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What is the difference between the canonical form and the direct form of implementations of a...

What is the difference between the canonical form and the direct form of implementations of a recursive difference equation? If a signal is delayed and added to itself, we may perceive it either as a single sound or as two separate sounds. What does it depend on?

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The canonical form implementation uses the minimal amount of delays, adders and multipliers in comparison with direct form implementation of a recursive difference equation.  Direct Form is well suitable for fixed point implementations, whereas canonical form is well suitable for floating point implementations. If a signal is delayed and added to itself, we may perceive it either as a single sound or as two separate sounds.

The perception depends on the delay time. if delay time is such that sampling theroem is satisfied , ie., if the sampling frequency is greater than twice the signal frequency, the same sound will be heard with delay.

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