PROGRAM :
Fourier series. The space of periodic square summable functions. Orthorormal basis. Fourier series. Gibbs phenomenon. Fourier transform of periodic absolute integrable functions. Applications: spectral methods for partial differential equations.
Fourier integrals Fourier integral of absolute integrable functions on R. Fourier transform of elementary fiunzions. Convolution. Approximate indentities. Inversion formula. Fourier transform of square integrable functions. Poisson summation formula. The Paley-Wiener theorem. Discrete Fourier transform. Fast Fourier Transform. Cosine transform.
Signal analysis. Shannon theorem. Hilbert transform. Gabor transform
SUGGESTED BOOKS:
V. Del Prete Introduzione all'analisi di Fourier Dispense on line.
Y. Katznelson An introduction to harmonic analysis Collocaz Bibl. DIMA 43-1968-07.
E. O. Brigham, The Fast Fourier Transform, Prentice Hall Englewood Cliffs, Boston,1974. -
H. Dym - H. P. Mc Kean, Fourier Series and Integrals, Academic Press, 1972.
I. Korner, Fourier Analysis, 1995.
- I. Korner, Exercises for Fourier Analysis, 1995.
E. Prestini, Applicazioni dell'analisi armonica. U.Hoepli,Milano, 1996I.
E. Prestini, The Evolution of Applied Harmonic Analysis. Models of the Real World Series, A Birkhäuser 2004.
G.B. Folland, Fourier analysis and its applications Collocaz Bibl. DIMA 42-1992-01. The examination os oral