IIR Too

Published:2011/8/12 0:51:00 Author:Amy From:SeekIC

Paul Goossens

In the digital domain, analogue signals can be easily manipulated without requir­ing different hardware for each operation (as is necessary for analogue circuits).

Other important advantages are that no noise is added during the operation (pro­vided it is programmed correctly) and that mathematical algorithms are easier to implement.

Unfortunately, the design of a digital fil­ter is not that straightforward. There are several methods for implementing a dig­ital filter. A relatively efficient filter imple­mentation is the IIR (Infinite Impulse Response) type. The filter is mathemati­cally represented as:

x(n] = a0-y[n] + a,-y[n-l]...-brx[n-l] -b2-x[n-2]...

Where x[n] is the output signal and y[n] is the input signal.

The values of the coefficients ax and bx determine the transfer function and therefore the characteristics of the filter. Calcu­lating the coefficients for a particular fil­ter is often a stumbling block for design­ers. To make this task much easier, we have written a program that not only calculates the coefficients for simple filters, but can also determine the frequency characteristic of IIR filters where the user calculated the coefficients themselves.

This software is available from the Free Downloads section at www.elektor-elec-tronics.co.uk under number 044050-1 (select month of publication). It does not need to be installed — double clicking the filename HRTool.exe is sufficient to launch the program. This program can simulate up to 10 different IIR filters. As an addi­tional bonus, it is possible to cascade mul­tiple filters in order to examine the total frequency characteristic.

Initially, after starting the program, all fil­ters are set as all-pass and without delay. At the top left you can see that filter1 is selected. The coefficients that are shown on the screen belong to this filter. To enter your own coefficients for this filter you only need to click the desired coefficient after which you can type in the new value. For example, try changing O) (the second value at the top of the column near a) from 0 to 0.5. Immediately after this change you will note that the graph of the frequency characteristic has changed.

At top left you can select another filter. Choose filter2. In the windows below it, the coefficients belonging to filter2 appear. This time change a1 to -0.5. There now appears a second frequency characteristic. This looks like the reverse of filter1. The color of each filter curve can be changed by clicking the button change color. This makes it easier to dis­tinguish the separate graphs.

In order to know what the total frequency characteristic will look like when a signal propagates through both these filters we can select filters 1 and 2 under the button cascade. Another curve will appear in the output window, which is the result of the two fillers cascaded. The program is not only able to simulate filters but can also generate 3 different types of simple fil­lers. These generators can be found under the menu generate. Here you can choose from bass-, mid- or treble-filters. With the bass and treble filter you can choose the cutoff frequency and the desired gain or attenuation. The bass filter provides gain or attenuation of frequencies lower than the cutoff point.

The tre­ble filter does the same for frequencies higher than the cutoff point. A practical example: first select filter num­ber 3, then choose generate followed by bass. In the window that appears, give the parameter frequency a value of 100 and gain a value of 5. Cain is the loca­tion where we enter the gain or attenua­tion (in dB). Nov/ click the button OK. The program will now quickly calculate the required coefficients. As a consequence the coefficients of filter 4 are changed and the result is shown in the graph. Gen­erating a treble filter follows exactly the same method.

Finally, the program can also design a mid filter. This filler provides gain/altenualion of signals around a specific fre­quency. When entering the parameters you will find, besides frequency and gain, a third parameter, namely Q. This repre­sents the quality factor of the filter. The higher the Q factor the narrower will be the frequency range of the filter. A Q fac­tor between 0.6 and 2 is typical for audio applications.

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