5
Experiment A1-10 Sampling Theorem Name: Brice Ott Email: [email protected] Date: 1/27/16 Section: 2 GTA: Ramaswamy Muthu Kumar Page of 1 5
Experiment A1-10 Sampling Theorem
Name: Brice OttEmail: [email protected]
Date: 1/27/16Section: 2
GTA: Ramaswamy Muthu Kumar
Page � of �1 5
Experiment A1-10: Sampling Theorem
Introduction:
In this experiment we implemented experimental verification of the sampling theorem to confirm the Nyquist Frequency (The highest frequency that can be represented in a digital signal of a specified sampling frequency) as well as investigated the aliasing (An effect produced when a signal is imperfectly reconstructed from the original signal which occurs when a signal is not sampled at a high enough frequency to create an accurate representation) that can occur in message reconstruction.
Lab Work:
1.) In the first part of the experiment we set up the arrangement illustrated in Figure 1 to model sampling a sine wave.
Our final TIMS set up is shown in Figure 2.
Page � of �2 5
Figure 1: The TIMS model for sampling a sine wave
Figure 2: TIMS model of Figure 1
2.) Next we displayed our message signal coming from the master signals panel of the TIMS on CH1-A of the oscilloscope. This signal is shown in Figure 3.
By inspection we can see that our peak to peak voltage is approximately 4 volts and its frequency is 2kHz.
3.) Due to the Nyquist criteria we know that the minimum sampling frequency for this message signal is 4kHz.
4.) Next we took a look at the sampled input signal on CH2-A of the oscilloscope. This signal is shown in Figure 4.
Page � of �3 5
Figure 3: Message signal to be sampled
Figure 4: Sampled message signal
We can also set up the scope to overlay the message and sampled message signal to show how they are related. This output is shown in Figure 5.
5.) Next we passed the sampled message through a low pass filter to see if we could recover the original signal. The output of the LPF is shown in Figure 6.
�6.) As we changed the sampling width we observed that the amplitude of the recovered signal changed accordingly.
Page � of �4 5
Figure 5: Superimposed sampled and message signal
Figure 6: Signal recovery from its samples
7.) The condition for recovering the original signal is that the sampling frequency is at least twice the highest frequency in the message signal. Since the sampling frequency was set to 8.3kHz from the TIMS masters signals panel, which is well above the minimum required 4kHz, we were able to return to the original signal.
8.) Finally we replaced the 2kHz message signal from the master signals panel with the output of the VCO module in order to vary the frequency both above and below the threshold frequency of 4.16kHz and observed its affects on the recovered signal. The results shown in Figures 7 and 8 show the experimental conformation of the sampling theorem.
��Summary:
In this experiment we experimentally verified the sampling theorem as well as viewed the difference between an aliased and non-aliased signal.
Page � of �5 5
Figure 7: message and output with signal below 4.16kHz showing recoverable signal
Figure 8: message and output with signal above 4.16kHz showing unrecoverable signal
