1) The document discusses the history of cosine modulated filterbanks and bases, including their development from the short-term Fourier transform and perfect reconstruction filterbanks in the 1970s.
2) Quadrature mirror filters were introduced in 1976 and allowed for perfect reconstruction with critical sampling by cancelling aliasing.
3) Pseudo QMFs and lapped orthogonal transforms were subsequently developed which also achieved perfect reconstruction using time domain aliasing cancellation.
4) These cosine modulated systems like the modulated lapped transform have found applications in audio and image compression standards due to their efficient implementations and good time-frequency localization properties.
2. Time-frequency representations Stanford Colloquium, 2010 time Signal, x(n) X k (m) time time Reconstructed Signal, x (n) Analysis/Decomposition Synthesis/Reconstruction
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5. Filter-banks Stanford Colloquium, 2010 H 0 M F 0 M H 1 M H K-1 M F 1 M F K-1 M + Signal, x(n) X k (m) Reconstructed Signal, x (n) X k (m)
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21. Properties of Sine/Cosine Transforms Stanford Colloquium, 2010 MDCT-II/ IMDCT-II x(2M-n-2n 0 ) Period 2M Period 2M – time reversed + x(n) MDST-II/ IMDST-II x(n) -x(2M-n-2n 0 ) + Controlled by n 0 Controlled by n 0
