Page 189 - Intelligent Communication Systems

I 60 INTELLIGENT COMMUNICATION SYSTEMS
i 2.3.4 Spectrum Transform

The transformation from the space domain to the frequency domain for an input
signal is performed, and the frequency spectrum is determined. Then a filtering
operation is performed on the spectrum.
To obtain the output image, an inverse frequency transform for the spectrum
is performed,

12.3.4.1 Fourier Transform
If function g(f) is a continuous function with period T, then g(f) can be represented
as direct current and components with frequency n/T (n = 1, 2,...)

g(t) = a 0 + a, cos2nt/T + a 2cos4nt/T + a^cos6nt/T + •••
sin 2ntl T + b 2 sin 4ntIT + b 3 sin 6 nt/T + • • •
+ b }

where, OQ, a n, b n are Fourier coefficients.
Fourier coefficients a 0, a n, b n are given in Eqs. (24), (25), and (26), respec-
tively.

12.3.4.2 Discrete Fourier Transform
When the period of a signal isT = N, the base frequency is/= UN, and the high
frequency is klN(k = 0,1, 2,..., N- 1), the Fourier expressions a(l/N) and b(l/N)
are as given in Eqs. (27) and (28), respectively.