By Richard Chia Tung Lee, Mao-Ching Chiu, Jung-Shan Lin
The writing of this booklet was once influenced through the authors' statement that convergence is requiring laptop technology scholars to achieve a greater knowing of communications strategies. The authors have for this reason written a ebook that addresses this hole, providing to the pc technology pupil the main necessities in an intensive demeanour. The e-book walks the reader in the course of the Fourier rework, analog and electronic modulation thoughts, a number of entry communications, spread-spectrum communications, and resource coding and channel coding. The publication has already been utilized in the school room and used to be met with nice good fortune in universities as an introductory textual content in electric engineering programs. Read more...
summary: The writing of this booklet used to be influenced by way of the authors' remark that convergence is requiring computing device technology scholars to achieve a greater realizing of communications techniques. The authors have accordingly written a e-book that addresses this hole, offering to the pc technological know-how pupil the foremost necessities in a radical demeanour. The publication walks the reader during the Fourier remodel, analog and electronic modulation options, a number of entry communications, spread-spectrum communications, and resource coding and channel coding. The publication has already been utilized in the school room and used to be met with nice luck in universities as an introductory textual content in electric engineering courses
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Additional info for Communications engineering : essentials for computer scientists and electrical engineers
One can see that Equation (3-107) can be obtained simply by substituting t ¼ t À Ts into Equation (3-106). This is expected because the function related to (3-108) is a time shift of that related to (3-106). The reader is encouraged to consult Figures 3-17(a) and 3-18. By examining Equation (3-97), we note that every Xðf Þ is associated with e j2pft . It is easy to prove that, if Xðf Þ ¼ a þ jb ¼ rejy , XðÀf Þ ¼ a À jb ¼ reÀjy where y ¼ tan¼1 ðb=aÞ. Thus, for every f, as we did before, we can easily prove that XðÀf ÞeÀj2pft þ Xðf Þe j2pft ¼ reÀjy eÀj2pft þ rejy e j2pft ¼ reÀjð2pftþyÞ þ rejð2pftþyÞ ¼ 2r cosð2pft þ yÞ ¼ 2jXðf Þj cosð2pft þ yÞ where y ¼ tanÀ1 ðb=aÞ.
First, let us examine Xk . Since 1 2p kTs sin ; kp T ð3-69Þ 1 2p kTs sin À ¼ ¼ Xk : Àkp T ð3-70Þ Xk ¼ we have XÀk Communications Engineering 44 Now consider XÀk eÀj2pk f0 t þ Xk ej2pk f0 t ¼ Xk ðcosð2pk f0 tÞ À j sinð2pk f0 tÞÞ þ Xk ðcosð2pk f0 tÞ þ j sinð2pk f0 tÞÞ ¼ 2Xk cosð2pk f0 tÞ: ð3-71Þ Consequently, in the Fourier series, every sine function disappears because XÀk ¼ Xk in this case and sinðÀyÞ ¼ ÀsinðyÞ. Thus, the complex exponential form Fourier series actually contains no imaginary parts.
The notations x ¼ Refzgand y ¼ Imfzg are often used. Communications Engineering 38 Figure 3-14 The complex plane The complex number z can also be represented in polar form as: z ¼ re jy ð3-51Þ where r ! 0 is the magnitude of z and y is the angle or phase of z. These quantities will often be written as r ¼ jzj and y ¼ ﬀ z. The relationship between these two representations of complex numbers can be determined either from the Euler’s formula: ejy ¼ cos y þ j sin y ð3-52Þ or by plotting z in the complex plane, as shown in Figure 3-14, in which the coordinate axes are Refzg along the horizontal axis and Im fzg along the vertical axis.
Communications engineering : essentials for computer scientists and electrical engineers by Richard Chia Tung Lee, Mao-Ching Chiu, Jung-Shan Lin