problem 1: A 12-bit analog-to-digital converter (ADC) works over the range of -5 volts to + 5 volts.
a) What is the voltage resolution of this converter?
b) Assuming -5 V is represented by 000 000 000 000 and +5 V is represented by 111 111 111 111, how would -4 V be represented?
problem 2: We want to measure a sinusoidal signal (frequency 100 Hz) expected to be of strength 1 mV RMS in the presence of noise of peak amplitude 3 mV.
a) If our A/D converter has a range of +10 volts to -10 volts, what amplifier gain should be used to process the signal before the A/D conversion in order to get best resolution without overloading the converter?
b) If the A/D converter can take 1000 samples per second, what are the characteristics of the filter we should use with the above amplifier to avoid aliasing? (What kind of filter? Concer frequency around what value?)
problem 3: You are trying to observe a 500 Hz signal of amplitude 2 mV in the presence of an interfering 4.0 kHz signal also of amplitude 2mV. Use a MATLAB .m script to plot the waveform you will observe from say 0 to 4 msec. You can assume that both the signal and the interference are at zero instantaneous voltage at time 0.
problem 4: You now pass the signal+interference through a 2-section 1.0 kHz low pass filter with a roll off of 40 dB/decade (similar to that of problem set 5). Make a plot of the waveform of the filter output over the time period 0 to 4 msec. (Consider the effect of the filter on both the amplitude and phase of the signals.)
Attention for 2-section 1.0 kHz low pass filter:|Vout/Vin|=1/(1+ω^{2}R^{2}C^{2}), f(-3dB) = 1000Hz, ω(-3dB) = 6280(1/s), at 3dB frequency, |Vout/Vin^{|2}= 1/2 (-3dB). You should find your RC first and find out the gain for the two components of signals respectively.