DSP Blockset

Two-Channel Synthesis Subband Filter

Reconstruct a signal from a high-frequency subband and a low-frequency subband

Library

Filtering / Multirate Filters

Description

Note    By connecting many copies of this block, you can implement a multilevel dyadic synthesis filter bank. In some cases, it is more efficient to use the Dyadic Synthesis Filter Bank block instead. For more information, see Creating Multilevel Dyadic Synthesis Filter Banks.

The Two-Channel Synthesis Subband Filter block reconstructs a signal from its high-frequency subband and low-frequency subband, each with half the bandwidth and half the sample rate of the original signal. Use this block to reconstruct signals decomposed by the Two-Channel Analysis Subband Filter block.

The block upsamples the high- and low-frequency subbands by 2, and then filters the results with a pair of highpass and lowpass FIR filters, as illustrated in the following figure.

Note the block implements the FIR filtering and downsampling steps together using a polyphase filter structure, which is more efficient than the straightforward interpolate-then-filter algorithm illustrated above.

You must provide the vector of filter coefficients for the two filters. Each filter should be a half-band filter that passes the frequency band that the other filter stops. To use this block to reconstruct the output of a Two-Channel Analysis Subband Filter block, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filters.

See other sections of this reference page for more information.

Sections of This Reference Page

• Specifying the FIR Filters
• Sample-Based Operation
• Frame-Based Operation
• Latency
• Creating Multilevel Dyadic Synthesis Filter Banks
• Examples
• Dialog Box
• References
• Supported Data Types
• See Also

Specifying the FIR Filters

You must provide the vector of numerator coefficients for the lowpass and highpass filters in the Lowpass FIR filter coefficients and Highpass FIR filter coefficients parameters.

For example, to specify a filter with the following transfer function, enter the vector [b(1) b(2) ... b(m)].

Each filter should be a half-band filter that passes the frequency band that the other filter stops. To use this block to reconstruct the output of a Two-Channel Analysis Subband Filter block, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filters.

The best way to design perfect reconstruction filters is to use the wfilters function in the Wavelet Toolbox for the filters in both this block and in the corresponding Two-Channel Analysis Subband Filter block. You can also use functions from the Filter Design toolbox and Signal Processing Toolbox. To learn how to design your own perfect reconstruction filters, see References.

The block initializes all filter states to zero.

Sample-Based Operation

Valid Sample-Based Inputs.   The block accepts any two M-by-N sample-based matrices with the same sample rates. The block treats each matrix as  independent subbands, where each matrix element is the high- or low-frequency subband of the corresponding channel in the output matrix. The input to the topmost input port should contain the high-frequency subbands.

Sample-Based Outputs.   Given valid sample-based inputs, the block outputs one sample-based matrix with the same dimensions as the inputs. The output sample rate is twice that of the input. Each element of the output is a single channel, reconstructed from the corresponding elements in each input matrix. Depending on the Simulink simulation parameters, some sample-based outputs may have one sample of latency, as described in Latency.

Frame-Based Operation

Valid Frame-Based Inputs.   The block accepts any two M-by-N frame-based matrices with the same frame rates. The block treats each input column as the high- or low-frequency subbands of the corresponding output channel. The input to the topmost input port should contain the high-frequency subbands.

Frame-Based Outputs.   Given valid frame-based inputs, the block outputs a frame-based matrix. Each output column is a single channel, reconstructed from the corresponding columns in each input matrix.

The sample rate of the output is twice that of the input. The Framing parameter sets whether the block doubles the sample rate by doubling the output frame size, or doubling the output frame rate:

• Maintain input frame size -- The input and output frame sizes are the same, but the frame rate of the output is twice that of the input. So, the overall sample rate of the output is twice that of the input. This setting causes the block to have one frame of latency, as described in Latency.
• Maintain input frame rate -- The input and output frame rates are the same, but the frame size of the output is twice that of the input. So, the overall sample rate of the output is twice that of the input.

Latency

In some cases, the block has nonzero tasking latency, which means that there is a constant delay between the time that the block receives an input, and produces the corresponding output, as summarized below and in the following table:

• For sample-based inputs, there are cases where the block exhibits one-sample latency. In such cases, when the block receives the nth input sample, it produces the outputs corresponding to the n-1th input sample. When the block receives the first input sample, the block outputs an initial value of zero in each output channel.
• For frame-based inputs, there are cases where the block exhibits one-frame latency. In such cases, when the block receives the nth input frame, it produces the outputs corresponding to the n-1th input frame. When the block receives the first input frame, the block outputs a frame of zeros.

