Fast Algorithm for Modulated Complex Lapped Transform

A new algorithm for the modulated complex lapped transform (MCLT) with a sine windowing function is presented. It is shown that by merging the windowing operation with the main computation, both the real and the imaginary parts of the MCLT with 2
N
inputs can be obtained from two
N
-point discrete cosine transforms of type II (DCTs-II) of appropriate inputs. The resulting algorithm is computationally very efficient. In general, the value of
N
is an even number. When
N
is a power of 2, the proposed algorithm uses only
N
log
N
+ 2 real multiplications (including the scaling factors in the DCT computation), with none of those being outside the DCT blocks.