Digital Signal Processing/Analog Filter Design

It may seem strange to have a section devoted to analog filter design in a digital signal processing book. However, there is a method to the madness. It turns out that digital filters can be modeled using analog filters, and analog techniques—which have been studied in depth for many years prior to digital systems—can be utilized to quickly and efficiently design digital filters.

The following chapters will show some of the techniques involved in designing analog filters, and transforming analog filters from one type to another. The section will culminate on a chapter on the bilinear transform, which transforms the mathematical representation for an analog filter into the equations for an equivalent digital filter.

Analog Design Process

Digital filters can be designed using analog design methods by following these steps:

1. Filter specifications are specified in the digital domain. The filter type (highpass, lowpass,bandpass etc.) is specified.
2. An equivalent lowpass filter is designed that meets these specifications.
3. The analog lowpass filter is transformed using spectral transformations into the correct type of filter.
4. The analog filter is transformed into a digital filter using a particular mapping.

There are many different types of spectral transformations and there are many mappings from analog to digital filters. the most famous mapping is known as the bilinear transform, and we will discuss that in a different chapter.

Butterworth

Butterworth ensures a flat response in the passband and an adequate rate of rolloff. A good "all rounder," the Butterworth filter is simple to understand and suitable for applications such as audio processing.

Chebyshev I

The Chebyshev 1 filter has ripple in the passband of the filter.

Chebyshev II

Chebyshev 2 has ripple in the stopband.

Elliptic

This filter has equiripple (the same amount of ripple in the passband and stopband).

Further reading

• Signals and Systems