TwoChannel Analysis Subband Filter
Decompose signal into highfrequency and lowfrequency subbands
Libraries:
DSP System Toolbox /
Filtering /
Multirate Filters
Description
The TwoChannel Analysis Subband Filter block decomposes the input into highfrequency and lowfrequency 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 filterthendecimate 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 halfband 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 MbyN. The columns in the input signal represent N independent channels.
The block supports variablesize input signals (frame length changes during simulation)
when you set Input processing to
Columns as channels (frame based)
and
Rate options to Enforce
singlerate processing
. When you specify variablesize
input signals, they can be of arbitrary frame length, that is, the input
frame length does not have to be even. When you specify fixedsize
signals, the frame length can be arbitrary under certain conditions. For
more details, see FrameBased Processing and SampleBased Processing.
When the input is fixed point, it must be signed only.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Output
Hi band — Highfrequency subband
column vector  matrix
The block outputs the highfrequency subband as a column vector or a matrix.
When you set Rate options to:
Enforce singlerate 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)byN for an input of size MbyN.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 FrameBased Processing and SampleBased Processing.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Lo band — Lowfrequency subband
column vector  matrix
The block outputs the lowfrequency subband as a column vector or a matrix.
When you set Rate options to:
Enforce singlerate 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)byN for an input of size MbyN.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 FrameBased Processing and SampleBased 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 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 thirdorder Daubechies wavelet. When you use the TwoChannel 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 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 thirdorder Daubechies wavelet. When you use the TwoChannel 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 FrameBased Processing and SampleBased Processing.
Rate options — Rate options
Enforce singlerate
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 singlerate 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 toColumns 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 fixedsize input signals — Allow arbitrary frame length for fixedsize input signals
off
(default)  on
Since R2023a
Specify whether fixedsize 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 fixedsize input signals and ignores it if the input has a variablesize.
When the input signal is a variablesize signal, the signal can have an arbitrary frame length, that is, the frame length does not have to be an even number.
For fixedsize input signals, if you:
Select the Allow arbitrary frame length for fixedsize input signals parameter, the frame length of the signal does not have to be even. The output is a variablesize signal.
Clear the Allow arbitrary frame length for fixedsize 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 singlerate
processing
.
Data Types Tab
Rounding mode — Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Select the rounding
mode for fixedpoint 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 fullprecision mode.
Saturate on integer overflow — Saturate on integer overflow
off
(default)  on
When you select this parameter, the block saturates the result of its
fixedpoint operation. When you clear this parameter, the block wraps
the result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint 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 fullprecision mode.
Coefficients — Data type of the coefficients
Inherit: Same word length as
input
(default)  fixd(1,16)
 fixd(1,16,0)
Specify the coefficients data type. See FixedPoint 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
fixedpoint 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
fixedpoint data types.
Product output — Product output data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 fixd(1,16,0)
Specify the product output data type. See FixedPoint 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
 fixd(1,16,0)
Specify the accumulator data type. See FixedPoint 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
 fixd(1,16,0)
Specify the output data type. See FixedPoint 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 fixedpoint 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 fixedpoint data types
Lock data type settings against changes by the fixedpoint tools — Prevent fixedpoint tools from overriding data types
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify in the block dialog box.
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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)]
.
$$H\left(z\right)=B\left(z\right)={b}_{1}+{b}_{2}{z}^{1}+\dots +{b}_{m}{z}^{(m1)}$$
Each filter should be a halfband filter that passes the frequency band that the other filter stops. You can use the TwoChannel 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 TwoChannel Synthesis Subband Filter
block. You can also use other DSP System Toolbox™ and Signal Processing Toolbox™ functions.
The TwoChannel Analysis Subband Filter block initializes all filter states to zero.
FrameBased Processing
When you set the Input processing parameter to
Columns as channels (frame based)
, the block accepts
an MbyN matrix. The block treats each column
of the input as the high or lowfrequency 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 singlerate 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 lowfrequency subband of the corresponding input column. The frame length of each output has an upper bound size ofceil
(M/2).In this mode, if you input a fixedsize signal (frame length does not change during simulation) and select the Allow arbitrary frame length for fixedsize 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 fixedsize input signals parameter, the input frame length must be an even number.
In this mode, if you input a variablesize signal (frame length changes during simulation), the Allow arbitrary frame length for fixedsize input signals parameter appears on the block dialog box but does not have any impact on the input frame length. You can input a variablesize signal of any frame length even if you do not select the Allow arbitrary frame length for fixedsize 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 toEnforce singlerate processing
.Input Signal Block Support for this Signal Support for Arbitrary Input Frame Length Input Size Output Size Fixedsize input signal Yes When you select Allow arbitrary frame length for fixedsize input signals MbyN Upper bound size of ceil
(M/2)byNVariablesize input signal Yes Always MbyN Upper bound size of ceil
(M/2)byNWhen you set the Rate options parameter to
Allow multirate processing
, the input and the two outputs of the TwoChannel 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 MbyN matrix input as N independent channels and decomposes each channel over time. The block outputs two MbyN matrices, where each column of the output is the high or lowfrequency subband of the corresponding input column.In this mode, the block accepts only fixedsize 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 toAllow multirate processing
.Input Signal Block Support for this Signal Support for Arbitrary Input Frame Length Input Size Output Size Fixedsize input signal Yes Always MbyN MbyN Variablesize 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.
SampleBased Processing
When you set the Input processing parameter to
Elements as channels (sample based)
, the block treats
an MbyN matrix input as M · N independent channels. The block decomposes each channel over time
and outputs two MbyN matrices whose sample
rates are half the input sample rate. Each element in the output matrix is the high
or lowfrequency subband output of the corresponding element of the input
matrix.
In this mode, the block accepts only fixedsize 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 

Fixedsize input signal  Yes  Always  MbyN  MbyN 
Variablesize 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 singlerate
processing
, the TwoChannel Analysis Subband Filter
block always has zerotasking latency. Zerotasking 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 TwoChannel 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 


Off
 None. 
On
 One sample. The first output sample in each channel always
has a value of  

On or Off
 One frame. All samples in the first output frame have a
value of 
Note
For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and TimeBased Scheduling and Code Generation (Simulink Coder).
Creating Multilevel Dyadic Analysis Filter Banks
The TwoChannel Analysis Subband Filter block is the basic unit of a dyadic analysis filter bank. You can connect several of these blocks to implement an nlevel 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 TwoChannel Analysis Subband Filter block.
In some cases, rather than connecting several TwoChannel 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 2^{n}.
You are decomposing the signal into n+
1
or 2^{n} subbands.
In all other cases, use TwoChannel 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 waveletbased filters that the block designs by using a wavelet you specify.
FixedPoint Data Types
Fixedpoint data types in the TwoChannel Analysis Subband Filter Bank block.
The TwoChannel Analysis Subband Filter Bank block is composed of two FIR Decimation blocks as shown in the following diagram.
For fixedpoint 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: WellesleyCambridge 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.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
If the input is fixed point, it must be a signed integer or a signed fixed point value with a poweroftwo slope and zero bias.
Version History
Introduced before R2006aR2023a: Support for arbitrary input frame length
This block supports input signals with arbitrary frame lengths when the:
Input signal is a fixedsize signal (frame length does not change during simulation) and the block allows for multirate processing.
Input signal is a fixedsize signal, the block enforces singlerate processing, and you select the Allow arbitrary frame length for fixedsize input signals parameter.
Input signal is a variablesize 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 FrameBased Processing and SampleBased Processing.
See Also
Functions
Blocks
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