Fast Fourier Transforms on Motorola's Digital Signal Processors

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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 SPLIT56 IDATA,COEF,POINTS,ODATA end ; ; Sine-Cosine Table Generator for rfft56.asm ; ; Last Update 11/11/92 ; sincosr macro points,coef sincosr ident 1,2 ; ; sincosr- macro to generate sine and cosine coefficient ; lookup tables for Decimati<strong>on</strong> in Time real 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 ; positive sine value in Y memory ; ; 8/12/92 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) org x:coef count set 0 Figure B-2 Real FFT for DSP56001/2 (sheet 2 of 5) B-6 MOTOROLA
dup points/4 dc @cos(@cvf(count)*freq1) count set count+1 endm org y:coef count set 0 dup points/4 dc @sin(@cvf(count)*freq1) count set count+1 endm endm ;end of sincosr macro bitrevtwd56 macro POINTS,COEF bitrevtwd56 ident 1,2 ; ; bitrevtwd - macro to sort sine and cosine coefficient ; lookup tables in bit reverse order for 56156 ; ; POINTS - number of points (2 - 32768, power of 2) ; COEF - base address of sine/cosine table ; negative cosine (Wr) and negative sine (Wi) in X memory ; ; Wei Chen ; July-28, 1992 ; move #COEF,r1 ;twiddle factor start address move #0,m0 ;bit reverse address move #POINTS/8,n0 ;sincosr use N/4 points data, ;offset for bit rev. is N/8 move #POINTS/4-1,n2 move r1,r0 ;r1 ptr to normal order data move (r1)+ ;no swap <strong>on</strong> 1st data move (r0)+n0 ;r0 ptr to bitrev do n2,_end_bit ;does N/4-1 points swap move r1,x0 move r0,b cmp x0,b jgt _swap move (r1)+ ;no swap but update points move (r0)+n0 jmp _nothing _swap move r1,r5 move r0,r4 move x:(r1),x0 y:(r5),y0 move x:(r0),a y:(r4),b move x0,x:(r0)+n0 y0,y:(r4) move a,x:(r1)+ b,y:(r5) _nothing nop _end_bit endm ;end of bitrevtwd macro Figure B-2 Real FFT for DSP56001/2 (sheet 3 of 5) MOTOROLA B-7
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Motorola’s High-Performance DSP T
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SECTION 1 Definition and History SE
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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
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5.2 Example of Optimization 5.2.1 F
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Pass 0 1 2 3 4 5 6 7 8 A B C D W=(1
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The fully optimized 1024-point comp
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6.1 Real-Valued Input FFT Algorithm
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The twiddle factors appear to be in
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X=A+jB Y=C+jD X’=A+C+j(D+B) - Y
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takes four points in and four point
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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 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: B.2 Real FFT for DSP56001/2 ; ; Thi
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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