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首页> 外文会议>2nd IET International Conference on Intelligent Signal Processing 2015 >Generalized distributions, sampling theorem revisited and an end to an impulse invariance error
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Generalized distributions, sampling theorem revisited and an end to an impulse invariance error

机译：广义分布，重新讨论采样定理，并结束了脉冲不变性误差

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摘要

Recently proposed generalized Functions of a complex variable extend the domains of existence of Laplace and z-transform. In this paper, basic properties of generalized distributions are extended. In particular, properties of generalized distributions in the context of sampling functions containing discontinuities are explored. Laplace and z-transforms of one-sided, two-sided periodic and exponentially modulated periodic impulses, hitherto nonexistent, and of which the Fourier transform does not exist, are evaluated using generalized distributions. Applications to the formulation of the sampling theorem are explored. The generalized distributions are shown to reveal an unusual anomaly in the well-known digital filtering approach of impulse invariance. The anomaly arises when Laplace and z-transform spectra are compared with the Mittag-Leffler Expansion. It is shown that the transformation, as is presently applied, does not produce the stated Fourier spectrum of the sampled signal. In fact it produces more spectral aliasing than claimed, and not the minimum desired. In converting an analog filter of even a small order to a digital filter, an appreciable spectral deviation error is produced. A new approach to impulse invariance, eliminating the error, is proposed. Matlab© still uses the erroneous approach. A generalization is effected to cover a wide class of one-sided, two sided and finite duration signals.
机译：最近提出的复杂变量的广义函数扩展了Laplace和z变换的存在域。本文扩展了广义分布的基本性质。特别地，在包含不连续性的采样函数的背景下，探索了广义分布的性质。使用广义分布对迄今不存在的，不存在傅立叶变换的一侧，两侧周期和指数调制周期脉冲的Laplace和z变换进行评估。探索了采样定理公式的应用。所示的一般分布揭示了在脉冲不变性的众所周知的数字滤波方法中的异常异常。将拉普拉斯光谱和z变换光谱与Mittag-Leffler展开进行比较时会出现异常。可以看出，目前所应用的变换没有产生所述采样信号的傅立叶频谱。实际上，它会产生比要求的更多的频谱混叠，而不是所需的最小值。在将甚至小阶的模拟滤波器转换为数字滤波器时，都会产生明显的频谱偏差误差。提出了一种消除误差的脉冲不变性的新方法。 Matlab©仍然使用错误的方法。进行概括可以覆盖一类广泛的单面，双面和有限持续时间信号。

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