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An alternate approach to single sideband modulation (SSB) for “saving” bandwidth is called quadrature phase multiplexing. The idea is behind this is that cos(wet) and sin(wet) are mutually orthogonal due to their π/2 phase difference. So we can send two message signals x₁(t) and x2(t), in the same frequency bands, by modulated by cos(wet) and sin(wet) respectively. Figure 4(a) provides the block schematic for implementing quadrature phase multi- plexing. x₁(t) x2 (t) cos(wet) X₁ (jw) y(t) 3-K. -WM X sin(wet) X (a) WM W (b) -WM Figure 4: Quadrature phase multiplexing 1 X₂ (jw) WM (Part a) Express Y(jw) in terms of X₁(jw), X₂(jw) and other relevant quantities. (Part b) Given X₁(jw) and X₂(jw) as in Figure 4(b), plot the real and imaginary components of the spectrum of y(t), i.e., sketch Re{Y(jw)} and Im{Y(jw)}. (Part c) Design and justify demodulation scheme(s) for obtaining x₁(t) and x₂(t) from y(t).

An alternate approach to single sideband modulation (SSB) for “saving” bandwidth is called quadrature phase multiplexing. The idea is behind this is that cos(wet) and sin(wet) are mutually orthogonal due to their π/2 phase difference. So we can send two message signals x₁(t) and x2(t), in the same frequency bands, by modulated by cos(wet) and sin(wet) respectively. Figure 4(a) provides the block schematic for implementing quadrature phase multi- plexing. x₁(t) x2 (t) cos(wet) X₁ (jw) y(t) 3-K. -WM X sin(wet) X (a) WM W (b) -WM Figure 4: Quadrature phase multiplexing 1 X₂ (jw) WM (Part a) Express Y(jw) in terms of X₁(jw), X₂(jw) and other relevant quantities. (Part b) Given X₁(jw) and X₂(jw) as in Figure 4(b), plot the real and imaginary components of the spectrum of y(t), i.e., sketch Re{Y(jw)} and Im{Y(jw)}. (Part c) Design and justify demodulation scheme(s) for obtaining x₁(t) and x₂(t) from y(t).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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6. An alternate approach to single sideband modulation (SSB) for "saving" bandwidth is called quadrature phase multiplexing. The idea is behind this is that cos(wet) and sin(wet) are mutually orthogonal due to their π/2 phase difference. So we can send two message signals x₁(t) and x2(t), in the same frequency bands, by modulated by cos(wet) and sin(wet) respectively. Figure 4(a) provides the block schematic for implementing quadrature phase multi- plexing. x₁ (t) x2 (t) cos(wet) X sin(wet) X (a) + y(t) X₁ (jw) 1 K. WM (b) -WM -WM Figure 4: Quadrature phase multiplexing ↑X₂ (jw) 1 WM 3 (Part a) Express Y(jw) in terms of X₁ (jw), X₂(jw) and other relevant quantities. (Part b) Given X₁(jw) and X₂(jw) as in Figure 4(b), plot the real and imaginary components the spectrum of y(t), i.e., sketch Re{Y(jw)} and Im{Y(jw)}. (Part c) Design and justify demodulation scheme(s) for obtaining x1₁(t) and x₂(t) from y(t).
Transcribed Image Text:6. An alternate approach to single sideband modulation (SSB) for "saving" bandwidth is called quadrature phase multiplexing. The idea is behind this is that cos(wet) and sin(wet) are mutually orthogonal due to their π/2 phase difference. So we can send two message signals x₁(t) and x2(t), in the same frequency bands, by modulated by cos(wet) and sin(wet) respectively. Figure 4(a) provides the block schematic for implementing quadrature phase multi- plexing. x₁ (t) x2 (t) cos(wet) X sin(wet) X (a) + y(t) X₁ (jw) 1 K. WM (b) -WM -WM Figure 4: Quadrature phase multiplexing ↑X₂ (jw) 1 WM 3 (Part a) Express Y(jw) in terms of X₁ (jw), X₂(jw) and other relevant quantities. (Part b) Given X₁(jw) and X₂(jw) as in Figure 4(b), plot the real and imaginary components the spectrum of y(t), i.e., sketch Re{Y(jw)} and Im{Y(jw)}. (Part c) Design and justify demodulation scheme(s) for obtaining x1₁(t) and x₂(t) from y(t).
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