For each signal of the following, find the required information: a. Find the period for a...

      

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For each signal of the following, find the required information: a. Find the period for a periodic signal with a fundamental frequency of 2.54 GHz. b. For the signals shown in the figure (1.1) below (x-axis is time in seconds and y-axis is amplitude in Volts), assume that the solid line represents sin(2t) and the dotted line represents A sin(2ft + p). What are the values of A, f, and p? c. Find the period and wavelength of the signal f(t) = (6 sin t). (HINT: use mathematical identities to change sin(t) into something simpler) d. The spectrum of a modulated signal is shown in figure (1.2) below, find the fundamental frequency and the effective (3dB) bandwidth. 2.0 1.0 2. (10 Marks) a. Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of (1920 x 1080) picture elements (pixels), where each pixel can take on one of 65536 intensity values. Assume that 32 pictures are sent per second. (This digital source is roughly equivalent to HDTV standards). Find the source data rate R (bps). b. Assume that the TV picture is to be transmitted over a channel with 160 MHz bandwidth and a 35-dB signal-to-noise ratio. Find the capacity of the channel (bps) and determine if that HDTV signal can be transmitted over that channel or not. 3. (4 Marks) Given a channel with an intended capacity of 54 Mbps, the bandwidth of the channel is 5 MHz. Assuming white thermal noise, what signal-to-noise ratio is required to achieve this capacity? 4. (10 Marks) The audio power of the human voice is concentrated at about 300 Hz. Antennas of the appropriate size for this frequency are impracticably large, so that to send voice by radio the voice signal must be used to modulate a higher (carrier) frequency for which the natural antenna size is smaller. a. What is the length of an antenna one-half wavelength long for sending radio at 300 Hz? b. An alternative is to use a modulation scheme for transmitting the voice signal by modulating a carrier frequency, so that the bandwidth of the signal is a narrow band centered on the carrier frequency. Suppose we would like a half-wave antenna to have a length of 5 centimeter. What carrier frequency would we use? 5. (10 Marks) Suppose a transmitter produces 25 W of power. a. Express the transmit power in units of dBm and dBW. b. If the transmitter's power is applied to a unity gain antenna with a 2.4 GHz carrier frequency, what is the received power in dBm at a free space distance of 100 m? c. Repeat (b) for a distance of 10 km. d. Repeat (c) but assume a receiver antenna gain of 3.8. 6. (10 Marks) Instead of assuming a free space environment in question 5, assume an urban area cellular radio environment. Use a path loss exponent of 3.5 and the same transmitter power (25W). a. If the transmitter's power is applied to a unity gain antenna with a 2.4 GHz carrier frequency, what is the received power in dBm at a free space distance of 100 m? b. Repeat (a) for a distance of 10 km. c. Repeat (b) but assume a receiver antenna gain of 3.8. 7. (15 Marks) A microwave transmitter has an output of 0.1 W at 2 GHz. Assume that this transmitter is used in a microwave communication system where the transmitting and receiving antennas are parabolas, each 1.2 m in diameter. a. What is the gain of each antenna in decibels? b. Taking into account antenna gain, what is the effective radiated power of the transmitted signal? c. If the receiving antenna is located 24 km from the transmitting antenna over a free space path, find the available signal power out of the receiving antenna in dBm units. 8. (15 Marks) For the following, assume K = 1.5 a. Determine the height of an antenna for a TV station that must be able to reach customers up to 80 km away (consumer antennas traditionally have much shorter heights than broadcast antennas. Hence, they are assumed to be at ground level.) b. Now, assume that a repeater to be used to reach further distance. Consider only the repeater's receiving antenna and assume it should be put at 120 Km away from the main TV station. What is the height for that antenna? 9. (6 Marks) What is the thermal noise level of a channel with a bandwidth of 20 MHz carrying 10 W of power and operating at 40 C? Compare the noise level to the operation power. 