A different compressive sensing framework, convolution with white random
waveform which has independent random entries subsampled at fixed (not random
selected) locations is studied in this paper. We show that it wins high
recovery probability for signals which are sparse in the representation basis
which has small coherence, denoted by mu, with the Fourier basis. In
particular, a n-dimensional signal which is S-sparse in such representation
basis can be recovered with probability exceed 1-delta from any fixed
m~O(mu^2*S*log(n/delta)^(3/2)) samples gathered from the output of the random
convolution, such as equal interval down-samples.