Shaping the power spectra of bipolar sequences with application to sub-Nyquist sampling

In the design of line codes for data transmission and modulation codes for data storage it is important to match the spectral properties of bipolar sequences (containing the symbols ±1) to the spectral properties of the transmission or storage medium. This paper demonstrates that spectral shaping is possible with bipolar sequences, and explores the advantage of bipolar sequences with shaped spectra in Analog-to-Digital Converters (ADCs) where they are used to modulate a sparse input waveform that is described by a small number of parameters. Performance is improved by matching the spectrum of the modulating waveform to prior information about the spectrum of the sparse input. The focus is on the Random Demodulator where sparse signals are reconstructed from sub-Nyquist samples.