| Signal Processing Blockset™ | |
Decompose signals into subbands with smaller bandwidths and slower sample rates
Filtering / Multirate Filters
dspmlti4
Note This block decomposes frame-based signals with frame size a multiple of 2n into either n+1 or 2n subbands. To decompose sample-based signals or frame-based signals of different sizes, use the Two-Channel Analysis Subband Filter block. (You can connect multiple copies of the Two-Channel Analysis Subband Filter block to create a multilevel dyadic analysis filter bank.) |
The Dyadic Analysis Filter Bank block decomposes 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 the figure n-Level Asymmetric Dyadic Analysis Filter Bank.
You can specify the filter bank's highpass and lowpass filters by providing vectors of filter coefficients. If you install the Wavelet Toolbox™ product, you can also 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.
Input can be a frame-based vector or frame-based matrix.
The input frame size must be a multiple of 2n, where n is the number of filter bank levels. For example, a frame size of 16 would be appropriate for a three-level tree (16 is a multiple of 23).
The block always operates along the columns of the inputs.
For an illustration of why the above input requirements exist, see the figure Outputs of a 3-Level Asymmetric Dyadic Analysis Filter Bank.
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 subbands
Symmetric — Block produces 2n output subbands
Output parameter setting can be Multiple ports or Single port. The following figure illustrates the difference between the two settings for a 3-level asymmetric dyadic analysis filter bank. For an explanation of the illustrated output characteristics, see the table Output Characteristics for an n-Level Dyadic Analysis Filter Bank.
For more information about the filter bank levels and structures, see Dyadic Analysis Filter Banks.
Outputs of a 3-Level 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 n-Level 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 Status | Sample-based | Frame-based |
| 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 Mi output yk has frame size Mo,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, Fso, k, are different from the input sample rate, Fsi:
|
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 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.) You must install the Wavelet Toolbox product 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:
| 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 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 the following Signal Processing Blockset™ demos, which use the Dyadic Analysis Filter Bank block:
Note To see the version of the demos that use the Dyadic Analysis Filter Bank and Dyadic Synthesis Filter Bank blocks, click the Frame-Based Demo button in the demos. Open the demos using one of the following methods:
|
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.
The type of filter used to determine the high- and low-pass FIR filters in the dyadic analysis 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 function wfilters 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.
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 half-band 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 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 half-band 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 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 Specifying Filters with the Filter Parameter and Related Parameters table.
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 n-level asymmetric structure has n+1 outputs, and an n-level symmetric structure has 2n outputs, as shown in the figures n-Level Asymmetric Dyadic Analysis Filter Bank and n-Level Symmetric Dyadic Analysis Filter Bank. The block's icon displays the value of this parameter in the lower-left corner.
The structure of the filter bank: Asymmetric, or Symmetric. See the figures n-Level Asymmetric Dyadic Analysis Filter Bank and n-Level Symmetric Dyadic Analysis Filter Bank.
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 to Single 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.
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: Wellesley-Cambridge Press, 1996.
Vaidyanathan, P. P. Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.
Double-precision floating point
Single-precision floating point
| Dyadic Synthesis Filter Bank | Signal Processing Blockset |
| Two-Channel Analysis Subband Filter | Signal Processing Blockset |
| DWT | Dyadic Synthesis Filter Bank | |
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