Scale periodicity and its sampling theorem
Scale periodicity and its sampling theorem
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DOI：
10.1109/78.599961
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发表时间：
1997-07
期刊：
影响因子：
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通讯作者：
H. Sundaram;S. Joshi;R. Bhatt
中科院分区：
文献类型：
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作者：
H. Sundaram;S. Joshi;R. Bhatt
标量变换是信号的一种新的表示形式，它提供了一种不同于傅里叶变换的视角。我们引入标量周期函数的概念。然后用离散尺度级数表示这些函数。我们还定义了严格尺度限制信号的概念。与香农插值公式类似，我们证明了这种信号可以在时域内从指数间隔的信号样本中精确地重建。作为一个有趣的实际应用，我们展示了尺度变换的独特属性如何使其在计算场景的深度图时非常有用。
The scalar transform is a new representation for signals, offering a perspective that is different from the Fourier transform. We introduce the notion of a scalar periodic function. These functions are then represented through the discrete scale series. We also define the notion of a strictly scale-limited signal. Analogous to the Shannon interpolation formula, we show that such signals can be exactly reconstructed from exponentially spaced samples of the signal in the time domain. As an interesting, practical application, we show how properties unique to the scale transform make it very useful in computing depth maps of a scene.