Question #1
Your objective is to specify the parameters of a complete PCM communications system on the order of the DS-1/E-1 systems. You have 4 audio channels that you want to communicate and you want higher performance than the standard phone system so you are going to use 10 bits instead of 8 bits per sample.
Audio bandwidth: 50 Hz – 10 kHzLow pass filter cutoff: 10 kHz
Sample rate: 1.2 X Nyquist10 bits/sample
8 bits are added to each frame for control purposes.
a. What is the sample rate?
b. What is the length of the frame?
c. What is the bit rate?
d. What is the SNR of your system?
Question #2
Review slides 4 & 5 of Module 6. This exercise is for you to gain some insight into what is a linear systems. In a truly linear system, the output signals just a scaled version of the input signals. No new signals can be generated.. Non-linear systems will create new signals that are not part of the input. Needless to say this isn’t desirable!
Consider an input signal consisting of the sum of two one volt sine waves: vin(t) = sin(2π1000t) +
sin(2π1500t). One is 1000 Hz and the other is 1500 Hz.
a. A linear system has a transfer function: vout(t) = 5(vin(t)). What is vout(t)?
b. What are the frequencies in the output voltage?
c. A non-linear system has a transfer function: vout(t) = 5(vin(t))2 What is vout(t)?
Hint: calculate [sin(A)+sin(B)]2 and sort out the pieces. You will need the trig identities (remember them?) for sin2, sin(A)sin(B), and cos(A+/-B). This calculation is straight forward but somewhat tedious. Be sure to complete the calculation as there are several steps. Be glad you aren’t being asked to vout(t) = 5(vin(t))3. While it is straight forward, it takes a half a page of math to complete.
d. List the output frequencies. Hint: There should be 5.
Question #3
An audio amplifier has the following frequency response:
At 50 Hz, gain = 30 dB.
At 100 Hz, gain = 37 dB.
At 200 Hz, gain = 40 dB.
At 1,000 Hz, gain = 40 dB.
At 10 kHz, gain = 40 dB. kHz,
At 12 kHz gain = 37 dB.
At 15 kHz, gain = 30 dB.
The gain of the amplifier is constant from 200 Hz to 10 kHz.
a. What is the 3 dB bandwidth of the amplifier, in kHz?
b. What is the 10 dB bandwidth of the amplifier in kHz?
c. A 1 kHz sine wave signal with a power level -20 dBm is applied to the input of the amplifier.
What is the power at the amplifier output in dBW?
d. A 12 kHz sine wave signal with a power level -20 dBm is applied to the input of the amplifier. What is the power at the amplifier output in dBW?
Question #4
A filter has the following characteristics:
Attenuation is 0 dB from 0 Hz to 2.5 kHz. The phase angle decreases linearly with increasing frequency above 2.5 kHz. Above 5 kHz the filter has steadily increasing attenuation. At 10 kHz attenuation is 6 dB and at 20 kHz attenuation is 24 dB
a. Is this a low pass, high pass, band pass or band stop filter?
b. What is the attenuation per octave between 10 kHz and 20 kHz?
c. If the filter is known to be a Butterworth filter, what is the value of its order, N?
Question #5
A signal has frequency content (i.e. a spectrum) that extends from 100 Hz to 2.5 kHz.
a. The signal is passed through the filter in Question #4 above. Will the signal be distorted at the output of the filter (Yes/No)?
b. A signal has frequency content (i.e. a spectrum) that extends from 100 Hz to 10 kHz.
The signal is passed through the filter in Question #3 above. Will the signal be distorted at the output of the filter (Yes/No)?
c. If your answer to either part (a) or part (b) above is yes, explain why the signal is distorted.
d. How could you compensate for the distortion and create a system that is linear from 0 Hz to 10 kHz? Specify the frequency response of any device you add to the filter output.
Question #6
A spectrum analyzer is connected to a signal that is known to be a rectangular pulse train.
The spectrum of the signal creates the following display on the spectrum analyzer.
A line spectrum with lines at 0 Hz, 2 kHz, 4 kHz, 8 kHz, 10 kHz, 14 kHz, 16 kHz ….
a. What is the period of the input signal in milliseconds?
b. What is the width of pulses in microseconds?
c. Is the rectangular pulse train unipolar or polar?
Question #7
A spectrum analyzer is connected to a signal that is known to consist of randomly occurring rectangular pulses. The vertical axis of the spectrum analyzer is calibrated in dBm.
The spectrum analyzer has the following display.
A continuous spectrum with magnitude 0 dBm at 0 Hz and zero magnitude at 2 kHz, 4 kHz, 6 kHz, 8 kHz….
a. What is the width of the pulses in milliseconds?
b. If the magnitude of the spectrum increases to +6 dBm at 0 Hz, what is the increase in the voltage of the rectangular pulses?
c. Thelocation of the zeroes in the spectrum suddenly changes to 5 kHz, 10 kHz, 15 kHz ….
What parameter of the rectangular pulses has changed and what is its new value?
d. What is the shape of the spectrum displayed by the spectrum analyzer?
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