Documentation 
Reconstruct signals from subbands with smaller bandwidths and slower sample rates or compute inverse discrete wavelet transform (IDWT)
Note This block always does framebased processing, and its inputs must be of certain sizes. To use input subbands that do not fit the criteria of this block, use the TwoChannel Synthesis Subband Filter block. (You can connect multiple copies of the TwoChannel Synthesis Subband Filter block to create a multilevel dyadic synthesis filter bank.) 
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 Wavelet 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's highpass and lowpass filters by providing vectors of filter coefficients. You can do so directly on the block mask, or, 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.
When you set the Input parameter to Multiple ports, you must provide each subband to the block through a different input port as a vector or matrix. You should input the highest frequency band through the topmost port. When you set the Input parameter to Single port, the block input must be a vector or matrix of concatenated subbands.
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. 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. 
The inputs to this block are usually the outputs of a Dyadic Analysis Filter Bank block. Since the Dyadic Analysis Filter Bank block can output from either a single port or multiple ports, the Dyadic Synthesis Filter Bank block accepts inputs to either a single port or multiple ports.
The Input parameter sets whether the block accepts inputs from a single port or multiple ports, and thus determines the input requirements, as summarized in the following lists and figure.
Note: Any output of a Dyadic Analysis Filter Bank block whose parameter settings match the corresponding settings of this block is a valid input to this block. For example, the setting of the Dyadic Analysis Filter Bank block parameter, Output, must be the same as this block's Input parameter (Single port or Multiple ports). 
Inputs must be vectors or matrices of concatenated subbands. The block always interprets the inputs as sample based.
Each input column contains the subbands for an independent signal.
Upper input rows contain the highfrequency subbands, and the lower rows contain the lowfrequency subbands.
Each subband must be provided as a vector or matrix to separate block input ports. The block always interprets the inputs as frame based.
The columns of each input contains a subband for an independent signal.
The input to the topmost input port is the subband containing the highest frequencies, and the input to the bottommost port is the subband containing the lowest frequencies.
Valid Inputs to a 3Level Asymmetric Dyadic Synthesis Filter Bank
For general information about the filter banks, see Dyadic Synthesis Filter Banks.
The following table summarizes the output characteristics for both types of inputs. For an illustration of why the output characteristics exist, see the figure Valid Inputs to a 3Level Asymmetric Dyadic Synthesis Filter Bank.
Input = Multiple ports  Input
= Single port (Concatenated Subband Inputs)  

Output Frame Rate  Same as the input frame rate.  Same as the input rate (the rate of the concatenated subband inputs). 
Output Frame Dimensions 
 The output has the same number of rows and columns as the input. 
For general information about the filter banks, see Dyadic Synthesis Filter Banks.
You must specify the highpass and lowpass filters in the filter bank by setting the Filter parameter to one of the following options:
User defined — Allows you to explicitly specify the filters with two vectors of filter coefficients in the Lowpass FIR filter coefficients and Highpass FIR filter coefficients parameters. The block uses the same lowpass and highpass filters throughout the filter bank. The two filters should be halfband filters, where each filter passes the frequency band that the other filter stops. To use this block to perfectly reconstruct a signal decomposed by a Dyadic Analysis Filter Bank block, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filter bank. To learn how to design your own perfect reconstruction filters, see References.
Wavelet such as Biorthogonal or Daubechies — The block uses the specified wavelet to construct the lowpass and highpass filters using the Wavelet Toolbox function wfilters. Depending on the wavelet, the block might enable either the Wavelet order or Filter order [synthesis / analysis] parameter. (The latter parameter allows you to specify different wavelet orders for the analysis and synthesis filter stages.) To use this block to reconstruct a signal decomposed by a Dyadic Analysis Filter Bank block, you must set both blocks to use the same wavelets with the same order. You must have a Wavelet Toolbox license to use wavelets.
Specifying Filters with the Filter Parameter and Related Parameters
Filter  Sample Setting for Related Filter Specification Parameters  Corresponding Wavelet Function Syntax 

