Figure 1 shows the 16‐APSK constellation with 3 different arrangements of transmitted carrier states on two rings with a ratio of 2.1756 between outer and inner rings radii. You are to write a MATLAB® program (m‐file) to implement each of these M‐ary APSK transmissions (where M = 16) through an AWGN channel, including modulation (symbol generation) at the transmitter, addition of white noise in the channel, and symbol detection and determination of bit error ratio (BER) at the receiver. Your message signal will be a random sequence consisting of 403200 integers that have values between 0 and M-1 with equal probability. For each value of Eb/No in the range 4 dB to 16 dB in steps of 0.5 dB, where Eb is the average energy per bit and No is the noise power per unit bandwidth, run your simulation of the system repeatedly until at least 101-bit errors occur before calculating BER. 1. This first question contains a number of unrelated problems that should each be given ashort answer.(a) Write down the Euler-Lagrange equations for a system with generalised coordinates(41, 92, ..., qN).(b) What is a symmetry? State the general definition (expressed just in words), and not anexample such as translational or rotational symmetry.(c) Give the general definition of the Poisson bracket for a Hamiltonian system describedby the scalar parameters (q, p). Write down the three fundamental Poisson bracketsand their values.(d) Demonstrate that the first integral of a time-independent Lagrangian is a constant ofmotion.(e) Starting from the conserved energy E = ² + V(q) for a scalar q, derive the integralformula for the time t = t(q) as a function of q.(f) Let H(q, p) be a Hamiltonian and (q(t), p(t)) a solution of its equations of motionfor a fixed energy E. We consider now a new Hamiltonian H'(q,p) obtained throughH'(q, p) = f(H(q, p)), where f is an arbitrary nonzero function. We denote (q (t), p'(t))the solutions for H' at fixed energy E' = f(E). Show that these trajectories are thesame as the previous ones, but are governed by a different time dependence.

Since it is not mentioned which question to attempt so considering the question number 1 given in…

Answered: 1. This first question contains a…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Figure 1 shows the 16‐APSK constellation with 3 different arrangements of transmitted carrier states on two rings with a ratio of 2.1756 between outer and inner rings radii. You are to write a MATLAB^® program (m‐file) to implement each of these M‐ary APSK transmissions (where M = 16) through an AWGN channel, including modulation (symbol generation) at the transmitter, addition of white noise in the channel, and symbol detection and determination of bit error ratio (BER) at the receiver. Your message signal will be a random sequence consisting of 403200 integers that have values between 0 and M-1 with equal probability. For each value of E_b/N_o in the range 4 dB to 16 dB in steps of 0.5 dB, where E_b is the average energy per bit and N_o is the noise power per unit bandwidth, run your simulation of the system repeatedly until at least 101-bit errors occur before calculating BER.

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