在一般的信号压缩应用中,转换特性可透过利用将窗函数wn(n = 0, ..., 2N-1)乘以MDCT中的xn及IMDCT中的yn作进一步的改良,为了避免在n = 0 and 2N的边界点产生不连续并且使函数于这些点可以变得平滑而趋近零(即window the data before the MDCT and after the IMDCT)。原则上,x和y可以有不同的窗函数,而窗函数再资料区块转换时可以改变(尤其是当两个不同尺寸的资料区块结合在一起时)。但为简单起见,我们考虑给相同尺寸的资料区块应用的窗函数。
转换仍然是可逆的(即TDAC依然可以正常作用),考虑一个对称的窗wn = w2N-1-n,只要w满足Princen-Bradley condition:
Henrique S. Malvar, Signal Processing with Lapped Transforms (Artech House: Norwood MA, 1992).
John P. Princen and Alan B. Bradley, "Analysis/synthesis filter bank design based on time domain aliasing cancellation," IEEE Trans. Acoust. Speech Sig. Proc.ASSP-34 (5), 1153-1161 (1986).(Described a precursor to the MDCT using a combination of discrete cosine and sine transforms.)
J. P. Princen and A. W. Johnson and A. B. Bradley, "Subband/transform coding using filter bank designs based on time domain aliasing cancellation," IEEE Proc. Intl. Conf. on Acoustics, Speech, and Signal Processing(ICASSP)12, 2161-2164 (1987).(Initial description of what is now called the MDCT.)
A. W. Johnson and A. B. Bradley, "Adaptive transform coding incorporating time domain aliasing cancellation," Speech Comm.6, 299-308 (1987).
V. Britanak and K. R. Rao, "A new fast algorithm for the unified forward and inverse MDCT/MDST computation," Signal Processing82, 433-459(2002)
Vladimir Nikolajevic and Gerhard Fettweis, "Computation of forward and inverse MDCT using Clenshaw's recurrence formula," IEEE Trans. Sig. Proc.51 (5), 1439-1444(2003)
Che-Hong Chen, Bin-Da Liu, and Jar-Ferr Yang, "Recursive architectures for realizing modified discrete cosine transform and its inverse," IEEE Trans. Circuits Syst. II: Analog Dig. Sig. Proc.50 (1), 38-45(2003)
J.S. Wu, H.Z. Shu, L. Senhadji, and L.M. Luo, "Mixed-radix algorithm for the computation of forward and inverse MDCTs," IEEE Trans. Circuits Syst. I: Reg. Papers.56 (4), 784-794(2009)
V. Britanak, "A survey of efficient MDCT implementations in MP3 audio coding standard: retrospective and state-of-the-art," Signal. Process.91 (4), 624-672(2011)
...and references thereof.
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