Design of two‐dimensional digital filters with complex coefficients
Yoshiaki Baba, Shinichi Takahashi, Kazuo Imamura · Electronics and Communications in Japan (Part I Communications) · 1984
Abstract In the field of one‐dimensional signal processing, the concept of analytic signal has been introduced in order to yield a low‐pass expression for band‐pass‐type signals. This analytic signal is obtained by adding the Hilbert transform of the real numbers as the imaginary part to the original signal. One important property of this signal is that its Fourier transform vanishes for negative frequencies, i.e., it “appears only in the positive frequency axis.” This property is applied to the design of one‐dimensional digital filters. In this paper, a signal processing algorithm using two‐dimensional digital filters with complex coefficients is proposed. This is done by extending the concept of analytic signal to two dimensions; the processing uses the fact that its Fourier Transform “exists only in the right half‐plane of the two‐dimension frequencies plane” or, in the case of quadrantal symmetry, “only in the first quadrant of the two dimension frequencies plane.” Using this algorithm, the degree of freedom for the design of 2D filters is increased and closed design methods for circularly symmetric filters and various new fan filters are possible. Moreover, difficulties of presently known methods such as high‐order requirements and limitations upon the cutoff frequency are greatly relaxed.