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## Elementary non-recirculating filter

We generalize the non-recirculating comb filter to the design shown in figure 8.7, called the non-recirculating elementary filter, of the first form.

To find the frequency response, as in Chapter 7 we feed the delay network a complex sinusoid whose frequency is , so that as before, . The th sample of the input is and that of the output is

so the transfer function is

This can be represented graphically as shown in Figure 8.8. Suppose we write the coefficient in polar form:

Then the gain of the filter is the distance from the point to the point in the complex plane. Analytically we can see this because

Graphically, the number is just the number rotated backwards (clockwise) by the angular frequency of the incoming sinusoid. The value is the distance from to in the complex plane, which is equal to the distance from to .

As the frequency of the input sweeps from 0 to , the point travels couterclockwise around the unit circle. At the point where , the distance is at a minimum, equal to . The maximum occurs which is at the opposite point of the circle. Figure 8.9 shows the transfer function for three different values of .

Next: Non-recirculating filter, second form Up: Designing filters Previous: Designing filters   Contents   Index
Miller Puckette 2005-04-01