Dyadic Analysis Filter Bank
Decompose signals into subbands with smaller bandwidths and slower sample rates or compute discrete wavelet transform (DWT)
Library
Filtering / Multirate Filters
dspmlti4
Description
Note
This block always interprets input signals as frames. The frame size of the input
signal must be a multiple of 2^{n}, where
n
is the value of the Number of levels
parameter. The block decomposes the input signal into either n+1 or
2^{n} subbands. To decompose signals with a frame size
that is not a multiple of 2^{n}, use the TwoChannel Analysis Subband Filter block. (You can connect multiple
copies of the TwoChannel Analysis Subband Filter block to create a multilevel
dyadic analysis filter bank.)
You can configure this block to compute the Discrete Wavelet Transform (DWT) or decompose a broadband signal into a collection of subbands with smaller bandwidths and slower sample rates. The block uses a series of highpass and lowpass FIR filters to repeatedly divide the input frequency range, as illustrated in Wavelet Filter Banks (the Asymmetric one).
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.
For the same input, the DWT configuration of this block does not produce the same
results as the Wavelet Toolbox
dwt
function. Because DSP System Toolbox™ is designed for realtime implementation and Wavelet Toolbox is designed for analysis, the products handle boundary conditions and
filter states differently. To make the output of the dwt
function
match the DWT output of this block, complete the following steps:
Set the boundary condition of the
dwt
function to zeropadding. To do so, typedwtmode('zpd')
at the MATLAB^{®} command line.To match the latency of the block (implemented using FIR filters), add zeros to the input of the
dwt
function. The number of zeros you add must be equal to the halflength of the filter.
Input Requirements
Input must be a vector or matrix.
The input frame size must be a multiple of 2^{n}, where n is the number of filter bank levels. For example, a frame size of 16 would be appropriate for a threelevel tree (16 is a multiple of 2^{3}).
The block always treats input signals as frames and operates along the columns.
For an illustration of why the above input requirements exist, see the figure Outputs of a 3Level Asymmetric Dyadic Analysis Filter Bank.
Output Characteristics
The output characteristics vary depending on the block's parameter settings, as summarized in the following list and figure:
Number of levels parameter set to n
Tree structure parameter setting:
Asymmetric
— Block produces n+1 output subbandsSymmetric
— Block produces 2^{n} output subbands
Output parameter setting can be
Multiple ports
orSingle port
. When you set the Output parameter toSingle port
, the block outputs one vector or matrix of concatenated subbands. The following figure illustrates the difference between the two settings for a 3level asymmetric dyadic analysis filter bank. For an explanation of the illustrated output characteristics, see the table Output Characteristics for an nLevel Dyadic Analysis Filter Bank.
For more information about the filter bank levels and structures, see Dyadic Analysis Filter Banks.
Outputs of a 3Level Asymmetric Dyadic Analysis Filter Bank
The following table summarizes the different output characteristics of the block when it is set to output from single or multiple ports.
Output Characteristics for an nLevel Dyadic Analysis Filter Bank
Single Output Port  Multiple Output Ports  

Output Description  Block concatenates all the subbands into one vector or matrix, and outputs the concatenated subbands from a single output port. Each output column contains subbands of the corresponding input channel.  Block outputs each subband from a separate output port. The topmost port outputs the subband with the highest frequencies. Each output column contains a subband for the corresponding input channel. 
Output Frame Rate  Not applicable  Same as input frame rate 
Output Dimensions (Frame Size)  Same number of rows and columns as the input.  The output has the same number of columns as the input. The number of output rows is the output frame size. For an input with frame size M_{i} output y_{k} has frame size M_{o},_{k}:

Output Sample Rate  Same as input sample rate.  Though the outputs have the same frame rate as the input, they have different frame sizes than the input. Thus, the output sample rates, F_{so}, k, are different from the input sample rate, F_{si}:

Filter Bank Filters
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.Wavelet such as
Biorthogonal
orDaubechies
— The block uses the specified wavelet to construct the lowpass and highpass filters using the Wavelet Toolboxwfilters
function. 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.) 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
 None 
Haar  None  wfilters('haar') 
Daubechies  Wavelet order =
 wfilters('db4') 
Symlets  Wavelet order =
 wfilters('sym3') 
Coiflets  Wavelet order =
 wfilters('coif1') 
Biorthogonal  Filter order [synthesis / analysis] =
 wfilters('bior3.1') 
Reverse Biorthogonal  Filter order [synthesis / analysis] =
 wfilters('rbio3.1') 
Discrete Meyer  None  wfilters('dmey') 
Examples
Wavelets
The primary application for dyadic analysis filter banks and dyadic synthesis filter banks is coding for data compression using wavelets.
At the transmitting end, the output of the dyadic analysis filter bank is fed to a lossy compression scheme, which typically assigns the number of bits for each filter bank output in proportion to the relative energy in that frequency band. This represents the more powerful signal components by a greater number of bits than the less powerful signal components.
At the receiving end, the transmission is decoded and fed to a dyadic synthesis filter bank to reconstruct the original signal. The filter coefficients of the complementary analysis and synthesis stages are designed to cancel aliasing introduced by the filtering and resampling.
See Calculate Channel Latencies Required for Wavelet Reconstruction for an example using the Dyadic Analysis and Dyadic Synthesis Filter Bank blocks.
Examples
See the floatingpoint framebased version of the DSP System Toolbox Wavelet Reconstruction and Noise Reduction example, which uses the Dyadic Analysis Filter Bank and Dyadic Synthesis Filter Bank blocks.
Parameters
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.
 Filter
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
orDaubechies
to specify a waveletbased filter. The block uses the Wavelet Toolboxwfilters
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 Specifying Filters with the Filter Parameter and Related Parameters. Lowpass FIR filter coefficients
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. The default values of this parameter specify a filter based on a Daubechies wavelet with wavelet order3
. Highpass FIR filter coefficients
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. The default values of this parameter specify a filter based on a Daubechies wavelet with wavelet order3
. Wavelet order
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 Specifying Filters with the Filter Parameter and Related Parameters table.
 Filter order [synthesis / analysis]
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 thewfilters
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. Number of levels
The number of filter bank levels. An nlevel asymmetric structure has n+1 outputs, and an nlevel symmetric structure has 2^{n} outputs, as shown in Wavelet Filter Banks. The block's icon changes depending on the value of this parameter.
The default setting of this parameter is
2
. Tree structure
The structure of the filter bank:
Asymmetric
, orSymmetric
. See Wavelet Filter Banks.The default setting of this parameter is
Asymmetric
for the Dyadic Analysis Filter Bank block, andSymmetric
for the DWT block. Output
Set to
Multiple ports
to output each output subband on a separate port (the topmost port outputs the subband with the highest frequency band). Set toSingle port
to concatenate the subbands into one vector or matrix and output the concatenated subbands on a single port. For more information, see Output Characteristics.The default setting of this parameter is
Multiple ports
for the Dyadic Analysis Filter Bank block, andSingle port
for the DWT block.
References
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.
Supported Data Types
Port  Supported Data Types 

Input 

Output 
