Nonseparable Three-Dimensional IIR Notch Filter Design Using Outer Product Expansion

Abstract

This brief emphasizes on the 3-D digital notch filter design problem. A standard form of notch filter design is presented in nonseparable form. A rank reduction technique is conducted to expand the 3-D design problem. The 3-D digital notch problem is initially expanded into the 2-D and 1-D filter design problems. Then, the 2-D problem is expanded again into two 1-D problems by using the singular value decomposition technique. A simple algebraic method is subsequently used to approximate and design each 1-D infinite impulse response (IIR) notch filter. These individual 1-D IIR notch designs are finally combined to construct a standard form of 3-D digital notch filter design. The purposed system not only has a closed-form transfer function but also satisfies bounded-input-bounded-output stability condition. At the end of this brief, the simulation of the purposed magnitude response is presented, together with implementation on a 3-D image.