# Time Assignment Speech Interpolation System Mechanic Professional

Introduction, Uncertainty, Imprecision and Vagueness, Fuzzy systems, Brief history of Fuzzy logic, Foundation of Fuzzy Theory, Fuzzy Sets and Systems, Fuzzy Systems in Commercial Products, Research Fields in Fuzzy Theory, Classical sets and Fuzzy sets, Classical Relations, Fuzzy relations, Membership Functions, Fuzzy to crisp conversions, Fuzzy arithmetic, Numbers, Vectors and the extension principle, Classical logic and Fuzzy logic, Mathematical background of Fuzzy Systems, Classical (Crisp) vs, Fuzzy sets, Representation of Fuzzy sets, Types of Membership Functions, Basic Concepts (support, singleton, height, a-cut projections), Fuzzy set operations, S-and T- Norms, Properties of Fuzzy sets, Sets as Points in Hypercube, Cartesian Product, Crisp and Fuzzy Relations, Examples, Liguistic variables and hedges, Membership function design. Basic Principles of Inference in Fuzzy Logic, Fuzzy IF-THEN Rules, Canonical Form, Fuzzy Systems and Algorithms, Approximate Reasoning, Forms of Fuzzy Implication, Fuzzy Inference Engines, Graphical Techniques of Inference, Fuzzyifications/ DeFuzzification, Fuzzy System Design and its Elements, Design options. Fuzzy Events, Fuzzy Measures, Possibility Distributions as Fuzzy Sets, Possibility vs, Probability, Fuzzy Systems as Universal Approximators, Additive Fuzzy Systems (standard additive model).

In telecommunication, a **time-assignment speech interpolation** (TASI) was an analog technique used on certain long transmission links to increase voice-transmission capacity.

TASI takes advantage of the fact that in typical person-person conversation, speech in a single direction occurs for approximately 40% of the time, the remaining time being occupied with pauses and/or silence. Statistical analysis demonstrated that for an average voice channel usage of 40%, over 74 speech conversations could be handled using 37 full Duplex speech circuits^{[1]} thereby doubling potential revenue for a small capital outlay relative to a highly expensive cable. e.g. £12.5 million (£263 million as of 2014) cost of the TAT-1 cable on which TASI was implemented.^{[2]}

TASI worked by switching additional users onto any channel temporarily idled because an original user has stopped speaking. When the original user resumes speaking, that user would, in turn, be switched to any channel that happened to be idle. The speech detector function is called voice activity detection. Clipping or loss of speech would occur for all conversations that needed to be assigned to an available idle channel and in practice lasted at least 17 ms whilst information required to re-connect both parties was signalled by the TASI control circuits. An additional freezeout period lasting between 0 and 500 ms would depend on the instantaneous loading of voice circuits. In actual use, these delays presented few problems in typical conversations.

One of the issues with using this type of technology was that the users listening on an idled channel can sometimes hear the conversation that has been switched onto it. Generally the sound heard was of very low volume and individual words are not distinguishable. See also crosstalk for a similar phenomenon in telecommunications. Another potential issue was ensuring that non-voice type circuits (e.g. Music or radio type circuits where pauses would occur infrequently) were not routed via TASI speech channels since these could seriously degrade the level of service where callers would encounter frequent clipped speech and breaks in the conversation.

TASI was invented by Bell Labs in the early 1960s to increase the capacity of transatlantic telephone cables. It was one of their first applications requiring electronic switching of voice circuits.

Later Digital Circuit Multiplication Equipment included TASI as a feature, not as distinct hardware.

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