Sampling of Signals Bandlimited to a Disc in the Linear Canonical Transform Domain for IEEE Signal Processing Letters
Sampling of Signals Bandlimited to a Disc in the Linear Canonical Transform Domain for IEEE Signal Processing Letters
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DOI：
10.1109/lsp.2018.2875341
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发表时间：
2018-10
影响因子：
3.9
通讯作者：
A. Zayed
中科院分区：
文献类型：
--
作者：
A. Zayed
我们推导了在线性正则变换（LCT）域中带宽限制为半径为$R$的圆盘的信号的采样公式。通过LCT域内圆盘$D$中的带宽限制，我们的意思是信号$f(t)$的LCT $F(\omega)$在圆盘$D.$外消失。我们首先用极坐标表示信号，然后得到采样公式。角度$\theta$的采样点在单位圆上的$2N+1$均匀分布点，径向距离$r$的采样点在贝塞尔函数零点处。作为一种特殊情况，我们得到了分数阶傅里叶变换域中带宽限制在圆盘上的信号的采样公式。
We derive sampling formula for signals that are bandlimited to a disc of radius $R$ in the linear canonical transform (LCT) domain. By bandlimitedness in a disc $D$ in the LCT domain, we mean that the LCT $F(\omega)$ of a signal $f(t)$ vanishes outside the disc $D.$ We first express the signal in polar coordinates and then obtain the sampling formula. The samples of the angle $\theta$ are taken at $2N+1$ uniformly distributed points on the unit circle while the samples of the radial distance $r$ are taken at the zeros of the Bessel function. As a special case, we obtain sampling formula for signals that are bandlimited to a disc in the fractional Fourier transform domain.