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Description

The `DyadicAnalysisFilterBank` object uses a series of highpass and lowpass FIR filters to provide approximate octave band frequency decompositions of the input. Each filter output is downsampled by a factor of two. With the appropriate analysis filters and tree structure, the dyadic analysis filter bank is a discrete wavelet transform (DWT) or discrete wavelet packet transform (DWPT).

To obtain approximate octave band frequency decompositions of the input:

1. Define and set up your dyadic analysis filter bank. See Construction.

2. Call `step` to get the octave half band frequency decompositions of the input according to the properties of `dsp.DyadicAnalysisFilterBank`. The behavior of `step` is specific to each object in the toolbox.

Note

Starting in R2016b, instead of using the `step` method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, ```y = step(obj,x)``` and `y = obj(x)` perform equivalent operations.

Construction

`dydan = dsp.DyadicAnalysisFilterBank` constructs a dyadic analysis filter bank object, `dydan`, that computes the level-two discrete wavelet transform (DWT) of a column vector input. For a 2-D matrix input, the object transforms the columns using the Daubechies third-order extremal phase wavelet. The length of the input along the first dimension must be a multiple of 4.

```dydan = dsp.DyadicAnalysisFilterBank('PropertyName',PropertyValue, ...)``` returns a dyadic analysis filter bank object, `dydan`, with each property set to the specified value.

Properties

`Filter`

Type of filter used in subband decomposition

Specify the type of filter used to determine the high and lowpass FIR filters in the dyadic analysis filter bank as `Custom` , `Haar`, `Daubechies`, `Symlets`, `Coiflets`, `Biorthogonal`, ```Reverse Biorthogonal```, or `Discrete Meyer`. All property values except `Custom` require Wavelet Toolbox™ software. If the value of this property is `Custom`, the filter coefficients are specified by the values of the `CustomLowpassFilter` and `CustomHighpassFilter` properties. Otherwise, the dyadic analysis filter bank object uses the Wavelet Toolbox function `wfilters` to construct the filters. The following table lists supported wavelet filters and example syntax to construct the filters:

FilterExample SettingSyntax for Analysis Filters
HaarN/A`[Lo_D,Hi_D]=wfilters('haar');`
Daubechies extremal phase`WaveletOrder=3;``[Lo_D,Hi_D]=wfilters('db3');`
Symlets (Daubechies least-asymmetric)`WaveletOrder=4;``[Lo_D,Hi_D]=wfilters('sym4');`
Coiflets `WaveletOrder=1;``[Lo_D,Hi_D]=wfilters('coif1');`
Biorthogonal`FilterOrder='[3/1]';````[Lo_D,Hi_D,Lo_R,Hi_R]=... wfilters('bior3.1');```
Reverse biorthogonal`FilterOrder='[3/1]';````[Lo_D,Hi_D,Lo_R,Hi_R]=... wfilters('rbior3.1');```
Discrete MeyerN/A`[Lo_D,Hi_D]=wfilters('dmey');`

`CustomLowpassFilter`

Lowpass FIR filter coefficients

Specify a vector of lowpass FIR filter coefficients, in powers of z-1. Use a half-band filter that passes the frequency band stopped by the filter specified in the `CustomHighpassFilter` property. This property applies when you set the `Filter` property to `Custom`. The default specifies a Daubechies third-order extremal phase scaling (lowpass) filter.

`CustomHighpassFilter`

Highpass FIR filter coefficients

Specify a vector of highpass FIR filter coefficients, in powers of z-1. Use a half-band filter that passes the frequency band stopped by the filter specified in the `CustomLowpassFilter` property. This property applies when you set the `Filter` property to `Custom`. The default specifies a Daubechies 3rd-order extremal phase wavelet (highpass) filter.

`WaveletOrder`

Order for orthogonal wavelets

Specify the order of the wavelet selected in the `Filter` property. This property applies when you set the `Filter` property to an orthogonal wavelet: `Daubechies` (Daubechies extremal phase), `Symlets` (Daubechies least-asymmetric), or `Coiflets`. The default is `2`.

`FilterOrder`

Analysis and synthesis filter orders for biorthogonal filters

Specify the order of the analysis and synthesis filter orders for biorthogonal filter banks as `1 / 1`, `1 / 3`, ```1 / 5```, `2 / 2`, `2 / 4`, `2 / 6`, `2 / 8`, ```3 / 1```, `3 / 3`, `3 / 5`, `3 / 7`, `3 / 9`, ```4 / 4```, or `5 / 5`, ```6 / 8```. Unlike orthogonal wavelets, biorthogonal wavelets require different filters for the analysis (decomposition) and synthesis (reconstruction) of an input. The first number indicates the order of the synthesis (reconstruction) filter. The second number indicates the order of the analysis (decomposition) filter. This property applies when you set the `Filter` property to `Biorthogonal` or ```Reverse Biorthogonal```. The default is ```1 / 1```.

`NumLevels`

Number of filter bank levels used in analysis (decomposition)

Specify the number of filter bank analysis levels a positive integer. A level-N asymmetric structure produces N+1 output subbands. A level-N symmetric structure produces 2N output subbands. The default is 2. The size of the input along the first dimension must be a multiple of 2N, where N is the number of levels.

`TreeStructure`

Structure of filter bank

Specify the structure of the filter bank as `Asymmetric` or `Symmetric`. The asymmetric structure decomposes only the lowpass filter output from each level. The symmetric structure decomposes the highpass and lowpass filter outputs from each level. If the analysis filters are scaling (lowpass) and wavelet (highpass) filters, the asymmetric structure is the discrete wavelet transform, while the symmetric structure is the discrete wavelet packet transform.

When this property is `Symmetric`, the output has 2N subbands each of size M/2N. In this case, M is the length of the input along the first dimension and N is the value of the `NumLevels` property. When this property is `Asymmetric`, the output has N+1 subbands. The following equation gives the length of the output in the kth subband in the asymmetric case:

`${M}_{k}=\left\{\begin{array}{ll}\frac{M}{{2}^{k}}\hfill & 1\le k\le N\hfill \\ \frac{M}{{2}^{N}}\hfill & k=N+1\hfill \end{array}$`
The default is `Asymmetric`.

Methods

 reset Reset filter states step Decompose input with dyadic filter bank
Common to All System Objects
`clone`

Create System object with same property values

`getNumInputs`

Expected number of inputs to a System object

`getNumOutputs`

Expected number of outputs of a System object

`isLocked`

Check locked states of a System object (logical)

`release`

Allow System object property value changes

Examples

expand all

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent `step` syntax. For example, myObject(x) becomes step(myObject,x).

Denoise square wave input using dyadic analysis and synthesis filter banks.

