#### First-Order Delay-Filter Design

The first-order case is very simple while enabling separate control of low-frequency and high-frequency reverberation times. For simplicity, let's specify and , denoting the desired decay-time at dc () and half the sampling rate ( ). Then we have determined the coefficients of a one-pole filter:

The dc gain of this filter is , while the gain at is . From Eq.(3.9) (or Eq.(3.8)), we obtain two equations in two unknowns:

where denotes the th delay-line length in seconds. These two equations are readily solved to yield

The truncated series approximation

has been found to work well in practical FDN reverberators.

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Orthogonalized First-Order Delay-Filter Design
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Damping Filters for Reverberation Delay Lines