When developing analysis algorithms, you may need to generate and simulate noise signals with specific statistical properties to observe the behavior of the algorithm under deviant conditions. The robustness of the analysis algorithm and its successful implementation depends upon the development of a good model for noise signals.
LabVIEW and the LabVIEW DSC module contain an efficient random number generator you can use to model probabilistic events. In addition, a subset of the analysis VIs can generate random patterns with specific statistical characteristics. The Uniform White Noise and the Gaussian White Noise VIs, for example, generate two common random patterns for modeling noisy environments.
The following illustration depicts the front panel and block diagram of a VI that generates a noisy signal whose expected statistical properties are known beforehand. The VI then uses descriptive statistical analysis VIs to verify the model and the properties of the noise signal.
The appropriate statistical properties in this example are the mean, standard deviation, skewness, kurtosis, histogram, and mode. The mean and standard deviation are well-known statistics. Skewness is a measure of symmetry. Kurtosis is a measure of peakedness. Skewness and kurtosis correspond to the third and fourth order moments about the mean, respectively. The histogram is an indication of the distribution, and the mode is the value that occurs most often.
The expected values for a (0:1) Gaussian-distributed, white-noise signal are as follows.
The histogram should resemble a bell-shaped curve.
The following graphs show the result of generating a (0:1) Gaussian-distributed noise signal, as well as its histogram, which resembles a bell-shaped curve corresponding to a Gaussian distribution.
The following controls show the computed values for the mean, standard deviation, skewness, kurtosis, and mode to be compared to the actual expected values.
Generating random numbers using a digital computer is impossible because you cannot create a true random sequence with a deterministic machine. However, the analysis VIs generate finite length sequences, at least 290 samples, that closely mimic noise signals.
Refer to Probability Density and Distribution Functions for more information about statistical analysis.