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AM, FM, and Digital Modulated Systems Chap. 5
The need for the constraint of Eq. (5–32) will now be proven. Assume that s(t) is a DSB-
SC signal. Then, by the use of Eqs. (5–14) and (5–31), the spectrum of the VSB signal is
S VSB (f) = A c
2 [M(f - f c)H v (f) + M(f + f c )H v (f)]
Referring to Fig. 4–14, we see that the product detector output is
v out (t) = [A 0 s VSB (t) cos v c t] * h(t)
where h(t) is the impulse response of the low-pass filter having a bandwidth of B hertz. In the
frequency domain, this equation becomes
V out (f) = A 0 ES VSB (f) * C 1 2 d (f - f c) + 1 2 d (f + f c)DFH( f)
where H(f) = 1 for |f| 6 B and 0 for f elsewhere. Substituting for S VSB (f) and using the convolutional
property x( f) * d( f - a) = x(f - a) yields
V out (f) = A cA 0
4
[M(f)H v (f - f c ) + M(f)H v (f + f c )], |f| 6 B
or
V out (f) = A cA 0
4
M(f)[H v (f - f c ) + H v (f + f c )], |f| 6 B
If H v ( f) satisfies the constraint of Eq. (5–32), this equation becomes
V out (f) = KM(f)
or V out (t) = Km(t), where K = A c A 0 4, which shows that the output of the product detector is
undistorted when Eq. (5–32) is satisfied.
As discussed in Chapter 8, both analog and digital broadcast television use VSB to
reduce the required channel bandwidth to 6 MHz. For analog TV, as shown in Fig. 8–31c, the
frequency response of the visual TV transmitter is flat over the upper sideband out to 4.2
MHz above the visual carrier frequency and is flat over the lower sideband out to 0.75 MHz
below the carrier frequency. The IF filter in the TV receiver has the VSB filter characteristic
shown in Fig. 5–6c, where f ∆ = 0.75 MHz. This gives an overall frequency response characteristic
that satisfies the constraint of Eq. (5–32), so that the video modulation on the visual
VSB TV signal can be recovered at the receiver without distortion.
Digital TV (in the United States; see Sec. 8–9) uses an r = 0.0575 square-root raised
cosine-rolloff filter at the transmitter to obtain VSB as shown in Fig. 8–39. In practice, a
square-root raised cosine-rolloff filter is used in both the digital TV transmitter and the
receiver to give the overall raised cosine-rolloff characteristic, thereby minimizing the
effect of channel noise as well as ISI. (See Sec. 3–6.) This overall response also satisfies
Eq. (5–32), so that the digital TV signal (8-level serial data) is recovered without
distortion or ISI.