Features of Empirical Data

• Real world is a fuzzy place
• Data usually has noise (random errors)
• Data must be smoothed
• Data is point sampled from an analog domain
• Potential aliasing artifacts
• Data may be wrong
• Error in experiment

Point Sampling Problems - Aliasing

• Used in a variety of domains
• Music (CD's)
• Computer Graphics ("jaggies")
• Scientific data acquisition

Point Sampling Theory

• Fourier Transforms (time domain <=> frequency domain)
• Nyquist Limit (sample at >= 2 X highest frequency)
• Prefiltering to remove high frequency data
• Increase sampling frequency

Filtering Data

• Postfiltering to smooth the data
• "Goal is to massage the data and not mutilate it."
• Identify noise characteristics (usually appears as high frequency component)
• Filtering methods
• Fourier transforms
• Moving weighted average
• Polynomial curve fitting

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