Abstract: A time assignment speech interpolation (TASI) system includes a speech buffer comprising storage packets which are assigned to the individual channels as required for the storage of the signals of each off-hook channel. For each inactive channel, the signals are stored sequentially and cyclically in one packet. When the channel becomes active, the sequential storage of signals continues in this and in further packets as required, signals stored before detection that the channel had become active being retained in the first packet to accommodate the response time of a speech detector of the system. Clipping of speech signals is thereby avoided. The channel is assigned a transmission facility and channel-to-facility assignment information is transmitted, following which the signals of the relevant channel are read sequentially from the buffer packets and transmitted via the facility.