论文标题
离散的贝塞尔功能并转换
Discrete Bessel functions and transform
论文作者
论文摘要
我们提出了bessel函数的直接离散化$ j_n（x）$ to离散对应物$ b^{（n）} _ n（x_m）$，$ n $ integer订单$ n $ n $ integer点上的$ n $ n $ n $ integer点$ x_m \ equiv m $，我们呼吁ivest ivestect bessel bessel bessel functions。这些是由Bessel积分生成功能构建的，将圆圈的傅立叶变换限制在$ n $点上。我们表明，离散的贝塞尔函数满足了几种线性和二次关系，尤其是Graf的乘积置换公式，它们是连续函数之间众所周知关系的确切类似物。值得注意的是，这些离散的贝塞尔函数非常接近近似于$ n + | m |中连续函数的值。 <n $。对于固定的$ n $，这提供了订单和位置功能之间的$ n $点转换，$ f_n $和$ \ widetilde {f} _m $，这对于有限衰减信号的傅立叶分析非常有效。
We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built from a Bessel integral generating function, restricting the Fourier transform over the circle to $N$ points. We show that the discrete Bessel functions satisfy several linear and quadratic relations, particularly Graf's product-displacement formulas, that are exact analogues of well-known relations between the continuous functions. It is noteworthy that these discrete Bessel functions approximate very closely the values of the continuous functions in ranges $n + |m| < N$. For fixed $N$, this provides an $N$-point transform between functions of order and of position,$f_n$ and $\widetilde{f}_m$, which is efficient for the Fourier analysis of finite decaying signals.
