Decompose signal into high-frequency and low-frequency subbands

Filtering / Multirate Filters

`dspmlti4`

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 illustrated in the following figure.

The block implements the FIR filtering and downsampling steps together using a polyphase filter structure, which is more efficient than the straightforward 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.

See the following topics for more information about this block:

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 in 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.

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 to the block can be an*M*-by-*N*matrix, where*M*is a multiple of two. 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. To maintain the input sample rate, the block decreases the output frame size by a factor of two.When you set the

**Rate options**parameter to`Allow multirate processing`

, the block treats an*M*_{i}-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. The input and output frame*sizes*are the same, but the frame*rate*of the output is half that of the input. Thus, the overall sample rate of the output is half that of the input.In this mode, the block has one frame of latency, as described in the Latency section.

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.

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

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 |
---|---|---|

| `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 |

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).

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 less 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 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.

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.

**Main Tab**

**Lowpass FIR filter coefficients**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 Specifying the FIR Filters.**Highpass FIR filter coefficients**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 Specifying the FIR Filters.**Input processing**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.

**Rate options**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.

**Data Types Tab**

**Rounding mode**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 is effectively operating in full precision mode.

**Saturate on integer overflow**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**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**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**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**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 may 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**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**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 Signal Data Types (Simulink) for more information.

**Output Minimum**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**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**Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block mask.

Double-precision floating point

Single-precision floating point

Fixed point (signed only)

8-, 16-, and 32-bit signed integers

[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.