TAILIEUCHUNG - Lecture Wireless and mobile computing – Chapter 8: Transmission fundamentals recap questions/solutions

Chapter 8 - Transmission fundamentals recap questions/solutions. The following will be discussed in this chapter: Frequency and period relationship; representation of a signal by sinusoids; frequency and wavelength relationship; amplitude, frequency and phase; decomposition of a signal; sinusoidal signal period; periodicity in case of linear combination of two signals; signal harmonics elimination (higher order or lower order); channel capacity computation; shannon formula and nyquist criterion; signal to noise ratio. | TRANSMISSION FUNDAMENTALS Recap Questions/Solutions Lecture 8 Overview Frequency and Period Relationship Representation of a signal by sinusoids Frequency and Wavelength Relationship Amplitude, Frequency and Phase Decomposition of a Signal Sinusoidal Signal Period Periodicity in Case of Linear Combination of two Signals Signal Harmonics Elimination (higher order or lower order) Channel Capacity Computation Shannon Formula and Nyquist Criterion Signal to Noise Ratio 2 Frequency Period Relationship Q-: A signal has a fundamental frequency of 1000 Hz. What is its period? 3 According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases. Note Frequency Period Relationship 4 Frequency Domain Concepts Signal is made up of many frequencies Components are sine waves Fourier analysis can show that any signal is made up of component sine waves Can plot frequency domain functions 5 5 In practice, an electromagnetic signal will be made up of many frequencies. It can be shown, using a discipline known as Fourier analysis, that any signal is made up of components at various frequencies, in which each component is a sinusoid. By adding together enough sinusoidal signals, each with the appropriate amplitude, frequency, and phase, any electromagnetic signal can be constructed. Addition of Frequency Components (T=1/f) c is sum of f & 3f (with different amplitudes) 6 6 In Stallings DCC8e Figure , the components of this signal are just sine waves of frequencies f and 3f, as shpwn in parts (a) and (b). 7 Q-1: A signal has a fundamental frequency of 1000 Hz. What is its period? Frequency Period Relationship 8 Q-1: A signal has a fundamental frequency of 1000 Hz. What is its period? Sol: Frequency Period Relationship Period = 1/1000 = s = 1 ms. 9 Q: Express the following in the simplest form you can: a. sin( - π) + sin( + π) b . sin 2πft + sin(2πft - π) 10 Sol: a: -2 sin (2πft) 10 11 b.

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