Use principles of signal sampling and reconstruction to construct an electronic
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ECET 350 Topic
2 Lab DeVry
ECET 350 Topic 2 Lab 2 Signal
Sampling and Reconstruction
Objectives
- Use principles of signal sampling and reconstruction to construct
an electronic circuit to sample, hold, and reconstruct the signal.
- Apply the antialiasing and anti-imaging filters to
perform proper simulation of signal sampling and reconstruction.
Software
- Multisim
Introduction
Signal sampling is usually performed by
sampling an analog signal at appropriate rates according to the Nyquist theorem
and then holding the sampled voltage during the time required for the ADC to
convert the voltage level to a binary code (digital value). The analog signal
should be band-limited so that the sampling frequency can be chosen according
to the Nyquist theorem, namely , in which is the maximum frequency or the upper
band of the analog signal.
To ensure that the signal is band-limited, an
antialiasing filter (restricting low-pass filter) is deployed as the first
block in the path of the input signal.
The digital value, the output of ADC, could
be processed using a DSP algorithm mainly composed of a digital filter. After
digitally processing the signal, it has to be reconstructed and delivered back
to the analog world, which is the binary code, and the result of DSP operation
is converted back to a sample and hold voltage level. The converted voltage
levels are further fed to the anti-image filter (smoothing low-pass filter) to
reconstruct the analog signal.
Figure 1A shows the complete signal sampling
and reconstruction system. To investigate signal sampling and reconstruction in
this lab experiment, a simplified system that omits the DSP section is shown in
Figure 1B.
Figures 1A and 1B: Signal Sampling and Reconstruction
If the sampling condition is violated, the
aliasing would occur. This effect will cause undesired frequencies known as
alias frequencies within the information frequency band.
To avoid aliasing, Figure 2A shows the
sampling and reconstruction using an antialiasing filter. Figure 2B shows the
simplified system that omits the DSP section and will be used in this lab
experiment for simulation.
Figures 2A
and 2B: Signal Sampling and Reconstruction With an Antialiasing Filter
Deliverables
Answer all questions, complete all tables, and paste all
figures and graphs in the Week 2 Lab Cover Sheet here (Links
to an external site.) .
Submit your Week 2 Lab assignment.
You can also download the cover sheet for Week 2 Lab in
the Files section of the Course Menu.
Required Software
Multisim
Lab Steps
STEP 1: Antialiasing and Anti-imaging Filter
Specifications
Using MultiSim, construct the circuit shown
as Figure 3.
Set the sampling
rectangular pulses (sampling clock) as the following.
Vp (pulse value) = -5
volts
Period: 0.125 ms
Pulse width 0.02 ms
Set the sinusoidal voltage
source as the following.
Frequency = 1000 Hz
Vp (amplitude)=1
volts=0.707 rms,
DC offset = 1 volt
Explanation of the circuit: Two opamps on the
top are the buffer amplifiers before and after the sampler. Sampler is a JFET
used as analog switch; its gate is driven by the narrow pulse train as
specified above. There are two identical active low-pass filters used for
antialiasing and anti-imaging with second order, Sallen-Key topology.
Before simulation, address the following
questions and include your answers in the Lab cover report.
- Determine the cutoff frequency of the antialiasing and anti-imaging
active filters used in the circuit.
- Frequency of the signal to be sampled
- Sampling period
- Sampling frequency
- Is the sampling theorem satisfied? Justify your answer.
- Predict the frequencies and estimated voltage
amplitude of each frequency in the range from 0 Hz to 10 kHz of the
sampled signals according to the sampling theorem.
Figure 3: Sampling and Reconstruction Circuit As Built in
MultiSim
STEP 2: Antialiasing and Anti-imaging Filter Simulation
Open the first spectrum analyzer by left
double clicking on the icon.
In the frequency section, set start to 0 Hz
and end to 10 kHz. Then click on Enter.
Set the amplitude range to 0.25 V/Div and
Lin(Linear) display.
Set the frequency resolution to 100 Hz.
Start the simulation by clicking on the power
switch in the top right hand corner of the window.
Copy the screen display on the spectrum
analyzer to include in your report, use Alt+Print Scrn buttons to capture the
spectrum analyzer view only when it is selected, and paste it in your Lab cover
report in the section marked antialiasing and anti-imaging spectrum analyzer
screen capture.
Using the mouse, move the cursor so that it overlays the
center of the spectral signal on the simulator. Use the cursor to measure the
frequency and RMS voltage for each peak from 0 to 10 kHz, and record your
measurements in Table 1 in your Lab cover report.
STEP 3: Signal Reconstruction Simulation
The original signal can be fully recovered by
low-pass filtering (anti-image filtering) the sampled signal if the sampling
condition is satisfied.
Left double click on the second spectrum
analyzer attached to the low-pass filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum analyzer to
include in your Lab cover report in the space provided, and label the graph.
Use the spectrum analyzer to answer the questions at the end of the lab.
Include your answers in the Week 2 Lab cover report in the space provided.
STEP 4: Antialiasing Simulation
Now disconnect the input sinusoidal source
from the antialiasing filter, and connect it directly to the buffer preceding
the sampler (see Figure 4).
Set the sinusoidal function as the following.
Frequency = 7000 Hz
Vp (amplitude) =1
volts=0.707 rms,
DC offset = 1 volt
Figure 4: Sampling and Reconstruction Circuit
While Skipping Antialiasing Filter
Left double click on the first spectrum
analyzer attached to the second buffer amplifier before the anti-imaging
filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum
analyzer to include in your Lab cover report. Label the graph.
The original signal cannot be fully recovered
by anti-image filtering the sampled signal if the sampling condition is not
satisfied.
Left double click on the second spectrum
analyzer attached to the anti-imaging filter.
Run the simulation using the same setting of
the spectrum analyzer.
Copy the screen display on the spectrum analyzer to
include in your Lab cover report. Label the graph.
STEP 5: Signal Reconstruction Simulation
Now, use the same setting for the sinusoidal
function as the following.
Frequency = 7000 Hz
Vp (amplitude) =1
volts=0.707 rms,
DC offset = 1 volt
Connect the sinusoidal function output to the
input of the antialiasing filter as in Figure 3.
Run the simulation using the same setting for
both of the spectrum analyzers.
Copy the screen display on the spectrum
analyzer 2 on the output of the anti-imaging filter to include in your Week 2
Lab cover report and paste it in the space provided.
Graded Questions
From the first spectrum analyzer captured in Step 3:
- What is the expected frequency after signal reconstruction?
- What is the frequency measured from the spectrum?
- Did you fully recover the original signal?
From the first spectrum analyzer captured in Step 4:
- Frequency of the signal to be sampled
- Sampling frequency
- Is the sampling theorem satisfied?
- List frequencies of the sampled signals in the range
from 0 to 10 kHz.
From the second spectrum analyzer captured in Step 4:
- Did you fully recover the original signal?
- List the aliasing frequencies, if any.
From the spectrum analyzer captured in Step 5:
- Frequency of the signal to be sampled
- Sampling frequency
- Is the sampling theorem satisfied?
- Can you find frequencies of the sampled signals for
the range from 0 to 10 kHz?
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