Understanding Digital Signal Processing by Richard G. Lyons

Author:Richard G. Lyons
Language: eng
Format: epub, pdf
Publisher: Prentice Hall
Published: 2011-04-08T16:00:00+00:00

For computational efficiency reasons, to avoid unnecessary arithmetic using the imaginary parts of the complex C values, we might decide to compute Q as

Show the validity (the correctness) of using Qefficient to compute our desired Q value.

Hint: Appendix A will help you solve this problem.

8.6 To show the value of using complex numbers in our derivations of real-valued functions, use the notation

cos(ϕ) = Re{ejϕ}

where Re{ejϕ} means “the real part of ejϕ” to prove the following trigonometric identity:

cos(α + β) = cos(α)cos(β) – sin(α)sin(β).

8.7 Given a continuous single sinusoidal x(t) signal whose three-dimensional spectrum is shown in Figure P8-7, write the time-domain equation for x(t) in trigonometric form. (Assume the magnitudes of the spectral components are 0.5.) Justify your answer.

Figure P8-7

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