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Extra resources for 3G Wireless Technology Quick Guide
We make two assumptions: 1. Causality, which means that the impulse response h(t) is zero for t < 0. 2. Finite support, which means that the impulse response of the filter is of some finite duration Tf, so that we may write h(t) = 0 for t ≥ Tf. 52) Let the input x(t), impulse response h(t), and output y(t) be uniformly sampled at the rate (1/Δτ ) samples per second, so that we may put t = nΔ τ and τ = kΔ τ where k and n are integers and Δτ is the sampling period. 52) by the convolution sum y ( nΔ τ ) = N–1 h(kΔ τ )x ( nΔ τ – kΔ τ )Δ τ k=0 where N Δτ = Tf.
9 teaches us two important things: 1. The scaled sinc function becomes more like a delta function. 2. 1 for a validation of this point. 8, is another way of realizing a delta function in the time domain. 9 Evolution of the sinc function 2W sinc(2Wt) toward the delta function as the parameter W progressively increases. fm Page 32 Friday, November 16, 2012 9:24 AM 32 EXAMPLE 4 Chapter 2 Fourier Analysis of Signals and Systems Evolution of the Sum of Complex Exponentials toward the Delta Function in the Frequency Domain For yet another entirely different example, consider the infinite summation term ∞ exp ( j2πmf ) over the interval – 1 ⁄ 2 ≤ f < 1 ⁄ 2 .
Block Diagram of Digital Communication System Typically, in the design of a digital communication system the information source, communication channel, and information sink (end user) are all specified. The challenge is to design the transmitter and the receiver with the following guidelines in mind: • Encode/modulate the message signal generated by the source of information, transmit it over the channel, and produce an “estimate” of it at the receiver output that satisfies the requirements of the end user.
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