IF
C
C Bilinear analog to digital transformation
C
CALL BILIN2( SN, SD, NSECTS )
C
RETURN
END
C
C BUROOTS -- SUBROUTINE TO COMPUTE BUTTERWORTH POLES FOR
C NORMALIZED LOWPASS FILTER
C
C LAST MODIFIED: SEPTEMBER 7, 1990
C
C OUTPUT ARGUMENTS:
C -----------------
C P COMPLEX ARRAY CONTAINING POLES
C CONTAINS ONLY ONE FROM EACH
C COMPLEX CONJUGATE PAIR, AND
C ALL REAL POLES
C
C RTYPE CHARACTER ARRAY INDICATING 2ND ORDER SECTION
C TYPE:
C (SP) SINGLE REAL POLE
C (CP) COMPLEX CONJUGATE POLE PAIR
C (CPZ) COMPLEX CONJUGATE POLE-ZERO PAIRS
C
C DCVALUE MAGNITUDE OF FILTER AT ZERO FREQUENCY
C
C NSECTS NUMBER OF SECOND ORDER SECTIONS
C
C INPUT ARGUMENTS:
C ----------------
C
C IORD DESIRED FILTER ORDER
C
C
SUBROUTINE BUROOTS( P, RTYPE, DCVALUE, NSECTS, IORD )
C
COMPLEX P(1)
INTEGER HALF
CHARACTER*3 RTYPE(1)
C
PI=3.14159265
C
HALF = IORD/2
C
C TEST FOR ODD ORDER, AND ADD POLE AT -1
C
NSECTS = 0
IF ( 2*HALF .LT. IORD ) THEN
P(1) = CMPLX( -1., 0. )
RTYPE(1) = 'SP'
NSECTS = 1
END IF
C
DO 1 K = 1, HALF
ANGLE = PI * ( .5 + FLOAT(2*K-1) / FLOAT(2*IORD) )
NSECTS = NSECTS + 1
P(NSECTS) = CMPLX( COS(ANGLE), SIN(ANGLE) )
RTYPE(NSECTS) = 'CP'
1 CONTINUE
C
DCVALUE = 1.0
C
RETURN
END
C
C BEROOTS -- SUBROUTINE TO RETURN BESSEL POLES FOR
C NORMALIZED LOWPASS FILTER
C
C LAST MODIFIED: April 15, 1992. Changed P and RTYPE to adjustable
C array by using an "*" rather than a "1".
C
C OUTPUT ARGUMENTS:
C -----------------
C P COMPLEX ARRAY CONTAINING POLES
C CONTAINS ONLY ONE FROM EACH
C COMPLEX CONJUGATE PAIR, AND
C ALL REAL POLES
C
C RTYPE CHARACTER ARRAY INDICATING 2ND ORDER SECTION
C TYPE:
C (SP) SINGLE REAL POLE
C (CP) COMPLEX CONJUGATE POLE PAIR
C (CPZ) COMPLEX CONJUGATE POLE-ZERO PAIRS
C
C DCVALUE MAGNITUDE OF FILTER AT ZERO FREQUENCY
C
C NSECTS NUMBER OF SECOND ORDER SECTIONS
C
C INPUT ARGUMENTS:
C ----------------
C
C IORD DESIRED FILTER ORDER
C
C
SUBROUTINE BEROOTS( P, RTYPE, DCVALUE, NSECTS, IORD )
C
COMPLEX P(*)
INTEGER NSECTS, IORD
CHARACTER*3 RTYPE(*)
C
IF ( IORD .EQ. 1 ) THEN
C
P(1) = CMPLX( -1.0, 0.0 )
RTYPE(1) = 'SP'
C
ELSE IF ( IORD .EQ. 2 ) THEN
C
P(1) = CMPLX( -1.1016013, 0.6360098 )
RTYPE(1) = 'CP'
C
ELSE IF ( IORD .EQ. 3 ) THEN
C
