Cosine-modulated filter banks (CMFB’s) are filter 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. Even though 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 efficient algorithm to compute the expansion of a signal are also given.