IIR Filter Topology

Publish Date: Sep 08, 2008 | 16 Ratings | 2.31 out of 5 | Print | Submit your review

Overview

This example illustrates the effects of filter topology, order, filter type, and other characteristics important to digital filter design. A broadband white noise signal (power spectral density constant over all frequencies) sent through the filter shows the frequency response of the filter. The user can define the filter to be lowpass, highpass, bandpass or bandstop and can interactively change the filter characteristics. The example shows the response of several IIR filter topologies.

Background

Digital filter design, as with all other engineering practices, involves tradeoffs. For instance, Finite Impulse Response (FIR) filters are simple, and can be designed to provide a linear phase response or constant group delay. Infinite Impulse Response (IIR) filters might achieve the same levels of attenuation as FIR filters with fewer coefficients. This means that the IIR filter can be implemented more efficiently. The different filter topologies discussed below are explored in this example. However, if the design requires constant group delay (linear phase), guaranteed stability, or multi band specifications, then the designer should consider using FIR filters before using these IIR filter topologies.

Butterworth

The Butterworth topology seeks to flatten the frequency response in the passband as much as possible while decreasing the transition band and stop band monotonically. For instance, if the filter type is set to be a lowpass filter, then the amplitude response of the lower frequencies will be a raised flat line before steadily decreasing at a constant rate, beginning at the low frequency cut-off through the stop band. The transition band is inversely proportional to the filter order; therefore, increasing the filter order results in a sharper constant decrease rate between the lowpass cut-off and the stop band.

Chebyshev & Inverse Chebyshev

The Chebyshev topology can improve the transition band rolloff by allowing ripples in the passband. Contrast this with the Inverse Chebyshev which improves the transition band by allowing ripples in the stop band. Increasing the filter order improves transition band performance for both Chebyshev and Inverse Chebyshev but increases the ripple in either the passband or stopband, respectively.

Elliptical

The Elliptical topology permits ripple in both the passband and stopband while still seeking to optimize the transition band.

Bessel

The Bessel topology is designed to optimize constant group delay characteristics. Thus, the Bessel Filter approximates linear phase characteristic of FIR filters while still using the fewer coefficients characteristic of IIR filters. The tradeoff is in the flatness of the passband and sharpness of the transition band, both of which are not as optimized as in the other topologies.

The following diagram summarizes this discussion from the perspective of digital filter design:

For more information on IIR filters, see: http://zone.ni.com/reference/.../lvanlsconcepts/iir_filters/

Demonstration

1. Create a lowpass Butterworth filter by setting the following under the IIR filter specifications. Topology: Butterworth, Type: Lowpass, Order: 8, Lower Frequency: 500, Upper Frequency: 2.00k, Pass Band Ripple: 20, Stop Band Attenuation: 60

2. Change the filter topology to each of the topologies mentioned above and observe the Frequency Response and Phase Response graphs. Compare the graph results to the description for that particular topology.

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IIR_Filter_Design.vi

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