Fast Fourier Transforms on Motorola's Digital Signal Processors

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fftlength=1024 ; fg4=fftlength/4 ; fg4m1=fg4-1 ; x=0:fg4m1 ; a=bitrev(x) ; a=a(2:fg4) ; i=1 ; c(i)=1 ; s(i)=0 ; i=i+1 ; kon=2*pi/fftlength ; for k=1:fg4m1 c(i)=cos(kon*a(k)) ; s(i)=sin(kon*a(k)) ; i=i+1 ; c(i)=cos(kon*a(k)*3) ; s(i)=sin(kon*a(k)*3) ; i=i+1 ; c(i)=cos(kon*a(k)*2) ; s(i)=sin(kon*a(k)*2) ; i=i+1 ; end c=c’ ;% real part of twiddle factor (cos) s=s‘ ;% imaginary part of twiddle factor (sin) end Optimized Complex FFT for the DSP56001/2 page 132,60 opt nomd,mex,loc,nocex,mu include ‘sincosc’ include ‘bitrevtwd56’ include ‘gen56’ include ‘cfft56’ ; Latest revision - 14-Oct.-92 reset equ 0 start equ $40 POINTS equ 512 IDATA equ $0 COEF equ $800 ODATA equ $1000 sincosc POINTS,COEF gen56 POINTS,IDATA opt mex org p:reset jmp start org p:start movep #0,X:$FFFE ;0 wait states bitrevtwd56 POINTS,COEF CFFT56 IDATA,COEF,POINTS,ODATA Figure A-1 Optimized Complex FFT for the DSP96002(sheet 10 of 20) A-10 MOTOROLA
nop nop jmp * end ; ; Sine-Cosine Table Generator for rfft56.asm and cfft56.asm ; ; Last Update 10/28/92 ; sincosc macro points,coef sincosc ident 1,2 ; ; sincosc - macro to generate sine and cosine coefficient ; lookup tables for Decimation in Time complex FFT ; twiddle factors. Only points/4 coefficients ; are generted. For real FFT another points/4 ; ; coefficients with higher freq. are created. ; points - number of points (2 - 32768, power of 2) ; coef - base address of sine/cosine table ; positive cosine value in X memory ; ; ; 8/12/92 positive sine value in Y memory pi equ 3.141592654 ;freq equ 2.0*pi/@cvf(points*2) ; org x:coef-points/2 ;count set 0 ; dup points/2 ; dc @cos(@cvf(count)*freq) ;count set count+1 ; endm ; ; org y:coef-points/2 ;count set 0 ; dup points/2 ; dc -@sin(@cvf(count)*freq) ;count set count+1 ; endm freq1 equ 2.0*pi/@cvf(points) ; int i,j=1,k,tmp=0; ; k=1
Page 1 and 2:
Motorola’s High-Performance DSP T
Page 3 and 4:
SECTION 1 Definition and History SE
Page 5 and 6:
SECTION 5 Optimizing Performance of
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APPENDIX B Real-Valued Input FFT Ta
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Figure 4-3 Figure 4-4 Figure 4-5 Fi
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Table 8-1 Table 8-2 Table 8-3 Table
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When interpreted as an infinite sum
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2. Pattern-Based ⎯ Many problems
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In summary, the basic nature of the
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ecause: j2πfnT+j2πn e T - ⎛ ---
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2.2 Windowing and Windowing Effects
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xf () x(nT) 1 0.9 0.8 0.7 0.6 0.5 0
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Note that many textbooks simply def
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“Since there are two independent
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appropriately called the decimation
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x(0) x(4) Figure 3-4 Decimation-in-
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Binary Index 000 x(0) 001 010 011 1
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3.4 The Decimation-in- Frequency Ra
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DSP56001/2 and DSP96002 hardware fe
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4. Bit-reversed addressing mode 5.
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4.3 Complexity of a Radix-2 DIT FFT
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The data paths are 24 bits wide, th
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The kernel shown in Figure 4-4 exec
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;Alters Program Control Registers ;
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PORT A CLK 4 ADDRESS 32 Control 19
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;r0 ➨ A ;r1 ➨ B ;r4 ➨ C ;r5
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5 5 7 ADDRESS Sigma Delta Codec PI/
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limits its results to those bits. T
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flow in the FFT calculation is to s
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of the sine table, 256 points. Howe
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normal_order=output_pointer; bitrev
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A′ A CW c BW b DW c W b = + + ( +
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;r0->A,r4->B, r1->C, r6->D; ;r1->A
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Ar′ = Ar + Br + ( Dr + Cr) Ai′
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“Optimization saves . . . 2067 in
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plexity to practical complexity ref
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5.1.2 Optimization for Fast
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3. pass. This change results in lon
Page 77 and 78: 5.2 Example of Optimization 5.2.1 F
Page 79 and 80: Pass 0 1 2 3 4 5 6 7 8 A B C D W=(1
Page 81 and 82: The fully optimized 1024-point comp
Page 83 and 84: 6.1 Real-Valued Input FFT Algorithm
Page 85 and 86: The twiddle factors appear to be in
Page 87 and 88: X=A+jB Y=C+jD X’=A+C+j(D+B) - Y
Page 89 and 90: takes four points in and four point
Page 91 and 92: Z( k) = DFT[ z( n) ] = DFT[ x( n) +
Page 93 and 94: F( k) a real sequence with N points
Page 95 and 96: Eight multiplications, five additio
Page 97 and 98: further: 1. Since the input data is
Page 99 and 100: 6.4 The Goertzel Algorithm Previous
Page 101 and 102: The power of magnitude of the DFT c
Page 103 and 104: SSI or HI The double buffering is i
Page 105 and 106: “To implement Eqn. 7-1, a two dim
Page 107 and 108: F( k) where: N - 1 2c( k) ---------
Page 109 and 110: 7.2.2 Two Dimensional DCT A one dim
Page 111 and 112: facturer may offer a higher perform
Page 113 and 114: 8.2.1.1 Complex FFT on Floating-Poi
Page 115 and 116: 8.2.2 FFT on Fixed-Point DSPs As me
Page 117 and 118: “Motorola's family of digital sig
Page 119 and 120: APPENDIX A Fully Optimized Complex
Page 121 and 122: ;**********************************
Page 123 and 124: ;**********************************
Page 125 and 126: movem 2,m5 movem 2,m7 move #data,r0
Page 127: ; ------------ NORMAL RADIX-2 BUTTE
Page 131 and 132: ; Input signal for FFT rfft56.asm a
Page 133 and 134: move #POINTS/2-1,m0 ;modulo address
Page 135 and 136: ; r0->A,r1->B,r4->A’,r5->B’,r6-
Page 137 and 138: _inner_pass do n3,_end_grp ;do grou
Page 139 and 140: APPENDIX B Real-Valued Input FFT B.
Page 141 and 142: count set 0 dup points/2 dc @cos(@c
Page 143 and 144: B.2 Real FFT for DSP56001/2 ; ; Thi
Page 145 and 146: dup points/4 dc @cos(@cvf(count)*fr
Page 147 and 148: macr y1,y0,a y:(r4),y0 ;a=Wi*H2r-Wr
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Fast Fourier Transforms on Motorola's Digital Signal Processors

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