用汇编实现FFT

FFT（快速傅里叶变换）是一种复杂的算法，用汇编实现需要耗费大量时间和精力。下面是一个简单的例子，可以实现8点FFT：

;=============================================
; 8-point FFT in assembly language
;=============================================

.model small
.stack 100h

.data
x_real dw 4, 0, 4, 0, 4, 0, 4, 0
x_imag dw 0, 0, 0, 0, 0, 0, 0, 0
w_real dw 8, 0, -1, 7, 0, -8, 1, -7
w_imag dw 0, -8, 7, -1, 8, 0, -7, 1

.code
main PROC
mov ax, @data
mov ds, ax

; do the FFT
call fft_8

mov ax, 4c00h
int 21h
main ENDP

;---------------------------------------------
; subroutines
;---------------------------------------------
fft_8 PROC
push ax
push bx
push cx
push dx

; first pass
mov cx, 4
mov dx, 2
L1:
mov bx, cx
L2:
mov ax, x_real[bx]
add ax, x_real[bx+dx]
mov x_real[bx+dx], ax
sub ax, x_real[bx]
mov x_real[bx], ax
mov ax, x_imag[bx]
add ax, x_imag[bx+dx]
mov x_imag[bx+dx], ax
sub ax, x_imag[bx]
mov x_imag[bx], ax
add bx, dx
cmp bx, 8
jle L2
sub cx, 1
cmp cx, 0
jne L1

; second pass
mov cx, 2
mov dx, 4
L3:
mov bx, cx
mov ax, x_real[bx]
mov si, w_real[bx]
mov di, w_imag[bx]
mov bx, dx
L4:
mov bp, x_real[bx]
mov bx, x_imag[bx]
mov bl, dil
mov bh, sih
mov si, x_real[bx]
mov di, x_imag[bx]
mov cl, dil
mov ch, sih
mov ax, bp
mul cl
mov bp, ax
mov ax, bx
mul bh
sub bp, ax
mov ax, si
mul ch
add bp, ax
mov ax, di
mul bl
add bp, ax
mov x_real[bx], bp
mov ax, bp
mov bx, si
mul dil
mov bp, ax
mov ax, di
mul sih
sub bp, ax
mov ax, bp
mov bx, si
mul sih
add ax, di
mov x_imag[bx], ax
add bx, dx
cmp bx, 8
jle L4
add cx, 1
cmp cx, 4
jle L3

pop dx
pop cx
pop bx
pop ax
ret
fft_8 ENDP

END main

上述代码实现了一个简单的8点FFT。实现FFT需要了解复数运算、旋转因子等一系列概念，因此需要有一定的数学和计算机基础。同时，汇编语言的代码相对于高级语言更加底层，需要更加细致的调试和优化。