Dyadic Synthesis Filter Bank
Reconstruct signals from subbands with smaller bandwidths and slower sample rates or compute inverse discrete wavelet transform (IDWT)
Libraries:
DSP System Toolbox /
Filtering /
Multirate Filters
Description
You can configure this block to compute the inverse discrete wavelet transform (IDWT) or reconstruct a signal from subbands with smaller bandwidths and slower sample rates. When the block computes the inverse discrete wavelet transform (IDWT) of the input, the output has the same dimensions as the input. Each column of the output is the IDWT of the corresponding input column. When reconstructing a signal, the block uses a series of highpass and lowpass FIR filters to reconstruct the signal from the input subbands, as illustrated in Multilevel Filter Banks (the Asymmetric one). The reconstructed signal has a wider bandwidth and faster sample rate than the input subbands.
You can specify the filter bank highpass and lowpass filters by providing vectors of filter coefficients. You can do so directly on the block dialog box. If you have a Wavelet Toolbox™ license, you can specify waveletbased filters by selecting a wavelet from the Filter parameter. You must set the filter bank structure to asymmetric or symmetric, and specify the number of levels in the filter bank.
Note
To use a dyadic synthesis filter bank to perfectly reconstruct the output of a dyadic analysis filter bank, the number of levels and tree structures of both filter banks must be the same. In addition, the filters in the synthesis filter bank must be designed to perfectly reconstruct the outputs of the analysis filter bank. Otherwise, the reconstruction is not perfect. For an example that shows perfect reconstruction, see Wavelet Reconstruction and Noise Reduction.
This block automatically computes waveletbased perfect reconstruction filters when the wavelet selection in the Filter parameter of this block is the same as the Filter parameter setting of the corresponding Dyadic Analysis Filter Bank block. The use of wavelets requires a Wavelet Toolbox license. To learn how to design your own perfect reconstruction filters, see References.
Ports
Input
Output
Parameters
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

References
[1] Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.
[2] Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA: WellesleyCambridge Press, 1996.
[3] Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.
Extended Capabilities
Version History
Introduced before R2006a