Waveform encoding of binary signals using a wavelet and its Hilbert transform

Orthogonal wavelets have been applied to communications since the early 90s. We prove that the Hilbert transform of a wavelet is orthogonal to its time shifts and it is also orthogonal to the corresponding wavelet and its time shifts. On the other hand, since the Hilbert transform only shifts the phase of the wavelet function by 90-degree, the magnitude spectrums of the wavelet and its transform are the same. Therefore they are located on the same frequency band. In order to utilize the above properties, we propose to use the wavelet and its Hilbert transform for waveform encoding of data bits. With this, we are able to double the bit rate without increasing the bandwidth or affecting the bit error rate (BER). Daubechies (1992) wavelets are used in the analyses of the proposed system