#### Practical Considerations

While the digital mass simulator has the desirable properties of the bilinear transform, it is also not perfect from a practical point of view: (1) There is a pole at half the sampling rate (). (2) There is a delay-free path from input to output.

The first problem can easily be circumvented by introducing a loss factor , moving the pole from to , where and . This is sometimes called the leaky integrator''.

The second problem arises when making loops of elements (e.g., a mass-spring chain which forms a loop). Since the individual elements have no delay from input to output, a loop of elements is not computable using standard signal processing methods. The solution proposed by Alfred Fettweis is known as wave digital filters,'' a topic taken up in §F.1.

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