Computational Data analysis of Fourıer Transformatıon by Numerical experiments(Numerical CODE)

  • Tadesse Lamessa Woalita sodo university
Keywords: Numerically, frequency, Fourier series, numerical code


 The Fourier series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time (FS) or discrete time (DFT). Both analyze signals into amplitude, phases, and frequencies of complex exponentials; both synthesize signals by linearly combining complex exponentials with appropriate amplitude, phase, and frequency. Finally, both transforms have aspects that are extremely important to remember and other aspects that are important, but can be adjusted as necessary. As we work through some of the details, we’ll identify these very important and the not so important aspects. Frequency analysis is one of the key issues in the IEEE Society. Using computers in numerical calculations means moving into a non-physical, synthetic environment. Numerically, discrete or fast Fourier transformations (DFT or FFT) are used to obtain the frequency contents of a time signal and these are totally different than mathematical definition of the Fourier transform. This article simple reviews DFT and FFT with characteristic examples.


Download data is not yet available.

Author Biography

Tadesse Lamessa, Woalita sodo university

College of Natural scince and Computational scince
Department of Applied Mathematics
Woalita sodo university,
sodo Ethiopia,


Baron Jean Baptiste Fourier (see, e.g.,

HP, “The Fundamentals of Signal Analysis”, Hewlett Packard Application note 243, 1994

L. Sevgi, F. Akleman, L. B. Felsen, “Ground Wave Propagation Modeling: Problem-matched Analytical Formulations and Direct Numerical Techniques”, IEEE Antennas and Propagation Magazine, Vol. 44, No.1, pp.55-75, Feb. 2002

L. Sevgi, Complex Electromagnetic Problems and Numerical Simulation Approaches, IEEE Press – John Wiley and Sons, June 2003

M. Levy, Parabolic equation methods for electromagnetic wave propagation, IEE, Institution of Electrical Engineers, 2000

F. J. Harris, “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform”, Proc. IEEE, Vol. 66, no. 1, pp.51-83, Jan 1978

Lima, F. (2018) What Exactly Is the Electric Field at the Surface of a Charged Conducting Sphere? Resonance, 23, 1215-1223.

Assad, G. (2012) Electric Field “On the Surface” of a Spherical Conductor: An Issue to Be Clarified. Revista Brasileira de Fesica, 34, 4701.

Griffiths, D. and Walborn, S. (1999) Dirac Deltas and Discontinuous Functions.

American Journal of Physics, 67, 446-447.

Fedak, W.A. (2002) Quantum Jumps and Classical Harmonics. American Journal of Physics, 70, 332-344.

Fan, G.-X. (2004) Fast Fourier Transform for Discontinuous Functions. IEEE

Transactions on Antennas and Propagation, 52, 461-465.

Janssen, J.M. (1950) The Method of Discontinuities in Fourier Analysis. Philips Research Reports, 5, 435-460.

Huang, X., Liu, X. and Mi, Y. (2013) The Fourier Series Approach to Investigate

Phase-Locking Behaviors of the Sinoatrial Node Cell. Europhysics Letters, 104, Article ID: 38002.

Thompson, W.J. (1992) Fourier Series and Gibbs Phenomenon. American Journal of Physics, 60, 425.

Tsagareishvill, V. (2017) On Fourier Coefficients of Functions with Respect to General Orthonormal Systems. Izvestiya Mathematics, 81, 179.

[ Kvernadze, G. (2003) Approximating the Jump Discontinuities of a Function by Its Fourier-Jacobi Coefficients. Mathematics of Computation, 73, 731-751.

[ Ageev, A.L. and Antonova, T.V. (2015) Approximation of Discontinuity Lines for aNoisy Function of Two Variables with Countably Many Singularities.