{'fraction_non_alphanumeric': 0.02043132803632236, 'fraction_numerical': 0.0, 'mean_word_length': 4.705501618122978, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Non-Canonical Topography of the z-Plane Discretized due to Quantization of the IIR Digital Filter Coefficients

It is known that all possible positions of the zeros and poles of IIR digital filters with finite word length form some discrete structure in z-plane. In this paper, this structure is called the z-plane topography. Discretization of the z-plane is explained by the fact that, due to quantization of the filter coefficients, not any of its points can be a zero or a pole. In their previous publications, the authors showed that for practically implemented digital filters, zeros and poles are elements of the algebraic number set. It was also shown that the topography of the sampled z-plane is completely determined by the degree of algebraic numbers and the bitness of fractional part of the transfer function coefficients. The corresponding topography is proposed to be called canonical. At the same time, structures are known for which the topography differs from the canonical one. For them, the name of non-canonical topography is suggested. These structures include the structure known as the coupled form, the normal form, the structure of Gold and Raider. This article is devoted to the study of such structures. It may seem that this is a completely new topography, not connected with the canonical one. However, this is not true. This paper establishes the relationship between the canonical topography and the topography of the coupled and other structures. It is shown that the coefficients of such structures are not independent. They are related by some additional equations. As a result, the number of possible zeros and poles is reduced. But the remaining zeros and poles are elements of the set that make up the canonical topography.