Discrete- and continuous-time local cosine bases with multiple overlapping

Abstract

Cosine modulated lter banks are lter banks whose impulse responses are obtained by modulating a window with cosines. Among their applications are video and audio compression and multitone modulation. Their continuous time counterpart is known as local cosine bases. While there is an extended literature on the discrete time case, both for single and multiple overlapping, the continuous time case has received less attention and only the single overlapping case has been solved. This work gives a solution to the problem of continuous time local cosine bases with multiple overlapping via a general theory that emphasizes the deep connection between discrete and continuous time. A sampling theorem for local cosine basis and an e cient algorithm to compute the expansion of a signal are also given.

Spline Modulation of Sinusoids for Signal Representation

“…Therefore, it is worthwhile to accept dual windows with infinite support, in order to include non-negative windows w with multiple overlapping in the signal processing tool-box. But even if one does not worry about phase artifacts and accepts real-valued windows with alternating signs, the condition of compact support for both w andw is very restrictive, and the design of such windows with additional desired features is hampered by various difficulties (see [6,32]). …”