If a Hadamard matrix HN of order N=BF is a Kronecker product HFHB of an order F Hadamard matrix and an order B Hadamard matrix, then transformation by HN may be implemented by a fast Hadamard transform at coarse scale followed by fast Hadamard transforms at fine scale. Alternatively, transformation by HN may be achieved by performing order B transforms on columns of a two-dimensional array and order B transforms on rows of the array. As another alternative, transformation by HN may be achieved by computing intermediate values based on linear combinations of input elements and then computing linear combinations of the intermediate values. For compressive signal acquisition, any row of HN may be generated by concatenating selectively modified copies of a corresponding row of HB. Thus, modulation patterns may be generated on the fly.