منابع مشابه
Walsh Summing and Differencing Transforms
Analogous to Fourier frequency transforms of the integration and differentiation of a continuous-time function, Walsh sequency transforms of the summing and differencing of an arbitrary discrete-time function have been derived. These transforms can be represented numerically in the form of matrices of simple recursive structure. The matrices are not orthogonal, but they are the inverse of each ...
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With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly important role. Nowadays, signals are not merely restricted to the physical domain, they have been extended to cover a much wider range of statistical sources (including financial signals, graph signals). Under the general assumption of discrete statistical signal sources, w...
متن کاملArbitrary-Length Walsh-Jacket Transforms
Due to the efficiency in implementation, the Walsh (Hadamard) transform plays an important role in signal analysis and communication. Recently, Lee generalized the Walsh transform into the Jacket transform. Since the entries of the Jacket transform can be ±2, it is more flexible than the Walsh transform. Both the Walsh transform and the Jacket transform are defined for the case where the length...
متن کاملFast Random Projections using Lean Walsh Transforms
We present a k× d random projection matrix that is applicable to vectors x ∈ R in O(d) operations if d ≥ k2+δ . Here, k is the minimal Johnson Lindenstrauss dimension and δ′ is arbitrarily small. The projection succeeds, with probability 1 − 1/n, in preserving vector lengths, up to distortion ε, for all vectors such that ‖x‖∞ ≤ ‖x‖2kd (for arbitrary small δ). Sampling based approaches are eithe...
متن کاملDense Fast Random Projections and Lean Walsh Transforms
Random projection methods give distributions over k × d matrices such that if a matrix Ψ (chosen according to the distribution) is applied to a finite set of vectors xi ∈ R the resulting vectors Ψxi ∈ R approximately preserve the original metric with constant probability. First, we show that any matrix (composed with a random ±1 diagonal matrix) is a good random projector for a subset of vector...
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ژورنال
عنوان ژورنال: IEEE Transactions on Electromagnetic Compatibility
سال: 1974
ISSN: 0018-9375,1558-187X
DOI: 10.1109/temc.1974.303343