On time warping and the random delay channel

Channels (i.e., operators) are studied that produce time warping, or delay modulation, in signals passing through them, and many interesting properties of these channels are developed. It is shown that a first-in first-out (FIFO) assumption for such channels is compelling on physical grounds and vastly simplifies ensuing analysis. Two descriptions of the channel, the "send-delay" and "receive-delay" functions, are compared, and it is shown that one is precisely the shape needed to equalize or unwarp signals warped by the other. A series expansion for time-warped signals is developed, and the unitary nature of the warp operators is exploited to generate rich sets of orthonormal signals. The random time-warp channel is then analyzed, and certain statistics such as the autocorrelation function of the output signals are developed, along with conditions on their stationarity. Finally, optimum linear filters for extracting a signal from a noisy and time-warped version are derived and compared with some previous results.