How to use DWT when sample size is smaller thn filter length

[Sidharth M]

Hi,
I am new member over here. I wanted to know how to perform discrete wavelet transform, probably using symmlet 8 wavelet with 16 Low/High pass filter coefficients using matrix transformation method when decomposing to a certain level the approximate coefficients i.e. sample size becomes less than the number of filter coefficients (say 8 samples compared to 16 filter coefficients).

Matrix method have been given in several books e.g. "Ripples in Mathematics: The Discrete Wavelet Transform" - A. Jensen and A.la Cour-Harbo.

However, the book only deals with cases where the number of filter coefficients are less than sample size.

 

[jvicens]

Hi there,

Thank you for your question! The discrete wavelet transform (DWT) is a powerful tool in signal processing and has many applications in various fields such as image processing, data compression, and noise reduction. It is a mathematical technique that decomposes a signal into different frequency components, allowing for the extraction of useful information.

Performing the DWT using the symmlet 8 wavelet with 16 low/high pass filter coefficients can be done using the matrix transformation method. This method involves representing the DWT as a set of matrix operations, making it easier to implement in software.

To perform the DWT using the matrix transformation method, you will need to follow these steps:

1. Define the signal and the wavelet: The first step is to define the signal that you want to analyze and the wavelet that you will use for the transformation. In this case, the signal size is 8 samples and the wavelet is symmlet 8 with 16 low/high pass filter coefficients.

2. Create the filter matrices: The next step is to create the matrices for the low and high pass filters. These matrices will have dimensions of 16x8, with each row representing a different filter coefficient. The values in these matrices will depend on the chosen wavelet.

3. Decompose the signal: Once the filter matrices are created, you can use them to decompose the signal into its approximate coefficients. This is done by multiplying the signal vector with the low pass filter matrix and high pass filter matrix separately.

4. Repeat the decomposition: After obtaining the approximate coefficients, you can repeat the decomposition process on the lowest frequency components. This will result in a multi-level decomposition, with each level reducing the sample size by half.

5. Reconstruction: Once the desired level of decomposition is reached, you can reconstruct the signal by performing the inverse DWT using the same filter matrices.

It is important to note that the matrix transformation method is just one way of performing the DWT and there are other methods available as well. I would recommend consulting the book you mentioned for a more detailed explanation and examples.

I hope this helps answer your question. Best of luck with your research!