Userdefined  Filters based on Daubechies wavelets with wavelet order 3:
 None 
Haar  None  wfilters('haar') 
Daubechies  Wavelet order = 4  wfilters('db4') 
Symlets  Wavelet order = 3  wfilters('sym3') 
Coiflets  Wavelet order = 1  wfilters('coif1') 
Biorthogonal  Filter order [synthesis / analysis] = [3/1]  wfilters('bior3.1') 
Reverse Biorthogonal  Filter order [synthesis / analysis] = [3/1]  wfilters('rbio3.1') 
Discrete Meyer  None  wfilters('dmey') 
The parameters displayed in the block dialog vary depending on the setting of the Filter parameter. Only some of the parameters described below are visible in the dialog box at any one time.
Note To use this block to reconstruct a signal decomposed by a Dyadic Analysis Filter Bank block, all the parameters in this block must be the same as the corresponding parameters in the Dyadic Analysis Filter Bank block (except the Lowpass FIR filter coefficients and Highpass FIR filter coefficients; see the descriptions of these parameters). 
The type of filter used to determine the high and lowpass FIR filters in the filter bank:
Select User defined to explicitly specify the filter coefficients in the Lowpass FIR filter coefficients and Highpass FIR filter coefficients parameters.
Select a wavelet such as Biorthogonal or Daubechies to specify a waveletbased filter. The block uses the Wavelet Toolbox wfilters function to construct the filters. Extra parameters such as Wavelet order or Filter order [synthesis / analysis] might become enabled. For a list of the supported wavelets, see the table Specifying Filters with the Filter Parameter and Related Parameters.
A vector of filter coefficients (descending powers of z) that specifies coefficients used by all the lowpass filters in the filter bank. This parameter is enabled when you set Filter to User defined. The lowpass filter should be a halfband filter that passes the frequency band stopped by the filter specified in the Highpass FIR filter coefficients parameter. To perfectly reconstruct a signal decomposed by the Dyadic Analysis Filter Bank, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filter bank. Otherwise, the reconstruction is not perfect. The default values of this parameter specify a perfect reconstruction filter for the default settings of the Dyadic Analysis Filter Bank (based on a Daubechies wavelet with wavelet order 3).
A vector of filter coefficients (descending powers of z) that specifies coefficients used by all the highpass filters in the filter bank. This parameter is enabled when you set Filter to User defined. The highpass filter should be a halfband filter that passes the frequency band stopped by the filter specified in the Lowpass FIR filter coefficients parameter. To perfectly reconstruct a signal decomposed by the Dyadic Analysis Filter Bank, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filter bank. Otherwise, the reconstruction is not perfect. The default values of this parameter specify a perfect reconstruction filter for the default settings of the Dyadic Analysis Filter Bank (based on a Daubechies wavelet with wavelet order 3).
The order of the wavelet selected in the Filter parameter. This parameter is enabled only when you set Filter to certain types of wavelets, as shown in the table Specifying Filters with the Filter Parameter and Related Parameters.
The order of the wavelet for the synthesis and analysis filter stages. For example, when you set the Filter parameter to Biorthogonal and set the Filter order [synthesis / analysis] parameter to [2 / 6], the block calls the wfilters function with input argument 'bior2.6'. This parameter is enabled only when you set Filter to certain types of wavelets, as shown in Specifying Filters with the Filter Parameter and Related Parameters.
The number of filter bank levels. An nlevel asymmetric structure has n+1 inputs, and an nlevel symmetric structure has 2^{n} inputs, as shown in Wavelet Filter Banks.
The default setting of this parameter is 2.
The structure of the filter bank: Asymmetric, or Symmetric. See Wavelet Filter Banks.
The default setting of this parameter is Asymmetric for the Dyadic Synthesis Filter Bank block, and Symmetric for the IDWT block.
Set to Multiple ports to accept each input subband at a separate port (the topmost port accepts the subband with the highest frequency band). Set to Single port to accept one vector or matrix of concatenated subbands at a single port. For more information, see Input Requirements.
The default setting of this parameter is Multiple ports for the Dyadic Synthesis Filter Bank block, and Single port for the IDWT block.
Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.
Strang, G. and T. Nguyen. Wavelets and Filter Banks. Wellesley, MA: WellesleyCambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.
Port  Supported Data Types 

Input 

Output 

Dyadic Analysis Filter Bank  DSP System Toolbox 
IDWT  DSP System Toolbox 
TwoChannel Synthesis Subband Filter  DSP System Toolbox 
See Multirate and Multistage Filters for related information.