```t = 0:.0001:.0511; x= square(2*pi*30*t); xn = x' + 0.08*randn(length(x),1); dydanl = dsp.DyadicAnalysisFilterBank;```

The filter coefficients correspond to a `haar` wavelet.

```dydanl.CustomLowpassFilter = [1/sqrt(2) 1/sqrt(2)]; dydanl.CustomHighpassFilter = [-1/sqrt(2) 1/sqrt(2)]; dydsyn = dsp.DyadicSynthesisFilterBank; dydsyn.CustomLowpassFilter = [1/sqrt(2) 1/sqrt(2)]; dydsyn.CustomHighpassFilter = [1/sqrt(2) -1/sqrt(2)]; C = dydanl(xn);```

Subband outputs.

`C1 = C(1:256); C2 = C(257:384); C3 = C(385:512);`

Set higher frequency coefficients to zero to remove the noise.

```x_den = dydsyn([zeros(length(C1),1);... zeros(length(C2),1);C3]);```

Plot the original and denoised signals.

```subplot(2,1,1), plot(xn); title('Original noisy Signal'); subplot(2,1,2), plot(x_den); title('Denoised Signal');```

Algorithms

This object implements the algorithm, inputs, and outputs described on the Dyadic Analysis Filter Bank block reference page. The object properties correspond to the block parameters, except:

 The dyadic analysis filter bank object always concatenates the subbands into a single column vector for a column vector input, or into the columns of a matrix for a matrix input. This behavior corresponds to the block's behavior when you set the Output parameter to `Single port`.