1. Infinite impulse response filters, recursive filters
The recursive structure makes it possible to produce high-performance transfer functions with a low number of coefficients. However, these z-transfer functions have poles, and their stability is not automatic. The transfer function of an RII (infinite impulse response) filter is highly sensitive to coefficient errors, the higher its degree. In practice, it is difficult to ensure the stability of such a filter with 16-bit coefficients if the degree reaches or exceeds three. In most cases, therefore, a recursive filter is constructed by connecting first- and second-order cells in series.
In what follows, we'll assume that the z-transform of a product of first- and second-order p-transfer functions is the product of the z-transforms of each of the p-functions.
In the vast majority of cases, a recursive...
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Infinite impulse response filters, recursive filters
Fourier transform filtering
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