Hi Neeharika,
I understand that you are looking for an explanation of how the "wrcoef" command in MATLAB works to reconstruct a signal from wavelet coefficients, and how it maintains the original number of samples after reconstruction.
I assume you are familiar with wavelet decomposition and reconstruction concepts.
Purpose of wrcoef:
The wrcoef function in MATLAB is used to reconstruct a specific detail or approximation component of a signal from its wavelet decomposition coefficients. It is part of the wavelet toolbox.
Reconstruction Process:
"wrcoef" requires the type of coefficients ('a' for approximation or 'd' for detail), the wavelet decomposition structure, the wavelet name, and the level of decomposition you want to reconstruct.
For example, if you want to reconstruct the approximation coefficients at level 3, you would call:
A3 = wrcoef('a', C, L, 'wname', 3);
Here, C is the wavelet decomposition vector, L is the bookkeeping vector, 'wname' is the wavelet name, and 3 is the level.
Maintaining the Original Signal Length:
The "wrcoef" function ensures that the reconstructed signal has the same length as the original signal by using the bookkeeping vector L, which contains information about the lengths of the various components at each level of decomposition.
This vector is generated during the decomposition process and is crucial for accurately reconstructing the signal to its original length.
Example of Usage:
Suppose you decompose a signal x using wavedec, and you have C and L as the output. To reconstruct the approximation at level 3:
[C, L] = wavedec(x, 3, 'wname');
A3 = wrcoef('a', C, L, 'wname', 3);
A3 will have the same number of samples as x, ensuring that the signal length is maintained.
Level-Specific Reconstruction:
The level you choose determines which part of the signal's frequency content you are reconstructing. Lower levels correspond to finer details, while higher levels correspond to coarser approximations.
Refer to the documentation of wrcoef for more details: https://www.mathworks.com/help/wavelet/ref/wrcoef.html
Refer to the documentation of wavedec for more details: https://www.mathworks.com/help/wavelet/ref/wavedec.html
Hope this helps!
