Assignment: 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.

Parts List

• Early Semester Course Lab Kit
• Multisim Software

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

PROCEDURE

Step 1.- ANTI-ALIASING 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 iLab cover report.

1. Determine the cutoff frequency of the antialiasing and anti-imaging active filters used in the circuit.

2. Frequency of the signal to be sampled

3. Sampling period

4. Sampling frequency

5. Is the sampling theorem satisfied? Justify your answer.

6. 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 iLab 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 iLab 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 iLab 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 iLab 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 iLab 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 iLab 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 iLab cover report and paste it in the space provided.

Questions

From the first spectrum analyzer captured in Step 3:

1. What is the expected frequency after signal reconstruction?
2. What is the frequency measured from the spectrum?
3. Did you fully recover the original signal?

From the first spectrum analyzer captured in Step 4:

4. Frequency of the signal to be sampled
5. Sampling frequency
6. Is the sampling theorem satisfied?
7. List frequencies of the sampled signals in the range from 0 to 10 kHz.

From the second spectrum analyzer captured in Step 4:

8. Did you fully recover the original signal?
9. List the aliasing frequencies, if any.

From the spectrum analyzer captured in Step 5:

10. Frequency of the signal to be sampled
11. Sampling frequency
12. Is the sampling theorem satisfied?
13. Can you find frequencies of the sampled signals for the range from 0 to 10 kHz?

https://www.dropbox.com/s/7nksuu1vfptvzjx/Lab-Signal%20Sampling%20and%20Reconstruction.rar?dl=0