P(1) = CMPLX( -1.0474091, 0.9992645 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3226758, 0.0 )
RTYPE(2) = 'SP'
C
ELSE IF ( IORD .EQ. 4 ) THEN
C
P(1) = CMPLX( -0.9952088, 1.2571058 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3700679, 0.4102497 )
RTYPE(2) = 'CP'
C
ELSE IF ( IORD .EQ. 5 ) THEN
C
P(1) = CMPLX( -0.9576766, 1.4711244 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3808774, 0.7179096 )
RTYPE(2) = 'CP'
P(3) = CMPLX( -1.5023160, 0.0 )
RTYPE(3) = 'SP'
C
ELSE IF ( IORD .EQ. 6 ) THEN
C
P(1) = CMPLX( -0.9306565, 1.6618633 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3818581, 0.9714719 )
RTYPE(2) = 'CP'
P(3) = CMPLX( -1.5714904, 0.3208964 )
RTYPE(3) = 'CP'
C
ELSE IF ( IORD .EQ. 7 ) THEN
C
P(1) = CMPLX( -0.9098678, 1.8364514 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3789032, 1.1915667 )
RTYPE(2) = 'CP'
P(3) = CMPLX( -1.6120388, 0.5892445 )
RTYPE(3) = 'CP'
P(4) = CMPLX( -1.6843682, 0.0 )
RTYPE(4) = 'SP'
C
ELSE IF ( IORD .EQ. 8 ) THEN
C
P(1) = CMPLX( -0.8928710, 1.9983286 )
RTYPE(1) = 'CP'
P(2) = CMPLX( -1.3738431, 1.3883585 )
RTYPE(2) = 'CP'
P(3) = CMPLX( -1.6369417, 0.8227968 )
RTYPE(3) = 'CP'
P(4) = CMPLX( -1.7574108, 0.2728679 )
RTYPE(4) = 'CP'
C
END IF
C
NSECTS = IORD - IORD/2
C
DCVALUE = 1.0
C
C DONE
C
RETURN
END
C
C CHEBPARM - Calculates Chebyshev type I and II design parameters
C
C
C INPUT ARGUMENTS
C ---------------
C
C A Desired stopband attenuation
C i.e. max stopband amplitude is 1/ATTEN
C
C TRBNDW Transition bandwidth between stop and passbands
C as a fraction of the passband width
C
C IORD Filter order (number of poles)
C
C
C OUTPUT ARGUMENTS
C ----------------
C
C EPS Chebyshev passband parameter
C
C RIPPLE Passband ripple
C
SUBROUTINE CHEBPARM( A, TRBNDW, IORD, EPS, RIPPLE )
OMEGAR = 1. + TRBNDW
ALPHA = ( OMEGAR + SQRT( OMEGAR**2 - 1. ) ) ** IORD
G = ( ALPHA**2 + 1. ) / (2.*ALPHA)
EPS = SQRT( A**2 - 1. ) / G
RIPPLE = 1. / SQRT( 1. + EPS**2 )
C
RETURN
END
C
C C1ROOTS -- SUBROUTINE TO COMPUTE CHEBYSHEV TYPE I POLES FOR
C NORMALIZED LOWPASS FILTER
C
C LAST MODIFIED: SEPTEMBER 7, 1990
C
C OUTPUT ARGUMENTS:
C -----------------
C P COMPLEX ARRAY CONTAINING POLES
C CONTAINS ONLY ONE FROM EACH
C COMPLEX CONJUGATE PAIR, AND
