Dyadic Synthesis Filter Bank

Reconstruct signals from subbands with smaller bandwidths and slower sample rates or compute inverse discrete wavelet transform (IDWT)

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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 wavelet-based 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 wavelet-based 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.

Examples

Wavelet Reconstruction and Noise Reduction

Uses the Dyadic Analysis Filter Bank and Dyadic Synthesis Filter Bank blocks to show both the perfect reconstruction property of wavelets and an application for noise reduction.

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Ports

Input

Input 1 — Data input

column vector | matrix

Specify the data input as a column vector or a matrix.

The input characteristics vary depending on the block parameter settings as summarized here:

• Number of levels parameter set to n

• Tree structure parameter setting:

  • Asymmetric — Block accepts n+1 input subbands

  • Symmetric — Block accepts 2ⁿ input subbands

  • Input parameter setting can be Multiple ports or Single port.

    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 to multiple ports.

    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

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 the Input parameter (Single port or Multiple ports) in this block.

Valid Inputs for Input Set to Single Port

• Input must be a vector or matrix of concatenated subbands.

• Each input column contains the subbands for an independent signal.

• Upper input rows contain the high-frequency subbands, and the lower rows contain the low-frequency subbands.

Valid Inputs for Input Set to Multiple Ports

• Each subband must be provided as a vector or a matrix to separate block input ports.

• 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.

This figure illustrates the difference between the two settings for a 3-level asymmetric dyadic synthesis filter bank.

Valid Inputs to a 3-Level Asymmetric Dyadic Synthesis Filter Bank

For general information about the filter banks, see Dyadic Synthesis Filter Banks.

Note

This block always performs frame-based processing, and its inputs must be of certain sizes. To use input subbands that do not fit the criteria of this block, use the Two-Channel Synthesis Subband Filter block. You can connect multiple copies of the Two-Channel Synthesis Subband Filter block to create a multilevel dyadic synthesis filter bank.

Data Types: single | double
Complex Number Support: Yes

Output

Output 1 — Reconstructed signal

column vector | matrix

The block outputs the reconstructed signal as a column vector or a matrix.

This 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 3-Level 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 columns as the inputs. The number of output rows depends on the tree structure of the filter bank: Asymmetric — The number of output rows is twice the number of rows in the input to the topmost input port. Symmetric — The number of output rows is the product of the number of input ports and the number of rows in an input to any input port.	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.

Data Types: single | double
Complex Number Support: Yes

Parameters

The parameters displayed in the block dialog box 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).

Filter — Type of filter used in filter bank

User-defined (default) | Haar | Daubechies | Symlets | Coiflets | Biorthogonal | Reverse Biorthogonal | Discrete Meyer

To determine the highpass 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 wavelet-based filter. The block uses the Wavelet Toolbox wfilters function to construct the filters. Extra parameters such as Wavelet order or Filter order [synthesis / analysis] become enabled. For a list of the supported wavelets, see the table Specifying Filters with the Filter Parameter and Related Parameters.

  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
  User-defined	Filters based on Daubechies wavelets with wavelet order 3: Lowpass FIR filter coefficients = [0.0352 -0.0854 -0.1350 0.4599 0.8069 0.3327] Highpass FIR filter coefficients = [-0.3327 0.8069 -0.4599 -0.1350 0.0854 0.0352]	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')

Filter order [synthesis / analysis] — Wavelet order for synthesis filter stage

[1 / 1] (default) | [1 / 3] | [1 / 5] | [2 / 2] | [2 / 4] | [2 / 6] | [2 / 8] | [3 / 1] | [3 / 3] | [3 / 5] | [3 / 7] | [3 / 9] | [4 / 4] | [5 / 5] | [6 / 8]

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'.

Dependencies

To enable this parameter, set the Filter parameter to Biorthogonal or Reverse Biorthogonal.

Wavelet order — Wavelet order

2 (default) | positive integer

Set the order of the wavelet selected in the Filter parameter.

Dependencies

To enable this parameter, set the Filter parameter to Daubechies, Symlets, or Coiflets.

Lowpass FIR filter coefficients — Lowpass FIR filter coefficients

[0.3327 0.8069 0.4599 -0.1350 -0.0854 0.0352] (default)

Specifies coefficients used by all the lowpass filters in the filter bank using a vector of filter coefficients (descending powers of z). This parameter is enabled when you set Filter to User defined. The lowpass filter should be a half-band 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).

Dependencies

To enable this parameter, set the Filter parameter to User-defined.

Highpass FIR filter coefficients — Highpass FIR filter coefficients

[0.0352 0.0854 -0.1350 -0.4599 0.8069 -0.3327] (default)

Specifies coefficients used by all the highpass filters in the filter bank using a vector of filter coefficients (descending powers of z). This parameter is enabled when you set Filter to User defined. The highpass filter should be a half-band 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).

Dependencies

To enable this parameter, set the Filter parameter to User-defined.

Number of levels — Number of filter bank levels

2 (default) | positive integer

Select the number of filter bank levels. An n-level asymmetric structure has n+1 inputs, and an n-level symmetric structure has 2ⁿ inputs, as shown in Multilevel Filter Banks.

Tree structure — Structure of filter bank

Asymmetric (default) | Symmetric

Select the structure of the filter bank: Asymmetric, or Symmetric. See Multilevel Filter Banks for more details on these structures.

The default setting of this parameter is Asymmetric for the Dyadic Synthesis Filter Bank block, and Symmetric for the IDWT block.

Input — Input

Multiple ports (default) | Single port

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 port description.

The default setting of this parameter is Multiple ports for the Dyadic Synthesis Filter Bank block, and Single port for the IDWT block.

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 a 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.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

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: Wellesley-Cambridge Press, 1996.

[3] Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Version History

Introduced before R2006a