A computer program to calculate discrete wavelet transform for one-dimensional signals

This is the most recent version of the True Basic program 'NDHAAR.TRU', which was part of the supplementary materials for the following publication: X. Dong, P. Nyren, B. Patton, A. Nyren, J. Richardson and T. Maresca, 2008. Wavelets for agriculture and biology: A tutorial with applications and outlook. BioScience 58: 445-453.

The original version (1.0, April 8, 2008) accepts a one-dimensional signal with 1024 data points. It was previously posted at http://www.ag.ndsu.edu/CentralGrasslandsREC/wavelets-for-agriculture-and-biology

Version 1.1 (June 1, 2010) accepts signals with a length of 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
32768, or 65536. This version with documentation was initially posted at www.infoclearinghouse.com. Later the website was closed. Now the documentation can still be accessed at https://www.scss.tcd.ie/Khurshid.Ahmad/Research/Wavelets/wva.pdf.

Version 1.2 is posted in this current upload. A major change in this version is the correction of a few typos existing in Version 1.1, so that the program can correctly process signals longer than 4096 (that is, with signal length as either of 8192, 16384, 32768, or 65536). Note that Version 1.1 is fine in correctly processing signals with a length at or shorter than 4096.

Two sample input data files are included. Also included is the original supplemental material Suppl_dong_2008.pdf. The first input data file 'pdsi.txt' has a length of 1024, and  the related output files are OO1.txt, OO2.txt, OO3.txt, OO4.txt and OO5.txt. These data files  are discussed in the original BioScience paper as well as in Suppl_dong_2008.pdf. 

The second sample input file 'warm.txt' has a length of 65536 and the related output files are OUT_1.txt, OUT_2.txt, OUT_3.txt, OUT_4.txt, and OUT_5.txt. The sample input file warm.txt contains NDVI values of winter wheat measured at Uvalde, TX, USA, from about 8 am to 10 am on April 12, 2018. The measurement was made using an ACS-430 Crop Circle sensor mounted to a push-wheel cart. This file and the associated output files are part of the intermediate results for Supplementary Figure S2 to the article entitled "Leaf water potential of field crops estimated using NDVI in ground-based remote sensing - opportunities to increase prediction precision" (PeerJ. 9:e12005 DOI 10.7717/peerj.12005), which can be accessed at https://zenodo.org/record/4574674#.YD7kI2hKiUk