0195136047.pdf

662 SIGNAL PROCESSING

x(t)

x(t)

T

− 4

T

− 2

T

4

T

2

(a) (b)

−T

e−t

T

t

2 T

1

−T T

t

1

− 1

x(t)

(c)

t

1

2

2 T

3

T

x(t)

(d)

T

3

t

1

T

− 4

−

T

− 2

T

4

T

2

x(t)

(e)

t

1

1

T

3

2

−TT^2 T −

− 3

T

3

2 T

3

x(t)

(f)

t

1

Figure P14.1.14

(b) Using the result of Figure E14.1.4(a), find

the Fourier coefficients ofv(t).

*14.1.18The waveforms of Figure E14.1.4(b) and (c) are
given to haveA=πandT= 0 .2 ms.
(a) For 0≤f≤30 kHz, sketch and label the
amplitude spectra.
(b) ForAn<A 1 /5 for allnf 1 <W(whereA
stands for amplitude), determine the value of
Win each case.
14.1.19Consider Figure 14.1.5, withx(t)=3 cos 2πt

+cos(2π 3 t+180°),|H(f)|=1, and constant

phase shiftθ(f)=−90°. Sketchx(t) andy(t).

14.1.20The frequency response of a transmission system

is given by

|H(f)|=

1

√

1 +(f/fco)^2

;

θ(f)=−tan−^1

f

fco

wherefco=ωco/ 2 π=5 kHz. In order to satisfy

Equation (14.1.20), over the range of 0≤f≤