fortran 实现汉克尔变换

汉克尔变换是一种数学变换，用于将时域信号转换为频域信号。Fortran可以使用快速傅里叶变换（FFT）算法来实现汉克尔变换。

以下是Fortran代码示例：

program hankel_transform
    implicit none
    integer :: i, j, n
    real :: pi, dx, x_min, x_max
    real, dimension(:), allocatable :: x, h, f, g

    ! 初始化变量
    n = 1000
    pi = 3.14159265358979323846
    x_min = 0.0
    x_max = 10.0*pi
    dx = (x_max-x_min)/real(n-1)
    allocate(x(n))
    allocate(h(n))
    allocate(f(n))
    allocate(g(n))

    ! 生成数据
    do i = 1, n
        x(i) = x_min + dx*real(i-1)
        f(i) = sin(x(i))
    end do

    ! 计算汉克尔变换
    do i = 1, n
        h(i) = 0.0
        do j = 1, n
            h(i) = h(i) + f(j)*besselj0(x(i)*x(j))/x(j)
        end do
    end do

    ! 输出结果
    do i = 1, n
        write(*,*) x(i), h(i)
    end do

    ! 释放内存
    deallocate(x)
    deallocate(h)
    deallocate(f)
    deallocate(g)

contains

    ! Bessel函数
    real function besselj0(x)
        real :: x, sum, term
        integer :: k, n

        n = 100
        sum = 0.0
        do k = 0, n
            term = (-1.0)**k/(factorial(k)*factorial(k))*x**(2*k)
            sum = sum + term
        end do
        besselj0 = sum
    end function besselj0

end program hankel_transform

该代码使用了Bessel函数来计算汉克尔变换。首先生成1000个sin函数值，然后通过循环计算每个汉克尔变换的值。最后输出结果。