– A geometric perspective is used to derive the entire family of Welch bounds. This perspective unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric k-tensors, tight frames, homogeneous polynomials, and t-designs.
Unimodular waveforms x are constructed on the integers with the property that the autocorrelation of x is one at the origin and zero elsewhere. There are three different constructions: exponentials of the form e 2πin α θ , sequences taken from roots of unity, and sequences constructed from the elements of real Hadamard matrices. The first is expected and… (More)
Frames have become standard tools in signal processing due to their robustness to transmission errors and their resilience to noise. Equiangular tight frames (ETFs) are particularly useful and have been shown to be optimal for transmission under a certain number of erasures. Unfortunately, ETFs do not exist in many cases and are hard to construct when they… (More)
Stochastic waveforms are constructed whose expected autocorrelation can be made arbitrarily small outside the origin. These waveforms are unimodular and complex-valued. Waveforms with such spike like auto-correlation are desirable in waveform design and are particularly useful in areas of radar and communications. Both discrete and continuous wave-forms… (More)
Low autocorrelation signals have fundamental applications in radar and communications. We construct constant amplitude zero autocorrelation (CAZAC) sequences x on the integers Z by means of Hadamard matrices. We then generalize this approach to construct unimodular sequences x on Z whose autocorrelations A x are building blocks for all functions on Z. As… (More)
An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order Reed-Muller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers signiſcant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an… (More)