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## Prefabricated low-, high-, and band-pass filters

Patches H01.low-pass.pd, H02.high-pass.pd, and H03.band-pass.pd (Figure 8.28) show Pd's built-in filters, which implement filter designs described in Sections 8.3.1, 8.3.2 and 8.3.4. Two of the patches also use a noise generator we have not introduced before. We will need four new Pd objects:

: one-pole low-pass filter. The left inlet takes a signal to be filtered, and the right inlet takes control messages to set the cutoff frequency of the filter. The filter is normalized so that the gain is one at frequency 0.

: one-pole, one-zero high-pass filter, with the same inputs and outputs as `lop~`, normalized to have a gain of one at the Nyquist frequency.

: resonant filter. The middle inlet takes control messages to set the center frequency, and the right inlet to set "q".

: white noise generator. Each sample is an independent pseudo-random number, uniformly distributed from -1 to 1.

Figure 8.28: Using prefabricated filters in Pd: (a) a low-pass filter, with white noise as a test input; (b) using a high-pass filter to remove a signal component of frequency 0.

The first three example patches demonstrate these three filters (see Figure 8.28). The `lop~` and `bp~` objects are demonstrated with noise as input; `hip~` as shown is used to remove the DC (zero frequency) component of a signal.

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