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The discrete wavelet transform (DWT) is well-suited for multiresolution analysis. The DWT decomposes high-frequency components of a signal with fine time resolution but coarse frequency resolution and decomposes low-frequency components with fine frequency resolution but coarse time resolution.
The following figure shows the frequency bands of the DWT for the db08 wavelet.
You can see that the central frequency and frequency bandwidth of the detail coefficients decrease by half when the decomposition level increases by one. For example, the central frequency and frequency bandwidth of D2 are half that of D1. You also can see that the approximation at a certain resolution contains all of the information about the signal at any coarser resolutions. For example, the frequency band of A2 covers the frequency bands of A3 and D3.
DWT-based multiresolution analysis helps you better understand a signal and is useful in feature extraction applications, such as peak detection and edge detection. Multiresolution analysis also can help you remove unwanted components in the signal, such as noise and trend.
The following figure shows the multiresolution results for a signal using the DWT.
You can see that the approximation at level 1 is the summation of the approximation and detail at level 2. The approximation at level 2 is the summation of the approximation and detail at level 3. As the level increases, you obtain lower frequency components, or large-scale approximation and detail, of the signal.
Refer to the Multiresolution Analysis - 1D Signal VI in the labview\examples\Wavelet Analysis\WAGettingStarted directory for an example of multiresolution analysis for a 1D signal.
Use the Multiresolution Analysis Express VI to decompose and reconstruct a signal at different levels and with different wavelet types.