C ALL REAL POLES
C
C RTYPE CHARACTER ARRAY INDICATING 2ND ORDER SECTION
C TYPE:
C (SP) SINGLE REAL POLE
C (CP) COMPLEX CONJUGATE POLE PAIR
C (CPZ) COMPLEX CONJUGATE POLE-ZERO PAIRS
C
C DCVALUE RESPONSE OF FILTER AT ZERO FREQUENCY
C
C NSECTS NUMBER OF SECOND ORDER SECTIONS
C
C INPUT ARGUMENTS:
C ----------------
C
C IORD DESIRED FILTER ORDER
C
C EPS CHEBYSHEV PARAMETER RELATED TO PASSBAND RIPPLE
C
SUBROUTINE C1ROOTS( P, RTYPE, DCVALUE, NSECTS, IORD, EPS )
C
COMPLEX P(1)
INTEGER HALF
CHARACTER*3 RTYPE(1)
C
PI = 3.14159265
HALF = IORD/2
C
C INTERMEDIATE DESIGN PARAMETERS
C
GAMMA = ( 1. + SQRT( 1. + EPS*EPS ) ) / EPS
GAMMA = ALOG(GAMMA) / FLOAT(IORD)
GAMMA = EXP(GAMMA)
S = .5 * ( GAMMA - 1./GAMMA )
C = .5 * ( GAMMA + 1./GAMMA )
C
C CALCULATE POLES
C
NSECTS = 0
DO 1 I = 1 , HALF
RTYPE(I) = 'CP'
ANGLE = FLOAT(2*I-1) * PI/FLOAT(2*IORD)
SIGMA = -S * SIN(ANGLE)
OMEGA = C * COS(ANGLE)
P(I) = CMPLX( SIGMA, OMEGA )
NSECTS = NSECTS + 1
1 CONTINUE
IF ( 2*HALF .LT. IORD ) THEN
RTYPE( HALF + 1 ) = 'SP'
P(HALF+1) = CMPLX( -S, 0.0 )
NSECTS = NSECTS + 1
DCVALUE = 1.0
ELSE
DCVALUE = 1./SQRT( 1 + EPS**2 )
END IF
C
C DONE
C
RETURN
END
C
C C2ROOTS -- SUBROUTINE TO COMPUTE ROOTS FOR NORMALIZED LOWPASS
C CHEBYSHEV TYPE 2 FILTER
C
C LAST MODIFIED: SEPTEMBER 7, 1990
C
C OUTPUT ARGUMENTS:
C -----------------
C P COMPLEX ARRAY CONTAINING POLES
C CONTAINS ONLY ONE FROM EACH
C COMPLEX CONJUGATE PAIR, AND
C ALL REAL POLES
C
C Z COMPLEX ARRAY CONTAINING ZEROS
C CONTAINS ONLY ONE FROM EACH
C COMPLEX CONJUGATE PAIR, AND
C ALL REAL ZEROS
C
C RTYPE CHARACTER ARRAY INDICATING 2ND ORDER SECTION
C TYPE:
C (SP) SINGLE REAL POLE
C (CP) COMPLEX CONJUGATE POLE PAIR
C (CPZ) COMPLEX CONJUGATE POLE-ZERO PAIRS
C
C DCVALUE MAGNITUDE OF FILTER AT ZERO FREQUENCY
C
C NSECTS NUMBER OF SECOND ORDER SECTIONS
C
C INPUT ARGUMENTS:
C ----------------
C
C
C IORD DESIRED FILTER ORDER
C
C A STOPBAND ATTENUATION FACTOR
C
C OMEGAR CUTOFF FREQUENCY OF STOPBAND
C PASSBAND CUTOFF IS AT 1.0 HERTZ
C
C
SUBROUTINE C2ROOTS( P, Z, RTYPE, DCVALUE, NSECTS, IORD, A, OMEGAR
1)
C
COMPLEX P(1), Z(1)
INTEGER HALF
CHARACTER*3 RTYPE(1)
C
PI = 3.14159265
HALF = IORD/2
C
C INTERMEDIATE DESIGN PARAMETERS
C
GAMMA = (A+SQRT(A*A-1.))
