Communication Technology Laboratory Fundamentals of Wireless Communications Homework 1 Solutions Problem 1 Identification of Ltv Systems
نویسندگان
چکیده
Fundamentals of Wireless Communications Homework 1 Solutions Handout date: April 1, 2014 Problem 1 Identification of LTV Systems 1. Suppose x stably identifiesQ. ForH1, H2 ∈ QwithH1x = H2xwe have 0 = H1x−H2x = (H1 −H2)x sinceH1, H2 are linear operators. Moreover,H1 −H2 ∈ Q. Since x stably identifiesQ, α‖H1 −H2‖H ≤ ‖(H1 −H2)x‖ = 0 with α > 0, which implies thatH1 −H2 = 0, i.e.,H1 = H2. 2. We start by computing the response ofH to the probing signal x(t) = √ T ∑ k∈Z δ(t+ kT )
منابع مشابه
Fundamentals of Time-Varying Communication Channels
Wireless communication systems, i.e., systems transmitting information via electromagnetic (radio) or acoustic (sound) waves, have become ubiquitous. In many of these systems, the transmitter or the receiver is mobile. Even if both link ends are static, scatterers — i.e., objects that reflect, scatter, or diffract the propagating waves — may move with significant velocities. These situations gi...
متن کاملLinearization of M-LINC Systems Using GMP and Particle Swarm Optimization for Wireless Communications
In this paper, an efficient algorithm for the efficiency maximization of the multilevel linear amplification using nonlinear components (M-LINC) systems is proposed regarding the linearity of the system. In this algorithm, we use the generalized memory polynomial (GMP) to provide a behavioral model for the power amplifier (PA) and calculate the power spectral density (PSD) of the output signal ...
متن کاملCommunication Technology Laboratory Fundamentals of Wireless Communications Homework 2 Solutions Problem 1 Linear Filters and Gaussian Noise
1. By using the sampling theorem to expand N (t − τ, ω) and h(τ) with respect to τ we obtain: Z(t, ω) = τ k∈Z h(kT) sinc π τ − kT T k∈Z N (t − kT, ω) sinc π τ − kT T dτ = T k∈Z h(kT)N (t − kT, ω) where we used orthogonality of the set of functions {sinc (π(τ − kT)/T)} k∈Z. 2. Since N (τ) is a complex Gaussian random process, for each finite set of epochs t 1 , ..., t K , the random variables {N...
متن کاملFundamentals of Digital Communication
This textbook presents the fundamental concepts underlying the design of modern digital communication systems, which include the wireline, wireless, and storage systems that pervade our everyday lives. Using a highly accessible, lecture style exposition, this rigorous textbook first establishes a firm grounding in classical concepts of modulation and demodulation, and then builds on these to in...
متن کاملRole and Application of RFID Technology in Internet of Things: Communication, Authentication, Risk, and Security Concerns
The Internet of Things (IoT) is a very encouraging and fast-growing area that brings together the benefits of wireless systems, sensor networks, actuators, etc.A wide range of IoT applications have been targeted and several aspects of this field have been identified to address specific issues, as well as technologies and standards developed in various domains such as in radio frequency id...
متن کامل