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Homework Assignment
1. Show Fourier transform pair; ej2πf0t x (t) ←FT→ X(f - fo) by direct evaluation of Fourier transform of ej2πf0t x(t) . Assuming X (f) is band limited by -100kHz to +100kHz around DC, sketch X(f - fo) with fo =10.7 MHz .
2. The thermal noise density is given by No= kT [watt / Hz] where k = 1.38 x10-23 Boltzmann constant and T is temperature in Kelvin scale, and 0°C =273° K. At room temperature 27°C = 300° K, the noise density No =1.38 x10-23 x 300 x1000 [miliwatt /Hz] is commonly expressed by dBm. 0 dBm = 10 log (1 miliwatt). Show that No =-174 [dBm / Hz]. Find the noise power in dBm when the noise bandwidth is 1MHz.
3. 6-PAM is shown as below; find symbol power (variance) assuming each symbol is equally likely (i.e., probability =1/6) using the definition of variance of a random variable.
4. The impulse response of a filter is shown below with g(t) ←FT→ G(f); g(t)
Find -∞∫+∞j |G(f )|2 df and Gp = max |G(f)|. What is the noise bandwidth (double sided) of this filter?
two antennas at the same location on earth receive a signal from a satellite directly overhead at altitude h 36.0
The two loads draw a total average power of 52,800 W at a power factor of 0.8 leading. One of them draws 40K VA at a power factor of 0.96 lagging. What is the power factor of the other load
Calculate the percentage of electricity generation by these fuel-cell systems compared to the annual electricity generation in the U.S. of 3.8x109 MW-hrs
The capacitance of a MOS structure is shown in the attached figure. (n+ polysilicon gate, SiO2 insulator, Si substrate). The plot is not necessarily to scale.
Determine the coefficients p, q, and the determinant (delta) of the system: y1'=y1 + 10y2 Y'2=7y1 - 8y2 Based on these values, what is the type and stability of the critical point
The voltage across an element is 12e to the power of -2t . The current entering the positive terminal of the element is 2e to thepower of -2t . Find the energy absorbed by the element in 1.5 s starting from t=0
The signal generated by a source with 50 ohm impedence is to beattenueated by a factor of 10. The output impedence of the sourcefollowed by the attenuator should also be 50 ohm. Choose values forthe resistive divider.
A binary waveform of 53000 bits/sec is converted into an 8192 level waveform that is passed through a channel with a raised cosine-rolloff filter characteristic. The channel has a conditioned (equalized) phase response out to 4.0 kHz.
A crossbar exchange is required to set up 5000 calls in the busy hour.The marker holding times may be assumed to be exponentially distributed,with an average holding time of 0.5 second.
The minimum useful bandwidth of the amplifier should range from 10Hz to 100KHZ, and this can be determined by the frequency of vin.The maximum peak value of vin is 0.5V. The specified coupling capacitors(non-polarized) are anticipated to comply wi..
A fluorescent tube fixture takes 1 ampere when connected to a 120-volt source. A wattmeter in the circuit reads 80 watts. What is the' operating power factor of this unit
Compute the correlation coefficient of two channels with frequency separation of 100 kHz and temporal separation 5 ms. Assume that the maximum Doppler shift of the channels is f_d=kv=100Hz and the rms delay spread is S_tao=1 µs.
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