Problem 1:

9. If a GSM timeslot consists of 6 trailing bits, 8.25 guard bits, 26 training bits, and 2 traffic bursts of 58 bits of data. Find the total number of bits in each time slot. If a frame has 8 slots, find the total number of bits in each frame, also calculate overhead bits in each frame and frame efficiency.

5.2-3 In a satellite radio system, 500 stations of stereo quality are to be multiplexed in one data stream. For each station, two (left and right) signal channels each of bandwidth 15,000 Hz are sampled, quantized, and binary-coded into PCM signals. (a) If the maximum acceptable quantization error in sample amplitudes is 1% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer. (b) If the sampling rate must be 8% higher than the Nyquist rate, find the minimum bit rate of the multiplexed data stream based on the quantizer of part (a). (c) If 2% more bits are added to the multiplexed data for error protection and synchronization, determine the minimum bandwidth needed to transmit the final data stream to receivers.

5.6-1 A DM system has input message signal m(t)=50 e^{-200 t} \cos 1000 \pi t \cdot u(t) (a) Determine the minimum step size E necessary to avoid DM slope overload. (b) Calculate the minimum average quantization noise power based on part (a).

A DSB-SC AM signal is modulated by the signal m(t)=2 \cos 2000 \pi t+\cos 6000 \pi t . The modulated signal is u(t)=100 m(t) \cos 2 \pi f_{c} t \text { where } f_{c}=1 \mathrm{MHz} 1. Determine and sketch the spectrum of the AM signal. 2. Determine the average power in the frequency components.

Consider the four waveforms shown in Figure P-8.3. 1. Determine the dimensionality of the waveforms and a set of basis functions. 2. Use the basis functions to represent the four waveforms by vectors S1, S2, S3, S4 3. Determine the minimum distance between any pair of vectors.

The message signal m(t) has the Fourier transform shown in Figure P-3.11(a). This signal is applied to the system shown in Figure P-3.11(b) to generate the signal y(t). 1. Plot Y (f), the Fourier transform of y(t). 2. Show that if y(t) is transmitted, the receiver can pass it through a replica of the system shown in Figure P-3.11 (b) to obtain m(t) back. This means that this system can be used as a simple scrambler to enhance communication privacy.

The message signal m(t) = 10 sinc(400t) frequency modulates the carrier c(t) = 100 cos(2 fet). The modulation index Bf = 6. 1. Write an expression for the modulated signal u(t)? 2. What is the maximum frequency deviation of the modulated signal? 3. Find the bandwidth of the modulated signal.

Consider the message signal m(t) = 20 cos(2át) volts, and carrier c(t) = 50 cos(100nt) volts.a. Sketch the resulting AM wave for 75 percent modulation (DSB-LC).b. Find the power developed across a load of 100 ohm due to this AM wave.

Q1. Determine the signal space representation of the four signals sk(t), k = 1, 2, 3, 4, shown below by using as basis functions the orthonormal functions o(t) and 2 (t). Plot the signal space diagram, and show that this signal set is equivalent to that for a four-phase PSK signal. (1) $2(1) 1-1-10 1.10 $₁,(1) $2(1) S4(1) 0 Q2. Consider the two 8-point QAM signal constellation shown below. The minimum distance between adjacent symbol is 2 in both constellations. (-2,2) (2,2) Constellation A $3(1) (2,-2) (-2./3) (013) (2,3) (0,√3) (-1,0) (1.0) (2.-√3) Constellation B i Determine the average transmitted energy per symbol for each constellation, assuming that all the signal points in each constellation are equally likely. ii Which of the above two constellations would you prefer to use on an AWGN channel and why?

Problem 4: For the common-gate circuit in Figure 4, the NMOS transistor parametersare: VTn = 1 V, Kn = 3 mA/V², and 1 = 0.(12 points) (a) Determine Ipso and VDsą (3 (b) Calculate gm and ro (c) Find the small-signal voltage gain (d) Find the value of resistance R,