Two-Channel Analysis Subband Filter

Decompose signal into high-frequency and low-frequency subbands

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Libraries:
DSP System Toolbox / Filtering / Multirate Filters

Description

The Two-Channel Analysis Subband Filter block decomposes the input into high-frequency and low-frequency subbands, each with half the bandwidth and half the sample rate of the input.

The block filters the input with a pair of highpass and lowpass FIR filters, and then downsamples the results by 2, as shown in this figure.

The block implements the FIR filtering and downsampling steps together using a polyphase filter structure, which is more efficient than the filter-then-decimate algorithm shown in the preceding figure. Each subband is the first phase of the respective polyphase filter. You can implement a multilevel dyadic analysis filter bank by connecting multiple copies of this block or by using the Dyadic Analysis Filter Bank block. See Creating Multilevel Dyadic Analysis Filter Banks for more information.

You must provide a vector of filter coefficients for the lowpass and highpass FIR filters. Each filter should be a half-band filter that passes the frequency band that the other filter stops.

Ports

Input

Input 1 — Data input

column vector | matrix

Specify the data input as a column vector or a matrix of size M-by-N. The columns in the input signal represent N independent channels.

The block supports variable-size input signals (frame length changes during simulation) when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing. When you specify variable-size input signals, they can be of arbitrary frame length, that is, the input frame length does not have to be even. When you specify fixed-size signals, the frame length can be arbitrary under certain conditions. For more details, see Frame-Based Processing and Sample-Based Processing.

If the input is fixed point, it must be a signed integer or a signed fixed point value with a power-of-two slope and zero bias.

Data Types: single | double | int8 | int16 | int32 | fixed point

Output

Hi band — High-frequency subband

column vector | matrix

The block outputs the high-frequency subband as a column vector or a matrix.

When you set Rate options to:

• Enforce single-rate processing –– The block maintains the input sample rate and decimates the signal by decreasing the output frame size by a factor of 2.

  The output has an upper bound size of ceil(M/2)-by-N for an input of size M-by-N.

• Allow multirate processing –– The block decimates the signal such that the output sample rate is half the input sample rate.

  The output frame size is the same as the input frame size.

For more details, see Frame-Based Processing and Sample-Based Processing.

Data Types: single | double | int8 | int16 | int32 | fixed point

Lo band — Low-frequency subband

column vector | matrix

The block outputs the low-frequency subband as a column vector or a matrix.

When you set Rate options to:

• Enforce single-rate processing –– The block maintains the input sample rate and decimates the signal by decreasing the output frame size by a factor of 2.

  The output has an upper bound size of ceil(M/2)-by-N for an input of size M-by-N.

• Allow multirate processing –– The block decimates the signal such that the output sample rate is half the input sample rate.

  The output frame size is the same as the input frame size.

For more details, see Frame-Based Processing and Sample-Based Processing.

Data Types: single | double | int8 | int16 | int32 | fixed point

Parameters

Main Tab

Lowpass FIR filter coefficients — Lowpass FIR filter coefficients

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

Specify 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. The default values of this parameter specify a filter based on a third-order Daubechies wavelet. When you use the Two-Channel Synthesis Subband Filter block to reconstruct the input to this block, you need to design perfect reconstruction filters to use in the synthesis subband filter. For more information, see Specify FIR Filters.

Highpass FIR filter coefficients — Highpass FIR filter coefficients

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

Specify 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. The default values of this parameter specify a filter based on a third-order Daubechies wavelet. When you use the Two-Channel Synthesis Subband Filter block to reconstruct the input to this block, you need to design perfect reconstruction filters to use in the synthesis subband filter. For more information, see Specify FIR Filters.

Input processing — Input processing

Columns as channels (frame based) (default) | Elements as channels (sample based)

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) (default) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

For more information, see Frame-Based Processing and Sample-Based Processing.

Rate options — Rate options

Enforce single-rate processing (default) | Allow multirate processing

Specify the rate processing rule for the block. You can set this parameter to one of the following options:

• Enforce single-rate processing — When you select this option, the block treats each column of the input as an independent channel and decomposes each channel over time. The output has the same sample rate as the input, but the output frame size is half that of the input frame size. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

• Allow multirate processing — When you select this option, the input and output of the block are the same size, but the sample rate of the output is half that of the input.

Some settings of this parameter cause the block to have nonzero latency. See Latency for more information.

Allow arbitrary frame length for fixed-size input signals — Allow arbitrary frame length for fixed-size input signals

off (default) | on

Since R2023a

Specify whether fixed-size input signals (whose size does not change during simulation) can have an arbitrary frame length, where the frame length does not have to be even. The block uses this parameter only for fixed-size input signals and ignores it if the input has a variable-size.

