Study of Sampling Process and Signal Reconstruction and Aliasing.
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.
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.
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 Reconstruction:-
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.
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.
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.
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