Fast Fourier Transforms on Motorola's Digital Signal Processors

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pg 16 equ points/16 pg 32 equ points/32 pg 64 equ points/64 pg 128 equ points/128 pg 4m1 equ points/4-1 pg 16m1 equ points/16-1 pg 64m1 equ points/64-1 ;****************************************************************************** ; ------------ FIRST 2 STAGES AS RADIX-4 BUTTERFLY ------------------------ * ;****************************************************************************** move #-1,m0 move m0,m1 move m0,m2 move m0,m3 move m0,m4 move m0,m5 move m0,m6 move m0,m7 move #data,r0 move #(data+pg4),r1 move #(data+2*pg4),r2 move #(data+3*pg4),r3 move #2,n0 move n0,n6 move n0,n5 move n0,n7 move #pg4m1,n1 jsr _sr4 ;**************************************************************************** ; ------------ PARTS OF 3. AND 4. STAGE AS SPECIAL RADIX-4 BUTTERFLY ------ * ;**************************************************************************** move #data,r0 move #(data+pg16),r1 move #(data+2*pg16),r2 move #(data+3*pg16),r3 move #pg 16m1,n1 jsr _sr4 ;**************************************************************************** ; ------------ PARTS OF 5. AND 6. STAGE AS SPECIAL RADIX-4 BUTTERFLY ------ * ;**************************************************************************** move #data,r0 move #(data+pg64),r1 move #(data+2*pg64),r2 move #(data+3*pg64),r3 move #pg 64m1,n1 jsr _sr4 Figure A-1 Optimized Complex FFT for the DSP96002(sheet 4 of 20) A-4 MOTOROLA
;**************************************************************************** ; ------------ REST OF 3. STAGE AS RADIX-2 BUTTERFLY ---------------------- * ;**************************************************************************** move #3,n6 ; step for twiddle addressing in r4tab move #(tab4+3),r6 ; address of sin cos table move #(data+pg4),r0 ; input vector move #(data+pg4+pg8),r1 move #3,n7 ; still 3 r2 groups to calculate move #(pg 8-3),r7 ; pg8 r2 butterflies in a group move #(pg 8+1),n0 ; step to next group jsr _nr2 ;**************************************************************************** ; ------------ REST OF 4. STAGE AS RADIX-2 BUTTERFLY ---------------------- * ;**************************************************************************** move #(tab4+6),r6 ; address of sin cos table move #(data+pg4),r0 ; input vector move #(data+pg4+pg16),r1 move #6,n7 ; still 6 r2 groups to calculate move #(pg16-3),r7 ; pg16 r2 butterflies in a group move #(pg16+1),n0 ; step to next group jsr _nr2 ;**************************************************************************** ; ------------ REST OF 5. STAGE AS RADIX-2 BUTTERFLY ---------------------- * ;**************************************************************************** move #(tab4+3),r6 ; address of sin cos table move #(data+pg16),r0 ; input vector move #(data+pg16+pg32),r1 move #15,n7 ; still 15 r2 groups to calculate move #(pg32-3),r7 ; pg32 r2 butterflies in a group move #(pg32+1),n0 ; step to next group jsr _nr2 ;**************************************************************************** ; ------------ REST OF 6. STAGE AS RADIX-2 BUTTERFLY ---------------------- * ;**************************************************************************** move #(tab4+6),r6 ; address of sin cos table move #(data+pg16),r0 ; input vector move #(data+pg16+pg64),r1 move #30,n7 ; still 30 r2 groups to calculate move #(pg64-3),r7 ; pg64 r2 butterflies in a group move #(pg64+1),n0 ; step to next group jsr _nr2 ;**************************************************************************** ; ------------ 7. STAGE AS RADIX-2 BUTTERFLY ------------------------------ * ;**************************************************************************** move #(tab4),r6 ; address of sin cos table move #(data),r0 ; input vector Figure A-1 Optimized Complex FFT for the DSP96002(sheet 5 of 20) MOTOROLA A-5
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
Page 7 and 8:
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
Page 13 and 14:
When interpreted as an infinite sum
Page 15 and 16:
2. Pattern-Based ⎯ Many problems
Page 17 and 18:
In summary, the basic nature of the
Page 19 and 20:
ecause: j2πfnT+j2πn e T - ⎛ ---
Page 21 and 22:
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
Page 27 and 28:
“Since there are two independent
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appropriately called the decimation
Page 31 and 32:
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
Page 47 and 48:
;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′
Page 69 and 70:
“Optimization saves . . . 2067 in
Page 71 and 72: plexity to practical complexity ref
Page 73 and 74: 5.1.2 Optimization for Fast
Page 75 and 76: 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: ;**********************************
Page 125 and 126: movem 2,m5 movem 2,m7 move #data,r0
Page 127 and 128: ; ------------ NORMAL RADIX-2 BUTTE
Page 129 and 130: nop nop jmp * end ; ; Sine-Cosine T
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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