Biology Reference
In-Depth Information
Additive noise: SD = constant 25 y-axis units
Phase reference point
(maximum at 0 hours)
Period
(still 24 hours)
1200
Time dependent oscillatory amplitude
(100 units decaying to 0 units with an
80 hour exponential decay life time)
1100
1000
900
800
700
600
500
400
300
200
100
0
Time dependent mean expression intensity
(1000 units decaying to 0 units with an
80 hour exponential decay life time)
100
0
24
48
72
96
120
144
168
192
216
240
Time (hours)
FIGURE 11-15.
Mean and variance nonstationary noisy cosine wave.
performing data analysis. Various algorithms exist for noise and trend
removal. We do not attempt to present them here in detail but, rather,
introduce them and concentrate on discussing their differences and
similarities.
A. Data Filtering
Data filtering is generally applied to remedy the presence of noise.
However, as with any preprocessing of data, data filtering may either
lead to information loss (''leaky filters'') or to altering the data by
introducing, for example, a phase change in the data. The filtering
software used for the examples in this chapter is called ARFILTER.
Its implementation uses a forward-backward linear exponential (i.e.,
first-order) autoregressive filtering strategy, as reported in Orr and
Hoffman (1974), and we refer the reader to this article for the
mathematical description and details. It should be stressed, however,
that a particularly attractive feature of ARFILTER is that it results in
zero phase change of the output. