### More General Allpass Filters

We have so far seen two types of allpass filters:- The series combination of feedback and feedforward comb-filters is allpass when their delay lines are the same length and their feedback and feedforward coefficents are the same. An example is shown in Fig.2.30.
- Any delay element in an allpass filter can be replaced by an allpass filter to obtain a new (typically higher order) allpass filter. The special case of nested first-order allpass filters yielded the lattice digital filter structure of Fig.2.32.

**Definition:**A linear, time-invariant filter is said to be

*lossless*if it

*preserves signal energy*for every input signal. That is, if the input signal is , and the output signal is , we must have

*causal*

^{3.14}for simplicity. It is straightforward to show the following: It can be shown [449, Appendix C] that stable, linear, time-invariant (LTI) filter transfer function is lossless if and only if

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Example Allpass Filters

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Nested Allpass Filters