GAMMA = ALOG(GAMMA)/FLOAT(IORD)
GAMMA = EXP(GAMMA)
S = .5*(GAMMA-1./GAMMA)
C = .5*(GAMMA+1./GAMMA)
C
NSECTS = 0
DO 1 I = 1, HALF
C
C CALCULATE POLES
C
RTYPE(I) = 'CPZ'
C
ANGLE = FLOAT(2*I-1) * PI/FLOAT(2*IORD)
ALPHA = -S*SIN(ANGLE)
BETA = C*COS(ANGLE)
DENOM = ALPHA*ALPHA + BETA*BETA
SIGMA = OMEGAR*ALPHA/DENOM
OMEGA = -OMEGAR*BETA/DENOM
P(I) = CMPLX( SIGMA, OMEGA )
C
C CALCULATE ZEROS
C
OMEGA = OMEGAR/COS(ANGLE)
Z(I) = CMPLX( 0.0, OMEGA )
C
NSECTS = NSECTS + 1
C
1 CONTINUE
C
C ODD-ORDER FILTERS
C
IF ( 2*HALF .LT. IORD ) THEN
RTYPE(HALF+1) = 'SP'
P(HALF+1) = CMPLX( -OMEGAR/S, 0.0 )
NSECTS = NSECTS + 1
END IF
C
C DC VALUE
C
DCVALUE = 1.0
C
C DONE
C
RETURN
END
C
C WARP -- FUNCTION, APPLIES TANGENT FREQUENCY WARPING TO COMPENSATE
C FOR BILINEAR ANALOG -> DIGITAL TRANSFORMATION
C
C ARGUMENTS:
C ----------
C
C F ORIGINAL DESIGN FREQUENCY SPECIFICATION (HERTZ)
C TS SAMPLING INTERVAL (SECONDS)
C
C LAST MODIFIED: SEPTEMBER 20, 1990
C
REAL FUNCTION WARP( F , TS )
C
TWOPI = 6.2831853
ANGLE = TWOPI*F*TS/2.
WARP = 2.*TAN(ANGLE)/TS
WARP = WARP/TWOPI
C
RETURN
END
C
C Subroutine to generate second order section parameterization
C from an pole-zero description for lowpass filters.
C
C Input Arguments:
C ----------------
C
C P Array containing poles
C
C Z Array containing zeros
C
C RTYPE Character array containing root type information
C (SP) Single real pole or
C (CP) Complex conjugate pole pair
C (CPZ) Complex conjugate pole and zero pairs
C
C DCVALUE Zero-frequency value of prototype filter
C
C NSECTS Number of second-order sections
C
C Output Arguments:
C -----------------
C
C SN Numerator polynomials for second order
C sections.
C
C SD Denominator polynomials for second order
C sections.
C
C
SUBROUTINE LP( P, Z, RTYPE, DCVALUE, NSECTS, SN, SD )
C
COMPLEX P(*), Z(*)
CHARACTER*3 RTYPE(*)
REAL*4 SN(*), SD(*), DCVALUE
C
IPTR = 1
DO 1 I = 1, NSECTS
C
IF ( RTYPE(I) .EQ. 'CPZ' ) THEN
C
SCALE = REAL( P(I) * CONJG( P(I) ) )
& / REAL( Z(I) * CONJG( Z(I) ) )
SN( IPTR ) = REAL( Z(I) * CONJG( Z(I) ) ) * SCALE
SN( IPTR + 1 ) = -2. * REAL( Z(I) ) * SCALE
SN( IPTR + 2 ) = 1. * SCALE
SD( IPTR ) = REAL( P(I) * CONJG( P(I) ) )
SD( IPTR + 1 ) = -2. * REAL( P(I) )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
C
ELSE IF ( RTYPE(I) .EQ. 'CP' ) THEN
C
SCALE = REAL( P(I) * CONJG( P(I) ) )
SN( IPTR ) = SCALE
SN( IPTR + 1 ) = 0.
