What are the differences between modern and classical filter theory?

Question

Anything will do. Brevity and exposition are equally appreciated.

Answer 1

I'll speak a bit more to the general control theory as I'm slightly more familiar with that topic. I'll try to add bits more relevant to filter theory as I think of them.

In classical control theory, we think of both the time domain representation of signals as well as the frequency / laplace domain view of signals. We design filters that are physically realizable through resistors, inductors and capacitors. Classical control theory may often be associated with PID controllers and compensation networks.

In modern control theory, we often describe systems through a state space representation. This is more akin to a differential set of equations expressed in matrix form. This leads to many possibilities of using linear algebra such as least squares estimators, optimal control schemes. See something like Kalman Filter might be a good example of this. State space also scales very well to systems with many variables, where as it might be harder to design such control schemes with classical control.

With regard to modern filter design, one of the major shifts, I think, would be digital signal processing. Rather than implementing filters in the analog domain, we can quantize signals to bring them into the digital domain, apply discrete filters, and then return back to the analog domain. This has benefits as we don't suffer from parasitics on filter components, we can control parameters more precisely than in the analog space. Here's a link that describes some of the pros and cons of analog vs digital filters

Answer 2

I think, it is not so easy to distinguish between "modern" and "classical" filter theory. Or do you mean filter "techniques"? As far as the theory of electrical filters is concerned, I think we can say the following:

• The "classical" theory is based on various alternatives for lowpass approximations (Butterworth, Chebyshev,...) to be realized as RLC ladder topolgies - developed in the first half of the 20th century (Brune, Cauer, Dasher, Darlington, Fialkov, Guillemin,..).

• The "modern" methods for realizing filter functions are characterized by three important development steps:

(a) Replacement of passive inductors (resp. the function of the inductors) by amplifiers (integrated opamps) in classical RLC structures: (a1) GIC techniques (GIC: Generalized impedance converter) as well as (a2) FDNR methods (Frequency Dependent Negative Resistors) - in conjunction with the famous/genious Bruton-transformation.

(b) Development of many novel active RC topologies for realizing conjugate-complex poles and zeros (starting with Sallen & Key in 1955).

(c) Fully integated filter topologies using (c1) switched-capacitor techiques (for replacing resistors) or (c2) OTA-C (gm-C) structures for simulating the role of the resistors.

Answer 3

Here is a quote from "Introduction to Filter Theory" by David Johnson, Prentice Hall, 1976.

Filter theory had its beginning in 1915 when Campbell in America and Wagner in Germany independently invented the electric-wave filter. The theory has evolved essentially along two independent lines, known in the literature as classical filter theory and modern filter theory. The classical theory was developed in the 1920s by Campbell, Zobel, and others, and is concerned with the design of passive lumped filters using the method of image-parameters.

Modern filter theory, developed in the 1930s by Cauer, Darlington, and others, is more general and more efficient than the classical theory. Essentially, it involves the approximation of the filter specifications by a transfer function, and the design of a network, using exact methods, which realizes the transfer function.

The transfer functions Johnson is referring to are the Butterworth, Chebyshev, Bessel, etc, polynomials.

Here is another quote from "The Analysis, Design, and Synthesis of Electrical Filters", by DeVerl Humpherys, Prentice Hall, 1970.

Within the 3-year interval 1938 to 1941, several contributers-Darlington in America, Cocci in Italy, Cauer and Piloty in Germany, essentially remolded the die of filter theory when they independently developed the so-called insertion-loss theory of filters. This approach, which starts from a prescribed insertion-loss function, was in sharp contrast to the building-block method of the image-parameter design.

In contrast to Zobel's earlier filter designs, the insertion-loss design was slow to be accepted. One reason for this was the horrendous amount of arithmetic involved.

In the immediate postwar period and mid-1950s an attempt was made to exploit the advantages of the insertion-loss filter design. The classic all-pole Chebyshev and Butterworth low-pass filter-element values were tablulated.

The insertion-loss design, however, did not really become popular until the advent of the digital computer. With the burden of performing lengthy arithmetic calculations on a desk calculator removed, the new design techniques could be used to quickly synthesize optimal filters which satisfied a given specification with a minimum complexity.