When the input signal is a variable-size signal, the signal can have an arbitrary frame length, that is, the frame length does not have to be an even number.

For fixed-size input signals, if you:

• Select the Allow arbitrary frame length for fixed-size input signals parameter, the frame length of the signal does not have to be even. The output is a variable-size signal.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be even.

Dependency

To enable this parameter, set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

Data Types Tab

Rounding mode — Rounding mode for fixed-point operations

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Select the rounding mode for fixed-point operations. The filter coefficients do not obey this parameter; they are always rounded to Nearest.

Note

The Rounding mode and Saturate on integer overflow settings have no effect on numerical results when all the following conditions exist:

• Product output is Inherit: Inherit via internal rule

• Accumulator is Inherit: Inherit via internal rule

• Output is Inherit: Same as accumulator

With these data type settings, the block effectively operates in full-precision mode.

Saturate on integer overflow — Saturate on integer overflow

off (default) | on

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Note

The Rounding mode and Saturate on integer overflow parameters have no effect on numeric results when all these conditions are met:

• Product output data type is Inherit: Inherit via internal rule.

• Accumulator data type is Inherit: Inherit via internal rule.

With these data type settings, the block operates in full-precision mode.

Coefficients — Data type of the coefficients

Inherit: Same word length as input (default) | fixdt(1,16) | fixdt(1,16,0)

Specify the coefficients data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the coefficients data type in this block. You can set it to:

• A rule that inherits a data type, for example, Inherit: Same word length as input

• An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Coefficients parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Coefficients Minimum — Minimum value of filter coefficients

[] (default) | scalar

Specify the minimum value of the filter coefficients. The default value is [] (unspecified). Simulink^® software uses this value to perform automatic scaling of fixed-point data types.

Coefficients Maximum — Maximum value of filter coefficients

[] (default) | scalar

Specify the maximum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform automatic scaling of fixed-point data types.

Product output — Product output data type

Inherit: Inherit via internal rule (default) | Inherit: Same as input | fixdt(1,16,0)

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:

• A rule that inherits a data type, for example, Inherit: Inherit via internal rule. For more information on this rule, see Inherit via Internal Rule.

  Note

  The actual product output word length can be equal to or greater than the calculated ideal product output word length, depending on the settings on the Hardware Implementation pane of the Configuration Parameters dialog box.

• An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Accumulator — Data type of accumulator

Inherit: Inherit via internal rule (default) | Inherit: Same as input | Inherit: Same as product output | fixdt(1,16,0)

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

• A rule that inherits a data type, for example, Inherit: Inherit via internal rule. For more information on this rule, see Inherit via Internal Rule.

• An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Output — Data type of output

Inherit: Same as accumulator (default) | Inherit: Same as input | Inherit: Same as product output | fixdt(1,16,0)

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set it to:

• A rule that inherits a data type, for example, Inherit: Same as accumulator

• An expression that evaluates to a valid data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Data Types of Signals (Simulink) for more information.

Output Minimum — Output minimum

[] (default) | scalar

Specify the minimum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Output Maximum — Output maximum

[] (default) | scalar

Specify the maximum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

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

More About

Specify 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)].

$$H\left(z\right)=B\left(z\right)=b_1+b_2{z}^{-1}+\dots +b_m{z}^{-(m-1)}$$

Each filter should be a half-band filter that passes the frequency band that the other filter stops. You can use the Two-Channel Synthesis Subband Filter block to reconstruct the input to this block. To do so, you must design perfect reconstruction filters to use in the synthesis subband filter.

The best way to design perfect reconstruction filters is to use the Wavelet Toolbox™ wfilters function to design both the filters both in this block and in the Two-Channel Synthesis Subband Filter block. You can also use other DSP System Toolbox™ and Signal Processing Toolbox™ functions.

The Two-Channel Analysis Subband Filter block initializes all filter states to zero.

Frame-Based Processing

When you set the Input processing parameter to Columns as channels (frame based), the block accepts an M-by-N matrix. The block treats each column of the input as the high- or low-frequency subbands of the corresponding output channel. You can use the Rate options parameter to specify how the block resamples the input:

• When you set the Rate options parameter to Enforce single-rate processing, the input and the two outputs of the block have the same sample rate. The block treats each column of the input as an independent channel and decomposes each channel over time. The block outputs two matrices, where each column of the output is the high- or low-frequency subband of the corresponding input column. The frame length of each output has an upper bound size of ceil(M/2).

  In this mode, if you input a fixed-size signal (frame length does not change during simulation) and select the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length can be arbitrary and does not have to be an even number. If you clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be an even number.

