Fast Fourier Transforms on Motorola's Digital Signal Processors

every output corresponding to every input. In the
Goertzel algorithm, only one DFT coefficient X(k) is
needed, and X(k) = y k (N). In other words, the complex
multiplication is carried out only once in an
entire DFT calculation. In frequency detection, only
the power of magnitude of the DFT coefficient is
needed. This observation may simplify the computation
even more.
;Goertzel algorithm to calculate energy of DFT coefficient
;
;
;
data equ $100
COEF equ $123456
LOOP equ 256
org p:$40
move #data,r0 ;r0 -> input data
clr a #0,b ;I(n-1)=0,I(n-2)=0
move #COEF,y0 ;y0=cos(2pik/N)
do #LOOP,_END_GOERT
neg b y:(r0)+,a a,x1 ;x1=I(n-1),b=-I(n-2),a=x[i]/2
macr y0,x1,a x1,y1 ;a=x[i]/2 + I(n-1)*COEF,y1=I(n-1)
addl b,a x1,b ;a=x[i] + 2*I(n-1)*CEOF - I(n-2),b=I(n-1)
_END_GOERT
mpy -y0,x1,a a,x0 ;a=-con(2pik/N)I(n),x0=I(n)
mpy x1,y1,b ;b=I(n-1)^2
mac x0,x0,b a,y0 ;b=I(n)^2+I(n-1)^2
mpy x1,y0,a ;a= -con(2pik/N)I(n)I(n-1)
addl b,a ;a= power of magnitude of DFT
Figure 6-6 DSP56001 assembly code that calculates energy of DFT
coefficients by single parameter
From Figure 6-6, the last output of the IIR filter is:
k
y
k
( N)
=
IN ( ) – W
N
IN ( – 1)
Eqn. 6-15
MOTOROLA 6-19