B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

130 ANALYSIS AND TRANSMISSION OF SIGNALS
end
Hq=Hq' ;
Yq=Gq . *Hg;
yk=ifft (Yq) ;
clf,stem(k,yk)
REFERENCES
1. R. V. Churchill and J. W. Brown, Fourier Series and Boundary Value Problems, 3rd ed., McGraw-Hill,
New York, 1978.
2. R. N. Bracewell, Fourier Transform and Its Applications, rev. 2nd ed., McGraw-Hill, New York,
1986.
3. B. P. Lathi, Signal Processing and Linear Systems, Oxford University Press, 2000.
4. E. A. Guillemin, Theory of Linear Physical Systems, Wiley, New York, 1963.
5. F. J. Harris, "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform,"
Proc. IEEE, vol. 66, pp. 51-83, Jan. 1978.
6. J. W. Tukey and J. Cooley, "An Algorithm for the Machine Calculation of Complex Fourier Series,"
Mathematics of Computation, Vol. 19, pp. 297-301, April 1965.
PROBLEMS
3.1-1 Show that the Fourier transform of g(t) may be expressed as
G(f) = 1-: g(t) cos 2nft dt - j L: g(t) sin 2nft dt
Hence, show that if g(t) is an even function of t, then
G(f) = 2 fo 00 g(t) cos 2nft dt
and if g(t) is an odd function oft, then
G(f) = -2) fo 00 g(t) sin 2nft dt
Hence, prove that the following.
If g(t) is:
a real and even function of t
a real and odd function of t
an imaginary and even function of t
a complex and even function of t
a complex and odd function of t
Then G(f) is:
a real and even function off
an imaginary and odd function off
an imaginary and even function off
a complex and even function off
a complex and odd function off
3.1-2 (a) Show that for a real g(t), the inverse transform, Eq. (3.9b), can be expressed as
g(t) = 2 fo 00 !Glf)i cos[2nft + 0g (2nf)]df