# 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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Last modified on February 11, 1999, G.
Scott Owen, owen@siggraph.org