IIR filters are typically obtained from well-established analog filter designs. This lesson will introduce you to the steps used by MATLAB to design IIR filters. Understanding these steps will enable you to design effective filters using software tools like MATLAB.

# IIR Filter Design

## Analog Filters Used for IIR Filter Design

In this lesson you will learn the characteristics of the four continuous-time or analog filters that are used as a starting point for discrete-time IIR filter design. The four filter types are Butterworth, Chebyshev I, Chebyshev II, and elliptic filters. They differ in the nature of their passband and stopband characteristics. Choosing one of these […]

## Continuous-Time Butterworth Filters

In this lesson you will learn the characteristics of continuous-time or analog Butterworth filters and how to design a Butterworth low-pass filter to satisfy passband and stopband constraints. The design procedure shows you how MATLAB chooses the filter order and cut-off frequency. Understanding the characteristics of the Butterworth filter is critical to deciding when to […]

## Continuous-Time Chebyshev and Elliptic Filters

In this lesson you will learn the characteristics of continuous-time or analog Chebyshev I, II, and elliptic filters. You will also learn how to design Chebyshev I and II low-pass filters to satisfy passband and stopband constraints. The design procedure shows you how MATLAB chooses the filter order, frequency and gain parameters. Understanding the characteristics […]

## Frequency Transformations for Continuous-Time Systems

Frequency transformations convert prototype lowpass filters to arbitrary lowpass, highpass, or bandpass filters. This lesson teaches you the three standard frequency transformations for continuous-time systems. You will learn why they work by studying the way they warp the frequency axis. Frequency transformations also exist for discrete-time systems. Continuous-time transformations are studied here to explain the […]

## The Bilinear Transform

A critical step in designing IIR filters is converting the continuous-time filter a discrete-time filter. In this lesson you will learn the bilinear transform, the most widely applicable method for converting a continuous-time transfer function to a discrete-time system function. The bilinear transform has several very desirable properties. Most importantly, if the continuous-time system is […]