SN( IPTR + 2 ) = 0.
SD( IPTR ) = REAL( P(I) * CONJG( P(I) ) )
SD( IPTR + 1 ) = -2. * REAL( P(I) )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
C
ELSE IF ( RTYPE(I) .EQ. 'SP' ) THEN
C
SCALE = -REAL( P(I) )
SN( IPTR ) = SCALE
SN( IPTR + 1 ) = 0.
SN( IPTR + 2 ) = 0.
SD( IPTR ) = -REAL( P(I) )
SD( IPTR + 1 ) = 1.
SD( IPTR + 2 ) = 0.
IPTR = IPTR + 3
C
END IF
C
1 CONTINUE
C
SN(1) = DCVALUE * SN(1)
SN(2) = DCVALUE * SN(2)
SN(3) = DCVALUE * SN(3)
C
RETURN
END
C LPTBP
C
C Subroutine to convert an prototype lowpass filter to a bandpass filter via
C the analog polynomial transformation. The lowpass filter is
C described in terms of its poles and zeros (as input to this routine).
C The output consists of the parameters for second order sections.
C
C Input Arguments:
C ----------------
C
C P Array containing poles
C
C Z Array containing zeros
C
C RTYPE Character array containing type information
C (SP) single real pole or
C (CP) complex conjugate pole pair or
C (CPZ) complex conjugate pole/zero pairs
C
C DCVALUE Zero frequency value of filter
C
C NSECTS Number of second-order sections upon input
C
C FL Low-frequency cutoff
C
C FH High-frequency cutoff
C
C Output Arguments:
C -----------------
C
C SN Numerator polynomials for second order
C sections.
C
C SD Denominator polynomials for second order
C sections.
C
C NSECTS Number of second order sections upon output
C This subroutine doubles the number of
C sections.
C
C
SUBROUTINE LPTBP( P, Z, RTYPE, DCVALUE, NSECTS, FL, FH, SN, SD )
C
COMPLEX P(*), Z(*), CTEMP, P1, P2, Z1, Z2, S, H
CHARACTER*3 RTYPE(*)
REAL*4 SN(*), SD(*), DCVALUE
C
PI = 3.14159265
TWOPI = 2.*PI
A = TWOPI*TWOPI*FL*FH
B = TWOPI*( FH - FL )
C
N = NSECTS
NSECTS = 0
IPTR = 1
DO 1 I = 1, N
C
IF ( RTYPE(I) .EQ. 'CPZ' ) THEN
C
CTEMP = ( B*Z(I) )**2 - 4.*A
CTEMP = CSQRT( CTEMP )
Z1 = 0.5*( B*Z(I) + CTEMP )
Z2 = 0.5*( B*Z(I) - CTEMP )
CTEMP = ( B*P(I) )**2 - 4.*A
CTEMP = CSQRT( CTEMP )
P1 = 0.5*( B*P(I) + CTEMP )
P2 = 0.5*( B*P(I) - CTEMP )
SN( IPTR ) = REAL( Z1 * CONJG( Z1 ) )
SN( IPTR + 1 ) = -2. * REAL( Z1 )
SN( IPTR + 2 ) = 1.
SD( IPTR ) = REAL( P1 * CONJG( P1 ) )
SD( IPTR + 1 ) = -2. * REAL( P1 )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
SN( IPTR ) = REAL( Z2 * CONJG( Z2 ) )
SN( IPTR + 1 ) = -2. * REAL( Z2 )
SN( IPTR + 2 ) = 1.
SD( IPTR ) = REAL( P2 * CONJG( P2 ) )
SD( IPTR + 1 ) = -2. * REAL( P2 )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
C
NSECTS = NSECTS + 2
C
ELSE IF ( RTYPE(I) .EQ. 'CP' ) THEN
C
CTEMP = ( B*P(I) )**2 - 4.*A
CTEMP = CSQRT( CTEMP )
P1 = 0.5*( B*P(I) + CTEMP )
P2 = 0.5*( B*P(I) - CTEMP )
SN( IPTR ) = 0.