For more information about block rates and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and the topic on the Simulation Parameters dialog box in the Simulink documentation.

Table 7-21: Amount of Block Latency for All Possible Block Settings

Input	Latency	No Latency
Sample-based	One sample of latency when Mode = MultiTasking or Auto in the Simulation Parameters dialog (Ctrl + E). First output sample of each channel is always 0.	Mode = SingleTasking in the Simulation Parameters dialog (Ctrl + E).
Frame-based	One frame of latency when Framing = Maintain input frame size. First output frame is always all zeros.	Framing = Maintain input frame rate

Creating Multilevel Dyadic Synthesis Filter Banks

The Two-Channel Synthesis Subband Filter block is the basic unit of a dyadic synthesis filter bank. You can connect several of these blocks to implement an n-level filter bank, as illustrated in the following figure. (For a review of dyadic synthesis filter banks, see Review of Dyadic Synthesis Filter Banks in the Dyadic Synthesis Filter Bank reference page.)

Note    When you create a filter bank by connecting multiple copies of this block, the output values of the filter bank differ depending on whether there is latency. (See Table 7-21, Amount of Block Latency for All Possible Block Settings,.) For instance, for frame-based inputs, the filter bank output values differ depending on whether you set the Framing parameter to Maintain input frame rate (no latency), or Maintain input frame size (one frame of latency for every block). Though the output values differ, both sets of values are valid; the difference arises from changes in latency.

In some cases, rather than connecting several Two-Channel Synthesis Subband Filter blocks, it is more efficient (faster and requires less memory) to use the Dyadic Synthesis Filter Bank block. In particular, use the Dyadic Synthesis Filter Bank to reconstruct a frame-based signal (with frame size a multiple of 2ⁿ) from 2ⁿ or n+1 subbands whose properties match those of the Dyadic Analysis Filter Bank's outputs. These properties are described in Output Characteristics (Setting the Output Parameter) of the Dyadic Analysis Filter Bank reference page.

The Dyadic Synthesis Filter Bank block allows you to specify the filter bank filters by providing vectors of filter coefficients, just as this block does. The Dyadic Synthesis Filter Bank block provides an additional option of using wavelet-based filters that the block designs by using a wavelet you specify.

Examples

See the following DSP Blockset demos, which use the Two-Channel Synthesis Subband Filter block:

• Multi-level PR filter bank
• Denoising
• Wavelet transmultiplexer (WTM)

Note    Open the demos using one of the following methods: Click the above links in the MATLAB Help browser (not in a web browser). Type demo blockset dsp at the MATLAB command line, and look in the Wavelets directory. By default, the demos open the versions using the Two-Channel Synthesis Subband Filter block. You can also see the version of the demos that use the Dyadic Synthesis Filter Bank block by clicking the Frame-Based Demo button in the demos.

Dialog Box

Lowpass FIR filter coefficients

A vector of lowpass FIR filter coefficients, in descending powers of z. 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 use this block to reconstruct the output of a Two-Channel Analysis Subband Filter block, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filters. For more information, see Specifying the FIR Filters.

Highpass FIR filter coefficients

A vector of highpass FIR filter coefficients, in descending powers of z. 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 use this block to reconstruct the output of a Two-Channel Analysis Subband Filter block, the filters in this block must be designed to perfectly reconstruct the outputs of the analysis filters. For more information, see Specifying the FIR Filters.

Framing

For frame-based inputs, the method by which to implement the interpolation: by doubling the output frame rate (Maintain input frame size), or doubling the output frame size (Maintain input frame rate). For more information, see Frame-Based Operation. Some settings of this parameter causes the block to have nonzero latency, as described in Latency.

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: Wellesley-Cambridge Press, 1996.

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

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Dyadic Synthesis Filter Bank	DSP Blockset
Two-Channel Analysis Subband Filter	DSP Blockset
fir1	Signal Processing Toolbox
fir2	Signal Processing Toolbox
firls	Signal Processing Toolbox
remez	Signal Processing Toolbox

For related information, see Multirate Filters. Also see Filtering for a list of all DSP Blockset filtering blocks.

Two-Channel Analysis Subband Filter

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