A memory-efficient 
system converting a 
signal from a first transform domain to a second transform domain. The 
system includes a first mechanism that obtains an input 
signal expressed via a first transform-domain 
signal representation. A second mechanism expresses the input signal via a second transform-domain signal representation without intermediate time-domain conversion. In the specific embodiment, the input signal is a 
Modified Discrete Cosine Transform (MDCT) signal. The second transform-domain signal representation is a 
Discrete Fourier Transform (DFT) signal. The second mechanism further includes a third mechanism that combines effects of an inverse MDCT, a synthesis 
window function, and an analysis 
window function, and provides a first signal in response thereto. A fourth mechanism converts the MDCT signal to the DFT signal based on the first signal. In a more specific embodiment, the synthesis 
window function is an MDCT synthesis window function, while the analysis window function is a DFT analysis window function. The fourth mechanism includes a mechanism for performing a fast transform on the MDCT signal and providing a first transformed signal in response thereto. The fourth mechanism further includes a mechanism for selectively delaying and updating the first transformed signal to yield second and third transformed signals, respectively, in response thereto. The fourth mechanism further includes a mechanism for operating on the first, second, and third transformed signals via third, second, and first combined window functions, respectively, and providing third, second, and first windowed signals, respectively, in response thereto. An 
adder adds the first, second, and third windowed functions to provide an added 
digital signal. An inverse DFT circuit performs an inverse DFT on the added 
digital signal to provide the DFT signal as output.