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信号解析

間引きおよび非間引き 1 次元ウェーブレット変換、1 次元離散ウェーブレット変換フィルターバンク、1 次元並列木変換、ウェーブレットパケット

離散ウェーブレット変換、並列木変換およびウェーブレットパケットを使用して信号を解析します。

関数

離散ウェーブレット変換

`wavedec`	1 次元ウェーブレット分解
`waverec`	1-D wavelet reconstruction
`dwtfilterbank`	Discrete wavelet transform filter bank
`appcoef`	1-D approximation coefficients
`detcoef`	1-D detail coefficients
`haart`	Haar 1-D wavelet transform
`ihaart`	Inverse 1-D Haar wavelet transform
`mlpt`	Multiscale local 1-D polynomial transform
`imlpt`	Inverse multiscale local 1-D polynomial transform
`mlptrecon`	Reconstruct signal using inverse multiscale local 1-D polynomial transform
`wrcoef`	Reconstruct single branch from 1-D wavelet coefficients

離散ウェーブレットパケット変換

`wpdec`	Wavelet packet decomposition 1-D
`wprec`	Wavelet packet reconstruction 1-D
`wpcoef`	Wavelet packet coefficients
`wprcoef`	Reconstruct wavelet packet coefficients
`besttree`	Best tree wavelet packet analysis
`wpspectrum`	Wavelet packet spectrum
`otnodes`	Order terminal nodes of binary wavelet packet tree
`depo2ind`	Node depth-position to node index
`ind2depo`	Node index to node depth-position

非間引き離散ウェーブレットおよびウェーブレットパケット変換

`modwt`	Maximal overlap discrete wavelet transform
`imodwt`	Inverse maximal overlap discrete wavelet transform
`modwtmra`	Multiresolution analysis based on MODWT
`modwtcorr`	Multiscale correlation using the maximal overlap discrete wavelet transform
`modwtvar`	Multiscale variance of maximal overlap discrete wavelet transform
`modwtxcorr`	Wavelet cross-correlation sequence estimates using the maximal overlap discrete wavelet transform (MODWT)
`swt`	Discrete stationary wavelet transform 1-D
`iswt`	Inverse discrete stationary wavelet transform 1-D
`modwpt`	Maximal overlap discrete wavelet packet transform
`imodwpt`	Inverse maximal overlap discrete wavelet packet transform
`modwptdetails`	Maximal overlap discrete wavelet packet transform details
`dddtree`	Dual-tree and double-density 1-D wavelet transform
`dddtreecfs`	Extract dual-tree/double-density wavelet coefficients or projections
`dtfilters`	Analysis and synthesis filters for oversampled wavelet filter banks
`idddtree`	Inverse dual-tree and double-density 1-D wavelet transform
`plotdt`	Plot dual-tree or double-density wavelet transform

フラクタル解析

`dwtleader`	Multifractal 1-D wavelet leader estimates
`wfbm`	Fractional Brownian motion synthesis
`wfbmesti`	Parameter estimation of fractional Brownian motion

ユーティリティ

`wenergy`	Energy for 1-D wavelet or wavelet packet decomposition
`wmaxlev`	Maximum wavelet decomposition level
`dwtmode`	Discrete wavelet transform extension mode
`wvarchg`	Find variance change points
`measerr`	Quality metrics of signal or image approximation
`wavemngr`	Wavelet manager
`dyaddown`	Dyadic downsampling
`dyadup`	Dyadic upsampling
`tnodes`	Determine terminal nodes
`treedpth`	Tree depth
`wpviewcf`	Plot wavelet packets colored coefficients
`labeledSignalSet`	Create labeled signal set
`signalLabelDefinition`	Create signal label definition

アプリ

信号多重解像度アナライザー

時間を揃えた成分に信号を分解

トピック

大きくサンプリングされている DWT

時系列データおよびイメージの Haar 変換

Haar 変換を使用した信号の変動性の解析、信号の Approximation および透かしイメージの作成。

Border Effects

Compensate for discrete wavelet transform border effects using zero padding, symmetrization, and smooth padding.

非間引き DWT

Analytic Wavelets Using the Dual-Tree Wavelet Transform

Create approximately analytic wavelets using the dual-tree complex wavelet transform.

Wavelet Cross-Correlation for Lead-Lag Analysis

Measure the similarity between two signals at different scales.

Nondecimated Discrete Stationary Wavelet Transforms (SWTs)

Use the stationary wavelet transform to restore wavelet translation invariance.

Critically Sampled and Oversampled Wavelet Filter Banks

Learn about tree-structured, multirate filter banks.

密度推定

ウェーブレットを使用した密度推定

ウェーブレットをノンパラメトリック確率密度推定に使用します。

フラクタル解析

1 次元非整数ブラウン運動合成

1 次元非整数ブラウン運動信号を合成する

Multifractal Analysis

Use wavelet to characterize local signal regularity using wavelet leaders.

ウェーブレットパケット解析

Wavelet Packets

Use wavelet packets indexed by position, scale, and frequency for wavelet decomposition of 1-D and 2-D signals.

1-D Wavelet Packet Analysis

Analyze a signal with wavelet packets using the Wavelet Analyzer app.

2-D Wavelet Packet Analysis

Analyze an image with wavelet packets using the Wavelet Analyzer app.

ウェーブレットパケット: Detail の分解

この例では、ウェーブレットパケットと離散ウェーブレット変換 (DWT) の違いを示します。

注目の例

Wavelet Analysis of Financial Data

Use wavelets to analyze financial data.

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不連続部分および不連続点の検出

動的システムにおける過渡信号のように急速に発展する信号は、ジャンプのような急激な変化、あるいは 1 階微分や 2 階微分で鋭い変化が起こる可能性があります。フーリエ解析では通常、これらのイベントを検出することはできません。この例の目的は、ウェーブレットによる解析で信号が変化するときの正確な瞬時、またその種類 (信号の破損または 1 階微分や 2 階微分での急激な変化) および変化の振幅を検出できる方法を示すことです。イメージ処理では、主な用途の 1 つがエッジ検出であり、これにも急激な変化の検出が必要です。

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Wavelet Analysis of Physiologic Signals

Use wavelets to analyze physiologic signals.

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Dual-Tree Complex Wavelet Transforms

Learn the advantages the dual-tree complex wavelet transform provides over the critically sampled discrete wavelet transform.

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$Multifractal Analysis$

Multifractal Analysis

Use wavelets to characterize local signal regularity. The ability to describe signal regularity is important when dealing with phenomena that have no characteristic scale. Signals with scale-free dynamics are widely observed in a number of different application areas including biomedical signal processing, geophysics, finance, and internet traffic. Whenever you apply some analysis technique to your data, you are invariably assuming something about the data. For example, if you use autocorrelation or power spectral density (PSD) estimation, you are assuming that your data is translation invariant, which means that signal statistics like mean and variance do not change over time. Signals with no characteristic scale are scale-invariant. This means that the signal statistics do not change if we stretch or shrink the time axis. Classical signal processing techniques typically fail to adequately describe these signals or reveal differences between signals with different scaling behavior. In these cases, fractal analysis can provide unique insights. Some of the following examples use pwelch and xcorr for illustration. To execute that code, you must have the Signal Processing Toolbox™.

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