  In this mode, if you input a variable-size signal (frame length changes during simulation), the Allow arbitrary frame length for fixed-size input signals parameter appears on the block dialog box but does not have any impact on the input frame length. You can input a variable-size signal of any frame length even if you do not select the Allow arbitrary frame length for fixed-size input signals parameter.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	When you select Allow arbitrary frame length for fixed-size input signals	M-by-N	Upper bound size of ceil(M/2)-by-N
  Variable-size input signal	Yes	Always	M-by-N	Upper bound size of ceil(M/2)-by-N

• When you set the Rate options parameter to Allow multirate processing, the input and the two outputs of the Two-Channel Analysis Subband Filter block are of the same size, but the sample rate of the output is half that of the input. In this mode, the block treats a M-by-N matrix input as N independent channels and decomposes each channel over time. The block outputs two M-by-N matrices, where each column of the output is the high- or low-frequency subband of the corresponding input column.

  In this mode, the block accepts only fixed-size signals and these signals can have arbitrary frame length. That is, the frame length does not have to be even.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Allow multirate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	Always	M-by-N	M-by-N
  Variable-size input signal	No	Not applicable	Not applicable	Not applicable

  In this mode, the block has one frame of latency, as described in the Latency section.

Sample-Based Processing

When you set the Input processing parameter to Elements as channels (sample based), the block treats an M-by-N matrix input as M · N independent channels. The block decomposes each channel over time and outputs two M-by-N matrices whose sample rates are half the input sample rate. Each element in the output matrix is the high- or low-frequency subband output of the corresponding element of the input matrix.

In this mode, the block accepts only fixed-size signals and these signals can have an arbitrary frame length.

This table summarizes the support for arbitrary input frame length when you set Input processing to Elements as channels (sample based). Rate options is automatically set to Allow multirate processing.

Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
Fixed-size input signal	Yes	Always	M-by-N	M-by-N
Variable-size input signal	No	Not applicable	Not applicable	Not applicable

Depending on the setting of your Simulink configuration parameters, the output may have one sample of latency, as described in the Latency section.

Latency

When you set the Input processing parameter to Columns as channels (frame based) and the Rate options parameter to Enforce single-rate processing, the Two-Channel Analysis Subband Filter block always has zero-tasking latency. Zero-tasking latency means that the block propagates the first input sample (received at time t=0) as the first output sample.

When you set the Rate options parameter to Allow multirate processing, the Two-Channel Analysis Subband Filter block may exhibit latency. The amount of latency depends on the setting of the Input processing parameter of this block, and the setting of the Simulink Treat each discrete rate as a separate task configuration parameter. The following table summarizes the conditions that produce latency when the block is performing multirate processing.

Input processing	Treat each discrete rate as a separate task	Latency
Elements as channels (sample based)	Off	None.
	On	One sample. The first output sample in each channel always has a value of 0.
Columns as channels (frame based)	On or Off	One frame. All samples in the first output frame have a value of 0.

Note

For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

Creating Multilevel Dyadic Analysis Filter Banks

The Two-Channel Analysis Subband Filter block is the basic unit of a dyadic analysis 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 analysis filter banks, see the Dyadic Analysis Filter Bank block reference page.

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. Though the output values differ, both sets of values are valid; the difference arises from changes in latency. See the Latency section for more information about when latency can occur in the Two-Channel Analysis Subband Filter block.

In some cases, rather than connecting several Two-Channel Analysis Subband Filter blocks, you can use the Dyadic Analysis Filter Bank block, which is faster and requires lesser memory. In particular, the Dyadic Analysis Filter Bank block is more efficient under the following conditions:

• The frame size of the signal you are decomposing is a multiple of 2ⁿ.

• You are decomposing the signal into n+1 or 2ⁿ subbands.

In all other cases, use Two-Channel Analysis Subband Filter blocks to implement your filter banks.

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

Fixed-Point Data Types

Fixed-point data types in the Two-Channel Analysis Subband Filter Bank block.

The Two-Channel Analysis Subband Filter Bank block is composed of two FIR Decimation blocks as shown in the following diagram.

For fixed-point signals, you can set the coefficient, product output, accumulator, and output data types of the FIR Decimation blocks as discussed in Parameters. For a diagram showing the usage of these data types, see the FIR Decimation block reference page.

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.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

R2023a: Support for arbitrary input frame length

This block supports input signals with arbitrary frame lengths when the:

• Input signal is a fixed-size signal (frame length does not change during simulation) and the block allows for multirate processing.

• Input signal is a fixed-size signal, the block enforces single-rate processing, and you select the Allow arbitrary frame length for fixed-size input signals parameter.

• Input signal is a variable-size signal (frame length changes during simulation).

When this block supports an input signal with an arbitrary frame length, the input frame length does not have to be even.

For more details, see Frame-Based Processing and Sample-Based Processing.