Chapter 12, Problem 12.3P

1. For each of the following differential equations, determine the transfer function Y/U. Determine if the transfer function is proper or strictly proper. is not strictly proper, determine the strictly proper part. If it (a) y(3) = -3y(2) - 3y(1) — 2y + u(2) — - (b) y(3)=-3.5y(2) — 3.5y(1) — y +u(3) — 3.5u(2) + 3.5u(¹) + 3u

.4. Find the transfer function Ø2/T of the mechanical system in Figure. TG K 02 b₁ b₂ b3

Matlab problem: 1) A BFSK signal is transmitted through a channel with AWGN. Generate similar BFSK received signal plots as shown below. (20 pts) BFSK for eb=1 and npower=0.01 with 500 samples BFSK for eb=1 and npower=0.1 with 500 samples 2.5 2.5 2 1.5 1 0.5 0 -0.5 -1 2 1.5 1 0.5 0.5 -1 -1.5 1.5 -1.5 -1 -0.5 0 0.5 1.5 2 2.5 -1.5 -0.5 0 0.5 1 1.5 2 2.5

example 7.1 question EXAMPLE 7.1Consider the signals s1(t), s2(t), s3(t), and s4(t) shown in Figure 7.3. Using the Gram-Schmidt orthogonalization procedure, determine a set of orthonormal basis functions.Using the waveforms derived and shown in Example 7.1:a) Sketch the simplified block diagram of the transmitter and receiver as shown in figure 7.2b) Estimate the receive voltages for each transmit signal and for each branch in the receiver.

EXAMPLE 7.2 Consider the two equally-likely signals s₁ (t) and s2(t) that are transmitted, over an AWGN channel with the noise power spectral density of No/2, to represent bits 1 and 0, where we have: S1(t)=-S2(t)=√√2 exp(-2t)u(t) The receiver makes its decision solely based on observation of the received signal over a restricted interval of interest. Determine the average bit error rate in terms of Q-function, assuming the interval is [0,3]. Contrast numerically with the performance of an optimum receiver that observes. all the received signal, i.e., the interval of interest is (-∞, ∞).

1) Compute the voltages at each receiver branch (Vo ad V₁ see block diagram next page) for each of the possible transmitted signals: Transmitted signals are generated as shown below: Binary wave in unipolar form (a) With basis functions: Inverter 41(t) Product modulator Product modulator 42(t) BFSK + signal + Si(t) P1(t)= √Eb = cos (2лfit+0₁) $2(t) 42(t)= √Eb 层 cos (2лf2t+ t+02) Generating signals: 2E Si(t) cos (2лfit+0₁), bit=0 Ть SBFSK (t) 2E |$2(t)= cos (2лf2t+02), bit=1

Find the disruptive voltage and visual corona voltage for 3-phase line consisting of 2.5 cm diameter conductor spaced equilateral triangular formation of 4 m. The following data can be assumed, temperature 25°c, pressure 73 cm of mercury, surface factor 0.84, irregularity factor 0.72.

A 3-phase, 4-wire distributor supplies a balanced voltage of 400/230 V to a load consisting of 8 A at p.f. 0-7 lagging for R-phase, 10 A at p.f. 0-8 leading for Y phase and 12 A at unity p.f. for B phase. The resistance of each line conductor is 0.4 2. The reactance of neutral is 0.2 2. Calculate the neutral current, the suppl voltage for R phase and draw the phasor diagram. The phase sequence is RYB. VR Phasor diagram

The three line leads of a 400/230 V, 3-phase, 4-wire supply are designated as R, Y and B respectively. The fourth wire or neutral wire is designated as N. The phase sequence is RYB. Compute the currents in the four wire when the following loads are connected to this supply: From R to N: 25 kW, unity power facto. From Y to N: 20 kVA, 0-7 lag. From B to N: 30 kVA, 0-6 lead.