By John G. Proakis, Masoud Salehi

Electronic Communications is a vintage ebook within the region that's designed for use as a senior or graduate point textual content. The textual content is versatile and will simply be utilized in a one semester path or there's sufficient intensity to hide semesters. Its entire nature makes it an outstanding e-book for college kids to maintain for reference of their expert careers. This all-inclusive consultant supplies an excellent creation to the research and layout of electronic communique structures. contains professional insurance of latest themes: Turbocodes, Turboequalization, Antenna Arrays, electronic mobile structures, and Iterative Detection. handy, sequential association starts off with a glance on the heritage and class of channel types and builds from there.

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**Extra info for Digital Communications, 5th Edition **

**Sample text**

1–2. f where x(t) = π1t x(t) is the Hilbert transform of x(t). The Hilbert transform of x(t) is obtained by introducing a phase shift of − π2 at positive frequency components of x(t) and π2 at negative frequencies. 1–4) Some of the properties of the Hilbert transform will be covered in the problems at the end of this chapter. 1–5) Obviously the spectrum of xl (t) is located around the zero frequency, and therefore it is in general a complex lowpass signal. This signal is called the lowpass equivalent or the complex envelope of x(t).

Similarly, √ the signals by the vectors s2 = (0, 2, 0)t , √ s2 (t),t s3 (t), and s4 (t)√are characterized s3 = ( 2, 0, 1) , and s4 = (− 2, 0, √ 1)t , respectively. 2–3. Their lengths are s1 = 2, s2 = 2, s3 = 3, and s4 = 3, and the corresponding signal energies are Ek = sk 2 , k = 1, 2, 3, 4. 2–4. We have demonstrated that a set of M finite energy waveforms {sm (t)} can be represented by a weighted linear combination of orthonormal functions {φn (t)} of dimensionality N ≤ M. The functions {φn (t)} are obtained by applying the Gram-Schmidt orthogonalization procedure on {sm (t)}.

More generally, a set of m vectors v k , 1 ≤ k ≤ m, are orthogonal if v i , v j = 0 for all 1 ≤ i, j ≤ m, and i = j. 2–5) i=1 which in the n-dimensional space is simply the length of the vector. A set of m vectors is said to be orthonormal if the vectors are orthogonal and each vector has a Proakis-27466 book September 25, 2007 13:9 Chapter Two: Deterministic and Random Signal Analysis 29 unit norm. A set of m vectors is said to be linearly independent if no one vector can be represented as a linear combination of the remaining vectors.