Chapter 4, Problem 4.11P

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8-1) similar to Lathi & Ding, Prob. P.5.1-2 The figure below shows the Fourier spectra of signals of g,(t) and g₁(t). Determine the Nyquist rate and the corresponding sampling interval for signals of g,(t), g,(t), g₁(1) - g¸(1), g¸³(t), and g₁(1)g₁(1). Hint: Use the frequency convolution and the width property of convolution. G₁(f) G₂(f) -8000 0 8000 f -20000 10 20000 f

• We will use the Wattmeter to find the average power supplied/absorbed by each component. The following figure shows how to connect the Wattmeter to measure the average power absorbed by the resistor. Note that the Wattmeter consists of a Voltmeter and an Ammeter. The Voltmeter must be connected in parallel with the component and the Ammeter must be connected in series with the component. You must pay attention to the polarity of the voltage across the component as well as the direction of the current flowing through the component. 5Vpk 1kHz 30° ww 40 Z=A-JB Wattmeter-XWM1 2.503 W Power factor: 1.00000 Voltage Current • • Similarly connect a second Wattmeter to measure the average power supplied by the source. Connect a third Wattmeter to measure the average power in the capacitor. Does this value agree with the theoretical value? Perform Interactive Simulation under Analysis and Simulation. Double click on Wattmeters to see the average power values. Note that the Wattmeter also…

• We will use the Wattmeter to find the average power supplied/absorbed by each component. The following figure shows how to connect the Wattmeter to measure the average power absorbed by the resistor. Note that the Wattmeter consists of a Voltmeter and an Ammeter. The Voltmeter must be connected in parallel with the component and the Ammeter must be connected in series with the component. You must pay attention to the polarity of the voltage across the component as well as the direction of the current flowing through the component. 5Vpk 1kHz 30° ww 40 Z=A-JB Wattmeter-XWM1 2.503 W Power factor: 1.00000 Voltage Current • • Similarly connect a second Wattmeter to measure the average power supplied by the source. Connect a third Wattmeter to measure the average power in the capacitor. Does this value agree with the theoretical value? Perform Interactive Simulation under Analysis and Simulation. Double click on Wattmeters to see the average power values. Note that the Wattmeter also…

8-3) Bandpass sampling A bandpass signal is confined to the frequency range from 7.5 to 10.5 kHz. Find the allowed ranges of the sampling rate for this signal. Sketch the amplitude spectrum of a hypothetical message, the amplitude spectrum of the sampled signal, and the transfer function of a suitable recovery filter if the sampling rate is chosen in the center of the lowest range available.

8-4) Similar to Lathi & Ding, Prob. P.5.1-5 6.1-4 A low-pass signal g(t) sampled at rate of fs > 2B needs reconstruction. The sampling interval is Ts = 1/fs. (a) If the reconstruction pulse used is p(1) = [1 - specify the equalizer filter E(f) to recover g (1). (b) If the reconstruction pulse used is p(t) = П Ts/2 specify the equalizer filter E(f) to recover g (1).

8-2) Lathi & Ding, Prob. P.5.1-1 Determine the Nyquist sampling rate for the following signals, explaining your method: (a) 4 sinc(420лt); (b) 5sinc² (6500лt); (c) sinc(1800лt)+ sinc² (2000лt); (d) 2 sinc(500лt) sin(300л)

2) A load consisting of a 1350 Q2 resistor in parallel with a 405 mH inductor is connected across the terminals of a sinusoidal voltage source Vg, where Vg = 90 cos(2500t) V. Find a) the average power delivered to the load, b) the reactive power for the load, c) the apparent power for the load, and d) the power factor of the load.

4) Find the phasor voltage Vs for the following circuit if loads L1 and L2 are absorbing 15 kVA at 0.6 pf lagging and 6 kVA at 0.8 pf leading, respectively. Express Vs in polar form. + j10 + 200/0° V(rms) | L1 Li L2