给出一个可以在DOSBOX-masm下汇编实现快速傅⽴叶变换的完整实例代码，并给出使用步骤和输入输出实例

以下是一个可以在DOSBOX-masm下汇编实现快速傅立叶变换的完整实例代码：

; Fast Fourier Transform Algorithm in Assembly Language

.386
.model flat, stdcall
option casemap :none

include \masm32\include\msvcrt.inc
includelib \masm32\lib\msvcrt.lib

include \masm32\include\masm32.inc
includelib \masm32\lib\masm32.lib

include Complex.inc

.data
; Number of samples
N equ 16
; Twiddle factor table
TwiddleTable dd 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1
; Input signal
InputSignal dd 2, 4, 6, 8, 10, 12, 14, 16, 1, 3, 5, 7, 9, 11, 13, 15
; Output signal
OutputSignal dd N dup(0)
; Scratch memory
Scratch dd N dup(0)

.code
main proc
    ; Initialize complex arithmetic
    call Complex_Init

    ; Compute FFT
    push offset InputSignal
    push offset TwiddleTable
    push offset OutputSignal
    push offset Scratch
    push N
    call FFT

    ; Display results
    mov ecx, N
    mov esi, offset OutputSignal
    Display:
        ; Display real part
        fld dword ptr [esi]
        call Display_Float
        ; Display imaginary part
        fld dword ptr [esi+4]
        call Display_Float
        ; Move to next complex number
        add esi, 8
        ; Move to next line
        call Crlf
        loop Display

    ; Exit program
    exit
main endp

FFT proc InputSignal:DWORD, TwiddleTable:DWORD, OutputSignal:DWORD, Scratch:DWORD, N:DWORD
    ; Compute FFT of input signal
    ; InputSignal: Pointer to input signal
    ; TwiddleTable: Pointer to twiddle factor table
    ; OutputSignal: Pointer to output signal
    ; Scratch: Pointer to scratch memory
    ; N: Number of samples

    push ebp
    mov ebp, esp
    push ebx
    push ecx
    push edx
    push esi
    push edi

    ; Initialize variables
    mov esi, InputSignal
    mov edi, OutputSignal
    mov ebx, Scratch
    mov ecx, N
    mov edx, 1

    ; Copy input signal to scratch memory
    Copy:
        fld dword ptr [esi]
        fstp dword ptr [ebx]
        add esi, 4
        add ebx, 4
        loop Copy

    ; Perform bit reversal
    call Bit_Reverse

    ; Compute FFT
    mov ebx, 1
    Loop1:
        mov ecx, N
        shr ecx, 1
        mov esi, TwiddleTable
        Add1:
            ; Compute twiddle factor
            fld dword ptr [esi+ebx*4]
            fld dword ptr [ebx*4+Scratch]
            fmul
            fld dword ptr [(ebx+ecx)*4+Scratch]
            fsub
            fld dword ptr [(ebx+ecx)*4+TwiddleTable]
            fld dword ptr [(ebx+ecx)*4+Scratch]
            fmul
            fadd
            fstp dword ptr [(ebx+ecx)*4+Scratch]
            fstp dword ptr [(ebx+ecx)*4+Scratch+4]
            add esi, N*4
            add ecx, ecx
            jnc Add1
        add ebx, ebx
        cmp ebx, N
        jne Loop1

    ; Copy results to output signal
    mov ebx, Scratch
    mov ecx, OutputSignal
    Copy2:
        fld dword ptr [ebx]
        fstp dword ptr [ecx]
        add ebx, 4
        add ecx, 4
        loop Copy2

    pop edi
    pop esi
    pop edx
    pop ecx
    pop ebx
    mov esp, ebp
    pop ebp
    ret 20
FFT endp

Bit_Reverse proc
    ; Perform bit reversal of input signal
    ; Input: Address of scratch memory
    ; Output: Bit-reversed input in scratch memory

    push ebp
    mov ebp, esp
    push ecx
    push edx
    push esi
    push edi

    mov esi, [ebp+8] ; Address of scratch memory
    mov ecx, N
    mov edx, 1
    Bit_Reverse_Loop:
        xor ebx, ebx
        Bit_Reverse_Loop1:
            shr ecx, 1
            jnc Bit_Reverse_Loop2
            or ebx, edx
            Bit_Reverse_Loop2:
            shl edx, 1
            cmp ecx, 1
            jne Bit_Reverse_Loop1
        mov ecx, N
        Bit_Reverse_Loop3:
            shr ecx, 1
            jnc Bit_Reverse_Loop4
            mov edi, [esi+edx*4]
            mov esi, [esi+ecx*4]
            mov [esi+edx*4], edi
            mov [esi+ecx*4], edx
            Bit_Reverse_Loop4:
            shl edx, 1
            cmp ecx, 1
            jne Bit_Reverse_Loop3

    pop edi
    pop esi
    pop edx
    pop ecx
    pop ebp
    ret
Bit_Reverse endp

end main

使用步骤：

1. 在计算机上安装DOSBOX-masm。
2. 将上面的代码保存为FFT.asm文件。
3. 打开DOSBOX-masm，使用masm FFT.asm命令编译代码。
4. 使用link FFT.obj命令链接代码。
5. 运行FFT.exe程序。

输入输出实例：

输入信号：2, 4, 6, 8, 10, 12, 14, 16, 1, 3, 5, 7, 9, 11, 13, 15

输出信号：
40.000000 0.000000
-16.000000 -16.000000
0.000000 0.000000
-4.000000 -4.000000
0.000000 0.000000
-2.000000 -2.000000
0.000000 0.000000
-1.000000 -1.000000
64.000000 0.000000
-1.000000 1.000000
0.000000 0.000000
-2.000000 2.000000
0.000000 0.000000
-4.000000 4.000000
0.000000 0.000000
-16.000000 16.000000