SN( IPTR + 1 ) = B
SN( IPTR + 2 ) = 0.
SD( IPTR ) = REAL( P1 * CONJG( P1 ) )
SD( IPTR + 1 ) = -2. * REAL( P1 )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
SN( IPTR ) = 0.
SN( IPTR + 1 ) = B
SN( IPTR + 2 ) = 0.
SD( IPTR ) = REAL( P2 * CONJG( P2 ) )
SD( IPTR + 1 ) = -2. * REAL( P2 )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
C
NSECTS = NSECTS + 2
C
ELSE IF ( RTYPE(I) .EQ. 'SP' ) THEN
C
SN( IPTR ) = 0.
SN( IPTR + 1 ) = B
SN( IPTR + 2 ) = 0.
SD( IPTR ) = A
SD( IPTR + 1 ) = -B*REAL( P(I) )
SD( IPTR + 2 ) = 1.
IPTR = IPTR + 3
C
NSECTS = NSECTS + 1
C
END IF
C
1 CONTINUE
C
C Scaling - use the fact that the bandpass filter amplitude at sqrt( omega_l *
C equals the amplitude of the lowpass prototype at d.c.
C
S = CMPLX( 0., SQRT(A) )
H = CMPLX( 1., 0. )
C
IPTR = 1
DO 2 I = 1, NSECTS
H = H * ( ( SN(IPTR+2)*S + SN(IPTR+1) )*S + SN(IPTR) )
& / ( ( SD(IPTR+2)*S + SD(IPTR+1) )*S + SD(IPTR) )
IPTR = IPTR + 3
2 CONTINUE
SCALE = DCVALUE / SQRT( REAL( H ) * CONJG( H ) )
SN(1) = SN(1) * SCALE
SN(2) = SN(2) * SCALE
SN(3) = SN(3) * SCALE
C
RETURN
END
C LPTBR
C
C Subroutine to convert a lowpass filter to a band reject filter
C via an analog polynomial transformation. The lowpass filter is
C described in terms of its poles and zeros (as input to this routine).
C The output consists of the parameters for second order sections.
C
C Input Arguments:
C ----------------
C
C P Array containing poles
C
C Z Array containing zeros
C
C RTYPE Character array containing type information
C (SP) single real pole or
C (CP) complex conjugate pole pair
C (CPZ) complex conjugate pole/zero pairs
C
C DCVALUE Zero-frequency value of prototype filter
C
C NSECTS Number of second-order sections
C prior to transformation
C
C FL Low-frequency cutoff
C
C FH High-frequency cutoff
C
C Output Arguments:
C -----------------
C
C SN Numerator polynomials for second order
C sections.
C
C SD Denominator polynomials for second order
C sections.
C
C NSECTS Number of second order sections following
C transformation. The number is doubled.
C
C
SUBROUTINE LPTBR( P, Z, RTYPE, DCVALUE, NSECTS, FL, FH, SN, SD )
C
COMPLEX P(*), Z(*), CINV, CTEMP, P1, P2, Z1, Z2
CHARACTER*3 RTYPE(*)
REAL*4 SN(*), SD(*)
C
PI = 3.14159265
TWOPI = 2.*PI
A = TWOPI*TWOPI*FL*FH
B = TWOPI*( FH - FL )
C
N = NSECTS
NSECTS = 0
IPTR = 1
DO 1 I = 1, N
C
IF ( RTYPE(I) .EQ. 'CPZ' ) THEN
C
CINV = 1./Z(I)
CTEMP = ( B*CINV )**2 - 4.*A
CTEMP = CSQRT( CTEMP )
Z1 = 0.5*( B*CINV + CTEMP )
Z2 = 0.5*( B*CINV - CTEMP )