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A Method for Sampling and Reconstructing Analog Signals that Guarantees the Maximum Point-by-Point Reconstruction Error in Time Domain

An analog signal and reconstruction error technology, applied in the direction of digital-to-analog converter, analog-to-digital conversion, analog-to-digital converter, etc., can solve the problems that the Shannon theory cannot be directly applied, the signal spectrum information cannot be obtained completely, and cannot be obtained in advance , to achieve the effects of easy analysis and implementation, and controllable reconstruction errors

Inactive Publication Date: 2020-11-03
LANZHOU UNIVERSITY
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Problems solved by technology

In some applications, we cannot obtain the spectrum information of the signal in advance, so we cannot directly apply Shannon's theory
In addition, circuits that reconstruct analog signals often use constant or linear interpolation, such as literature [17], but the sinc function used for interpolation in Shannon's theory cannot be fully obtained in practice

Method used

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  • A Method for Sampling and Reconstructing Analog Signals that Guarantees the Maximum Point-by-Point Reconstruction Error in Time Domain
  • A Method for Sampling and Reconstructing Analog Signals that Guarantees the Maximum Point-by-Point Reconstruction Error in Time Domain
  • A Method for Sampling and Reconstructing Analog Signals that Guarantees the Maximum Point-by-Point Reconstruction Error in Time Domain

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Embodiment Construction

[0029] The present invention and its effects will be further described below in conjunction with the accompanying drawings.

[0030] Let's start with a brief review of Shannon's sampling theory. Given an analog signal x(t) to be sampled with a bandwidth of W, first define a sampling impulse sequence signal

[0031]

[0032] where the sampling period T is determined below so as to guarantee perfect reconstruction.

[0033] The spectrum of s(t) can be written as

[0034]

[0035] where the sampling rate f s =1 / T.

[0036] Then the resulting sampling sequence is

[0037]

[0038] x s The spectrum of (t) can then be written as

[0039]

[0040] where * is the convolution operation.

[0041] Formula (4) tells us that in order to get perfect reconstruction, we need the following two conditions:

[0042] 1)

[0043] f s ≥2W (5)

[0044] 2) put x s (t) through an ideal low-pass filter Th(t)

[0045]

[0046] in

[0047] and

[0048] Wc s -W (7)

[0049...

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Abstract

The invention provides a simulation signal sampling and reconstruction method capable of ensuring a time domain point-by-point maximum reconstruction error. After a to-be-sampled simulation signal x(t) is subjected to simulation first-order differentiating circuit a plurality of times, a maximum amplitude value of an output signal is solved through a simulation circuit to be used for calculating asampling period, the to-be-sampled simulation signal x(t) obtained after delaying is sampled according to the sampling period, and when reconstruction is conducted, a piecewise polynomial is formed by various sampling values according to a Lagrange interpolating polynomial to approximate the to-be-sampled continuous simulation signal x(t). The method is a pure time domain-based method and is usedfor conducting effective uniform sampling on the premise of ensuring the pointwise maximum reconstruction error.

Description

technical field [0001] The invention relates to the technical field of signal sampling, in particular to a method for sampling and reconstructing an analog signal that ensures the maximum reconstruction error point by point in the time domain. Background technique [0002] In this digital age, converting an analog signal to digital before processing or storing it has become almost a standard procedure. Signal sampling is an essential step in this conversion process. So far, the basic theory used to determine the sampling rate is the classic Shannon sampling theory for band-limited signals (such as literature [1], [2]). The core content of the theory can be described as follows: For any signal x(t) with bandwidth W, if the sampling rate f s At least 2W, then x(t) can be determined by its sampling point and sinc function Refactored out perfectly. Shannon's theory can be regarded as a frequency-domain-based tool in sampler design, because its analysis basis is based on the...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H03M1/12H03M1/66
CPCH03M1/1245H03M1/665
Inventor 王小燕万毅
Owner LANZHOU UNIVERSITY
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