# 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

## Apps

Signal Multiresolution Analyzer | Decompose signals into time-aligned components |

Wavelet Signal Analyzer | Analyze and compress signals using wavelets (Since R2023a) |

Wavelet Signal Denoiser | Visualize and denoise time series data |

## Topics

### Wavelet Signal Analyzer

**Using Wavelet Signal Analyzer App**

Analyze and compress 1-D signals using wavelets.

- STEP 1:
**Select Signal to Analyze** - STEP 2:
**Decompose Signal** - STEP 3:
**Explore Signal Decomposition** - STEP 4:
**Compress Signal** - STEP 5:
**Share Results**

- STEP 1:
**Wavelet Decomposition of Complex-Valued Signal Using Wavelet Signal Analyzer**

Analyze a complex-valued signal using Wavelet Signal Analyzer.**Visualizing Wavelet Packet Terminal Nodes in Wavelet Signal Analyzer**

Learn how Wavelet Signal Analyzer visualizes wavelet packet decompositions.

### Signal Multiresolution Analyzer

**Using Signal Multiresolution Analyzer**

Learn how to visualize multilevel wavelet-based decompositions of real-valued signals.**Compare MODWTMRA and EMD Decompositions**

Learn how to compare fixed-bandwidth and data-adaptive decompositions using Signal Multiresolution Analyzer.**Share Results Using Signal Multiresolution Analyzer**

Learn how to share analyses generated by Signal Multiresolution Analyzer.**Visualize and Recreate EWT Decomposition**

Learn how to visualize an empirical wavelet transform decomposition using Signal Multiresolution Analyzer.**Visualize and Recreate TQWT Decomposition**

Learn how to visualize a tunable Q-factor wavelet transform decomposition using Signal Multiresolution Analyzer.**Visualize and Recreate VMD Decomposition**

Learn how to visualize the intrinsic mode functions and residual of a variational mode decomposition using Signal Multiresolution Analyzer.

### Critically Sampled DWT

**Critically Sampled and Oversampled Wavelet Filter Banks**

Learn about tree-structured, multirate filter banks.**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.**Wavelet Cross-Correlation for Lead-Lag Analysis**

Measure the similarity between two signals at different scales.**Comparing MODWT and MODWTMRA**

Learn the differences between the maximal overlap discrete wavelet transform (MODWT) and the multiresolution analysis based on the MODWT.**Nondecimated Discrete Stationary Wavelet Transforms (SWTs)**

Use the stationary wavelet transform to restore wavelet translation invariance.

### 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.**Wavelet Packets: Decomposing the Details**

This example shows how wavelet packets differ from the discrete wavelet transform (DWT).**Critically Sampled Wavelet Packet Analysis**

Obtain the wavelet packet transform of a 1-D signal and a 2-D image.