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Home Electrical and Electronics Analog & Digital Communication Study of Sampling Process and Signal Reconstruction and Aliasing
Analog & Digital Communication Lab Experiments

Study of Sampling Process and Signal Reconstruction and Aliasing



Aim

Study of Sampling Process and Signal Reconstruction and Aliasing.

Apparatus Required:

  1. ST2101 with power supply cord.
  2. Oscilloscope with connecting probe
  3. Connecting cords.

Theory

The signals we use in the real world, such as our voice, are called "analog" signals. To process these signals for digital communication, we need to convert analog signals to "digital" form. While an analog signal is continuous in both time and amplitude, a digital signal is discrete in both time and amplitude. To convert continuous time signal to discrete time signal, a process is used called as sampling. The value of the signal is measured at certain intervals in time. Each measurement is referred to as a sample.

Principle of sampling:- Consider an analogue signal x(t) that can be viewed as a continuous function of time, as shown in figure. We can represent this signal as a discrete time signal by using values of x(t) at intervals of nTs to form x(nTs) as shown in figure . We are “grabbing" points from the function x(t) at regular intervals of time, Ts, called the sampling period.

principle-of-sampling

Aliasing: A precondition of the sampling theorem is that the signal to be band limited. However, in practice, no time-limited signal can be band limited. Since signals of interest are almost always time-limited (e.g., at most spanning the lifetime of the sampling device in question), it follows that they are not band limited. However, by designing a sampler with an appropriate guard band, it is possible to obtain output that is as accurate as necessary. Aliasing is the presence of unwanted components in the reconstructed signal. These components were not present when the original signal was sampled. In addition, some of the frequencies in the original signal may be lost in the reconstructed signal. Aliasing occurs because signal frequencies can overlap if the sampling frequency is too low. As a result, the higher frequency components roll into the reconstructed signal and cause distortion of the signal Frequencies "fold" around half the sampling frequency. This type of signal distortion is called aliasing. We only sample the signal at intervals. We don't know what happened between the samples. A crude example is to consider a 'glitch' that happened to fall between adjacent samples. Since we don't measure it, we have no way of knowing the glitch was there at all.

aliasing

In a less obvious case, we might have signal components that are varying rapidly in between samples. Again, we could not track these rapid inter-sample variations. We must sample fast enough to see the most rapid changes in the signal. Sometimes we may have some a prior knowledge of the signal, or be able to make some assumptions about how the signal behaves in between samples.

Circuit Diagram:-

signal-sampling

Signal Reconstruction:-

signal-reconstruction

Procedure:-

A. Set up for Sampling and reconstruction of signal. Initial set up of trainer: Duty cycle selectors switch position: Position 5. Sampling selector switch: Internal position.

  1. Connect the power cord to the trainer. Keep the power switch in ‘Off’ position
  2. Connect 1 KHz Sine wave to signal Input.
  3. Switch ‘On’ the trainer's power supply & Oscilloscope.
  4. Connect BNC connector to the CRO and to the trainer’s output port.
  5. Select 320 KHz (Sampling frequency is 1/10th of the frequency indicated by the illuminated LED) sampling rate with the help of sampling frequency selector switch.
  6. Observe 1 KHz sine wave (TP12) and Sample Output (TP37) on Oscilloscope. The display shows 1 KHz Sine wave being sampled at 32 KHz, so there are 32 samples for every cycle of the sine wave.
  7. Connect the Sample output to Input of Fourth Order low pass Filter & observe reconstructed output on (TP46) with help of oscilloscope. The display shows the reconstructed original 1 KHz sine wave.
  8. By successive presses of sampling Frequency Selector switch, change the sampling frequency to 2KHz, 4KHz, 8KHz, 16KHz and back to 32KHz (Sampling frequency is 1/10th of the frequency indicated by the illuminated LED). Observe how SAMPLE output changes in each cases and how the lower sampling frequencies introduce distortion into the filter’s output waveform. This is due to the fact that the filter does not attenuate the unwanted frequency component significantly. Use of higher order filter would improve the output waveform.
  9. So far, we have used sampling frequencies greater than twice the maximum input frequency.

Conclusion:-As the sampling frequency increases the output of sample port has more number of samples of applied input signal.

B. Setup of Nyquist criteria and aliasing:-Initial set up of trainer: Duty cycle selector switch position: Position 5 Sampling selector switch: Internal position.

  1. Keep the power switch in ‘Off’ position.
  2. Connect 2 volts peak, 2 KHz sine wave from 600 ohms output of the Function Generator to the signal Input of the trainer.
  3. Switch ‘On’ the trainer's power supply & Oscilloscope.
  4. Connect BNC connector to the CRO and to the trainer’s output port.
  5. Select 320 KHz (Sampling frequency is 1/10th of the frequency indicated by the Illuminated LED) sampling rate with the help of sampling frequency selector Switch.
  6. Connect the sample output to fourth order low pass filter & observe the output (TP46) on oscilloscope. Observe the two waveforms (applied input signal & filter output) which are similar but the second waveform (filter output) is lagging in phase. This is as expected from filters phase/ frequency response.
  7. Decrease the sampling rate from 32 KHz to 2 KHz. Observe the distorted waveform at filter's output (TP46). This is due to the fact that we under-sampled the input waveform overlooking the Nyquist criteria and thus the output was distorted even though the signal lies below the cut-off frequency (3.4 KHz) of the filter. This explains the phenomena of Aliasing.

Conclusion:-As the input sampling frequency is smaller than the applied input signal then the output is distorted means the original signal cannot be reconstructed.