10. (10 Marks) Suppose that a car is moving though a suburban environment and has a wireless communication channel with a coherence time of 10 ms and a coherence bandwidth of 600 KHz. The bit rate of the signal is 50 Kbps and assume the signal bandwidth is equal to the bit rate. a. Is the channel fast or slow fading? b. Is the channel flat or frequency-selective fading? For each signal of the following, find the required information: a. Find the period for a periodic signal with a fundamental frequency of 2.54 GHz. b. For the signals shown in the figure (1.1) below (x-axis is time in seconds and y-axis is amplitude in Volts), assume that the solid line represents sin(2t) and the dotted line represents A sin(2ft + p). What are the values of A, f, and p? c. Find the period and wavelength of the signal f(t) = (6 sin t). (HINT: use mathematical identities to change sin(t) into something simpler) d. The spectrum of a modulated signal is shown in figure (1.2) below, find the fundamental frequency and the effective (3dB) bandwidth. 2.0 1.0 2. (10 Marks) a. Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix of (1920 x 1080) picture elements (pixels), where each pixel can take on one of 65536 intensity values. Assume that 32 pictures are sent per second. (This digital source is roughly equivalent to HDTV standards). Find the source data rate R (bps). b. Assume that the TV picture is to be transmitted over a channel with 160 MHz bandwidth and a 35-dB signal-to-noise ratio. Find the capacity of the channel (bps) and determine if that HDTV signal can be transmitted over that channel or not. 3. (4 Marks) Given a channel with an intended capacity of 54 Mbps, the bandwidth of the channel is 5 MHz. Assuming white thermal noise, what signal-to-noise ratio is required to achieve this capacity? 4. (10 Marks) The audio power of the human voice is concentrated at about 300 Hz. Antennas of the appropriate size for this frequency are impracticably large, so that to send voice by radio the voice signal must be used to modulate a higher (carrier) frequency for which the natural antenna size is smaller. a. What is the length of an antenna one-half wavelength long for sending radio at 300 Hz? b. An alternative is to use a modulation scheme for transmitting the voice signal by modulating a carrier frequency, so that the bandwidth of the signal is a narrow band centered on the carrier frequency. Suppose we would like a half-wave antenna to have a length of 5 centimeter. What carrier frequency would we use? 5. (10 Marks) Suppose a transmitter produces 25 W of power. a. Express the transmit power in units of dBm and dBW. b. If the transmitter's power is applied to a unity gain antenna with a 2.4 GHz carrier frequency, what is the received power in dBm at a free space distance of 100 m? c. Repeat (b) for a distance of 10 km. d. Repeat (c) but assume a receiver antenna gain of 3.8. 6. (10 Marks) Instead of assuming a free space environment in question 5, assume an urban area cellular radio environment. Use a path loss exponent of 3.5 and the same transmitter power (25W). a. If the transmitter's power is applied to a unity gain antenna with a 2.4 GHz carrier frequency, what is the received power in dBm at a free space distance of 100 m? b. Repeat (a) for a distance of 10 km. c. Repeat (b) but assume a receiver antenna gain of 3.8. 7. (15 Marks) A microwave transmitter has an output of 0.1 W at 2 GHz. Assume that this transmitter is used in a microwave communication system where the transmitting and receiving antennas are parabolas, each 1.2 m in diameter. a. What is the gain of each antenna in decibels? b. Taking into account antenna gain, what is the effective radiated power of the transmitted signal? c. If the receiving antenna is located 24 km from the transmitting antenna over a free space path, find the available signal power out of the receiving antenna in dBm units. 8. (15 Marks) For the following, assume K = 1.5 a. Determine the height of an antenna for a TV station that must be able to reach customers up to 80 km away (consumer antennas traditionally have much shorter heights than broadcast antennas. Hence, they are assumed to be at ground level.) b. Now, assume that a repeater to be used to reach further distance. Consider only the repeater's receiving antenna and assume it should be put at 120 Km away from the main TV station. What is the height for that antenna? 9. (6 Marks) What is the thermal noise level of a channel with a bandwidth of 20 MHz carrying 10 W of power and operating at 40 C? Compare the noise level to the operation power. 10. (10 Marks) Suppose that a car is moving though a suburban environment and has a wireless communication channel with a coherence time of 10 ms and a coherence bandwidth of 600 KHz. The bit rate of the signal is 50 Kbps and assume the signal bandwidth is equal to the bit rate. a. Is the channel fast or slow fading? b. Is the channel flat or frequency-selective fading?

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