Practice Problems

Practice Problems#

Problem 1#

What is aliasing and how can it be prevented?

Problem 2#

What are the three steps for converting an analog signal into digital?

Problem 3#

Given the following spectra, determine the minimum sampling frequency.

Problem 4#

Find the number of levels and resolution for an 8-bit ADC with

\(V_{\max} = 6\ \text{V}\) and \(V_{\min} = -4\ \text{V}\).

Problem 5#

Given a cosine input

\[ v_{in}(t) = 1 + 3\cos\!\left(360^\circ (50\,\text{kHz})t\right)\ \text{V}, \]

answer the following questions:

a. What is the Nyquist sampling frequency for this input signal?

b. Which of these sampling frequencies would you use:
75 kHz, 90 kHz, or 120 kHz?

c. What are the minimum and maximum values of the input signal?

d. Which of the following ADCs would work with this signal?

  • \(V_{\max} = 5\ \text{V}\) and \(V_{\min} = -3\ \text{V}\)

  • \(V_{\max} = 5\ \text{V}\) and \(V_{\min} = -1\ \text{V}\)

  • \(V_{\max} = 3\ \text{V}\) and \(V_{\min} = -3\ \text{V}\)

e. Using the \(V_{\max}\) and \(V_{\min}\) from part (d), how many bits would be required to achieve a resolution of \(600\ \text{mV}\) or better?

f. Given the number of bits calculated in part (e), what is the actual resolution of the ADC?

Problem 6#

An input signal

\[ v_{in}(t) = 6 + 5\cos\!\left(360^\circ (6\,\text{kHz})t\right) + 3\cos\!\left(360^\circ (15\,\text{kHz})t\right)\ \text{V} \]

is to be digitized using the ADC below.

Note: The 15 kHz portion of the signal is mainly noise and does not carry any useful information.

Is this a good ADC for this signal? Why or why not?
If not, what could you do to make this ADC work with this signal?

Problem 7#

What are the advantages of digital signals?

Problem 8#

T / F. Improving the resolution is always better.

Problem 9#

T / F. Increasing the sampling rate improves resolution.

Problem 10#

T / F. A smaller resolution is a better resolution.

Problem 11#

You want to convert \(v(t)\) to binary numbers to be stored. Your ADC has

\(V_{\max} = 0.5\ \text{V}\),
\(V_{\min} = -0.5\ \text{V}\),
and a 3-bit output.

\[ v(t) = 200 + 400\cos\!\left(360^\circ (200\,\text{kHz})t\right)\ \text{mV} \]

a. Draw the amplitude spectrum of \(v(t)\).

b. How would you prepare the signal? Design the transducer interface.

c. What sampling rate would you choose?

d. What is the resolution?

e. What is the encoded output if the input is \(315\ \text{mV}\)?

Problem 12#

What is the resolution of a 10-bit ADC with

\(V_{\max} = 5\ \text{V}\) and \(V_{\min} = -3\ \text{V}\)?

Problem 13#

Given the following signal, create an ADC to capture it with a 5-bit ADC and determine its resolution:

\[ V(t) = \cos\!\left(360^\circ (8\,\text{kHz})t\right) + 2\cos\!\left(360^\circ (15\,\text{kHz})t\right)\ \text{V} \]

b. Using this ADC, encode \(1.62\ \text{V}\).

Problem 14#

Given

\[ v_{in}(t) = 4 + 4\cos\!\left(360^\circ (2\,\text{kHz})t\right)\ \text{V}, \]

and \(\text{max } QE = 200\ \text{mV}\), find the unknowns in the figure above.

If a value of \(1.6\ \text{V}\) is measured, what would be the quantization error (QE) and the encoded value?

Contents