Characteristic Phase E-Sequences in Efficient Pulse-Compression Methods using Discrete Wavelet Decomposition

We derive a family of sequences which obey a characteristic-phase constraint as it applies to finite sequences. We show these sequences are special cases of the well-known Welti sequences. We construct a transmit waveform which allows extremely efficient decomposition, whose outputs are simultaneously interpretable as adjacent correlation-filter outputs, and as lossless input signal representations. We discuss implementation of receive and transmit functions.