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首页> 外文期刊>WSEAS Transactions on Signal Processing >Gaussian Circular 2D FIR Filters Designed Using Analytical Approach
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Gaussian Circular 2D FIR Filters Designed Using Analytical Approach

机译：高斯圆形2D FIR滤波器使用分析方法设计

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摘要

This paper proposes an analytical design procedure for a particular class of 2D filters, namely Gaussian-shaped FIR filters with circular symmetry. We approach both the low-pass and band-pass circular filters, which are adjustable in selectivity and peak frequency. The design starts from a specified 1D Gaussian prototype filter, approximated efficiently using Chebyshev series. A frequency transformation expressed in matrix form is applied to the prototype, generating the circular filter. These approximations and frequency mappings lead directly to the transfer function or frequency response of the circular filter with desired characteristics. Several relevant design examples are provided for both types of filters. The filters designed through this method are accurate in shape and efficient, of relatively low order, and their frequency response results in either a factored or nested form, convenient for implementation. Due to this parametric approach, the designed 2D filters are adjustable, therefore by changing the specifications, new 2D circular filters result in a straightforward manner and the design need not be resumed each time from the start, as generally is the case with most numerical optimization techniques.
机译：本文提出了一种特殊的二维滤波器的分析设计方法，即具有圆对称性的高斯型FIR滤波器。我们探讨了低通和带通圆形滤波器，它们的选择性和峰值频率都是可调的。该设计从一个指定的一维高斯原型滤波器开始，使用切比雪夫级数有效地逼近。将矩阵形式的频率变换应用于原型，生成圆形滤波器。这些近似和频率映射直接导致具有所需特性的圆形滤波器的传递函数或频率响应。为这两种类型的过滤器提供了几个相关的设计示例。通过这种方法设计的滤波器形状准确，效率高，阶数相对较低，其频率响应结果为因子形式或嵌套形式，便于实现。由于这种参数化方法，所设计的二维滤波器是可调的，因此通过改变规格，新的二维圆形滤波器以简单的方式产生，并且不需要从一开始就恢复设计，这通常是大多数数值优化技术的情况。

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