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Another Proof of Ambiguity of the Formula Describing Aliasing and Folding Effects in Spectrum of Sampled Signal

Borys Andrzej

International Journal of Electronics and Telecommunications

2022

Vol. 68, No. 1

115--122

In this paper, a new proof of ambiguity of the formula describing the aliasing and folding effects in spectra of sampled signals is presented. It uses the model of non-ideal sampling operation published by Vetterli et al. Here, their model is modified and its black-box equivalent form is achieved. It is shown that this modified model delivers the same output sequences but of different spectral properties. Finally, a remark on two possible understandings of the operation of non-ideal sampling is enclosed as well as fundamental errors that are made in perception and description of sampled signals are considered.

Spectrum Aliasing Does Occur Only in Case of Non-ideal Signal Sampling

Borys Andrzej Marek

International Journal of Electronics and Telecommunications

2021

Vol. 67, No. 1

79--85

In this paper, it has been shown that the spectrum aliasing and folding effects occur only in the case of non-ideal signal sampling. When the duration of the signal sampling is equal to zero, these effects do not occur at all. In other words, the absolutely necessary condition for their occurrence is just a nonzero value of this time. Periodicity of the sampling process plays a secondary role.

Spectrum Aliasing Does not Occur in Case of Ideal Signal Sampling

Borys Andrzej Marek

International Journal of Electronics and Telecommunications

2021

Vol. 67, No. 1

71--77

A new model of ideal signal sampling operation is developed in this paper. This model does not use the Dirac comb in an analytical description of sampled signals in the continuous time domain. Instead, it utilizes functions of a continuous time variable, which are introduced in this paper: a basic Kronecker time function and a Kronecker comb (that exploits the first of them). But, a basic principle behind this model remains the same; that is it also a multiplier which multiplies a signal of a continuous time by a comb. Using a concept of a signal object (or utilizing equivalent arguments) presented elsewhere, it has been possible to find a correct expression describing the spectrum of a sampled signal so modelled. Moreover, the analysis of this expression showed that aliases and folding effects cannot occur in the sampled signal spectrum, provided that the signal sampling is performed ideally.