A unified approach for the design of stable 1-D analog and digital filters having variable magnitude characteristics

A unified approach is presented that enables one to design analog and digital filters with variable magnitude characteristics. A basic signal-flow graph is given in which the forward transmittance branch can be a stable filter and the feedback transmittance is a variable constant. As there is a feedback loop, stability of the overall filter has to be ensured, which in turn determines the bounds of the constant in the feedback loop. This is determined by the partial fraction expansion of the ratio of even to odd (or odd to even) polynomials in the analog domain and the ratio of mirror-image to anti-mirror-image polynomials (or its reciprocal) of the denominator polynomial in the digital domain.<>