Sampling Analysis

Sampling is a means of obtaining a discrete data set from an analog or continuous signal of interest. This is commonly done digitally by computers and multimeters. Some important considerations are sampling rate, resolution, range, and the family of variables that are related to these.

1) Sample rate corresponds to a frequency, sampling frequency that is a measure of how frequently a signal of interest is measured. In the most common case the signal of interest is time-dependent, the sampling rate must meet certain requirements in order to yield accurate information. The sample rate or sampling frequency has a direct relation to how much information per unit time can be known about the signal of interest—the higher this frequency, the more accurately the measured signal can be represented. On the other extreme, the sampling rate can be too slow to be used for reconstructing the continuous signal.

2) The sampling theorem provides that the sampling frequency should be at least twice as large as the highest frequency in the measured signal of interest. Since the sampling frequency is that for one period of the signal, the Nyquist frequency, also known as the folding frequency, is less than or equal to half the sampling frequency of a discrete signal processing system. If the Nyquist frequency is too high, the system exhibits imperfect signaling known as aliasing. Also, the Nyquist frequency establishes the number of harmonics that can be measured i.e. harmonics can be measured up to fnyq.

Eqns 7.2, 7.3 ?

3) Aliasing is a phenomena that leads to a misinterpretation of data. When the sample rate on a continuous signal is less than twice the highest measured frequency, the discrete series that results appears to have a freq...

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...nsform making for a smoother average across the frequency outputs.

12) The most important factors when discussing data acquisition are range, sample rate, and resolution. First off, range and resolution are collaborative because of quantization error. Since it is defined as a input values being coded to correspond to adjacent coded outputs, the resolution is imperative because it determines the smallest step size that outputs are collected at; the smaller the step size, the better the accuracy will be because the sensitivity will increase. If the range of values selected also increases, the sensitivity would not change but precision would be much better. The sample rate is crucial because it decides what the nyquist or folding frequency will be, which in turn allows the user to know which frequency signals are aliasing and how many such harmonics there would be.