# Signal Analysis

Decimated and nondecimated 1-D wavelet transforms, 1-D discrete wavelet transform filter bank, 1-D dual-tree transforms, wavelet packets

Analyze signals using discrete wavelet transforms, dual-tree transforms, and wavelet packets.

## Functions

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 `wavedec` 1-D wavelet decomposition `waverec` 1-D wavelet reconstruction `dwtfilterbank` Discrete wavelet transform filter bank `dualtree` Kingsbury Q-shift 1-D dual-tree complex wavelet transform `idualtree` Kingsbury Q-shift 1-D inverse dual-tree complex wavelet transform `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 `dddtree` Dual-tree and double-density 1-D wavelet transform `idddtree` Inverse dual-tree and double-density 1-D wavelet transform `mlptrecon` Reconstruct signal using inverse multiscale local 1-D polynomial transform `wrcoef` Reconstruct single branch from 1-D wavelet coefficients
 `dwpt` Multisignal 1-D wavelet packet transform `idwpt` Multisignal 1-D inverse wavelet packet transform `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
 `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
 `dwtleader` Multifractal 1-D wavelet leader estimates `wfbm` Fractional Brownian motion synthesis `wfbmesti` Parameter estimation of fractional Brownian motion
 `appcoef` 1-D approximation coefficients `dddtreecfs` Extract dual-tree/double-density wavelet coefficients or projections `detcoef` 1-D detail coefficients `dtfilters` Analysis and synthesis filters for oversampled wavelet filter banks `dwtmode` Discrete wavelet transform extension mode `dyaddown` Dyadic downsampling `dyadup` Dyadic upsampling `labeledSignalSet` Create labeled signal set `measerr` Quality metrics of signal or image approximation `qbiorthfilt` First-level dual-tree biorthogonal filters `qorthwavf` Kingsbury Q-shift filters `plotdt` Plot dual-tree or double-density wavelet transform `signalLabelDefinition` Create signal label definition `tnodes` Determine terminal nodes `treedpth` Tree depth `wavemngr` Wavelet manager `wenergy` Energy for 1-D wavelet or wavelet packet decomposition `wmaxlev` Maximum wavelet decomposition level `wpviewcf` Plot wavelet packets colored coefficients `wvarchg` Find variance change points

## Apps

 Signal Multiresolution Analyzer Decompose signals into time-aligned components

## Topics

### Critically Sampled DWT

Haar Transforms for Time Series Data and Images

Use Haar transforms to analyze signal variability, create signal approximations, and watermark images.

Border Effects

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

### Nondecimated DWT

Analytic Wavelets Using the Dual-Tree Wavelet Transform

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

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.

### Density Estimation

Density Estimation Using Wavelets

Use wavelets for nonparametric probability density estimation.

### Fractal Analysis

1-D Fractional Brownian Motion Synthesis

Synthesize a 1-D fractional Brownian motion signal.

Multifractal Analysis

Use wavelets to characterize local signal regularity using wavelet leaders.

### Wavelet Packet Analysis

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.

Wavelet Packets: Decomposing the Details

This example shows how wavelet packets differ from the discrete wavelet transform (DWT).

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