Mathematical analysis wavelets characteristics and their applications

Document Type : Research Paper


Directorate of Scholarships and Cultural Relations, Ministry of Higher Education and Scientific Research of Iraq, Baghdad, Iraq


Wavelets are now perceived as a ground-breaking new mathematical apparatus in signal and picture handling, time arrangement analysis, geophysics, guess hypothesis, and numerous various zones. Wavelet analysis has been an effective way to deal with issues related to analysing a signal in both time and frequency areas. Analysing a non-stationary signal becomes difficult for the various transform methods. Wavelet transforms techniques like Fourier Transform (FT), short-time Fourier transforms (STFT), and wavelet transform (WT) methods and their application are also discussed in detail. Wavelet analysis can be applied to one-dimensional signals like audio signals as well as two-dimensional signals like images. However wavelet processing has wide applications, some of the applications and methods are discussed in the paper.


[1] M.R. Banham, N.P. Galatsanos and H.L. Gonzalez, “Multichannel restoration of single channel images using wavelet-based sub band decomposition”. IEEE Trans. Image Process. 3(6) (2016) 821–833.
[2] G. Boopathi and S. Arockiasamy “Image Compression: An approach using Wavelet Transform and Modified FCM”, Int. J. Computer Appl. 28(2) (2011).
[3] E. Ferrazzi, et al. Miscarriage diagnosis and gestational age estimation in the early first trimester of pregnancy: transabdominal versus transvaginal sonography, Ultra Sound Obstet Gynecol 3 (1993) 36–41.
[4] J. Gardosi and R.T. Geirsson, “Routine ultra sound has been the method of choice for dating pregnancy, Br. J. Obstet Gynaecol 105 (1998) 933–36.
[5] R.T. Geirsson and G. Have, Comparison of actual and ultra sound estimated second trimester gestational length in in-vitro fertilized pregnancies, Acta Obstet Gynecol Scand. 72 (1993) 344–46.
[6] F.P. Hadlock, R.L. Deter, R.J. Carpenter and S.K. Park, Estimating Fatal age: effect of head shape on BPD, AJR Am. J. Roentgenol 137 (1981) 83–85.
[7] F.P. Hadlock, R.L. Deter, R.B. Harrist and S.K. Park. Fatal biparietal diameter: a critical re evaluation of the relation to menstrual age through means of real-time ultra sound, J. Ultra Sound Med. 1 (1982) 97–104.
[8] A.H.M. Jaffar Iqbal Barbhuiya and K. Hemachandran, Wavelet tranformations and its major applications in digital image processing, Int. J. Engin. Res. Tech. 2(3) (2013).
[9] A. Kaur, Transvaginal ultrasonography in first trimester of pregnancy and its comparison along transabdominal ultrasonography, J pharm Bioallied Sci. 3 (2011) 329-38.
[10] A. Pesters, Dignostic implications of intra and interobserver reproducibility of transvaginal sonographic measurement of gestational sac and crown rump length at 6-9 weeks gestation, In: Ultra sound Obstet Gynecol 38 (2011) 510–15.
[11] K. Sui and H.G. Kim, Research on application of multimedia image processing technology based on wavelet transform, EURASIP J. Image Video Processing 2019 (2019).
[12] D.Z. Tian and M.H. Ha, Applications of wavelet transform in medical image processing, Machine Learning and
Cybernetics, Proceedings of 2004 Int. Conf. 3 (2004).
[13] H. Yun, B. Li and S. Zhang, Pixel-through-pixel absolute three-dimensional shape measurement along modified
Fourier transform profilometry, Appl. Optics 56(5) (2017) 1472.
Volume 13, Issue 1
March 2022
Pages 837-850
  • Receive Date: 03 April 2021
  • Revise Date: 15 July 2021
  • Accept Date: 29 July 2021