On low-complexity frequency selective digital filters and by Linnea Rosenbaum.

By Linnea Rosenbaum.

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G. a tree-structure, different modulation techniques, or individual design of each filter. 4. In this thesis, the M -channel filter banks are restricted to be cosine or sine modulated (Chapters 7 and 8), or complex modulated (Chapter 9) for efficiency reasons. 3. 3 Modulated filter banks For M -channel filter banks, it can be difficult to design and optimize 2M separate filters at the same time; especially for a large M . , 1987; Vaidyanathan, 1993) or modulation (Karp and Fliege, 1999). Two drawbacks of tree-structure filter banks, are that the number of channels is restricted to be a power of two, and that these filter banks have in general a longer delay compared to modulation or individual design.

A design with M independent analysis filters have instead a cost of about M × N/2 (if exploiting symmetry in the impulse response p(n)) 2 . The DFT synthesis filter bank has in the regular case the same complexity as the analysis bank. A drawback of this class of filter banks is, that since the impulse responses hak (n) are obtained by complex exponential modulation of p(n), the coefficients in hak (n) are in general complex, giving rise to complex xi (m), even with a real p(n). Complex signal processing is more expensive to implement compared to realvalued processing.

However, if the processing unit is not lossless, small deviations from the PR conditions can just as well be allowed. Filter banks with small errors are called near-PR (NPR) filter banks. Further, if phase errors is allowed by the application at hand, it is enough for the filter bank to have nearly perfect magnitude reconstruction (NPMR). That is, the constraints on V0 (z) can be relaxed to just consider its magnitude response. NPR and NPMR filter banks have been the focus of this thesis, since they allow more efficient realizations and implementations.

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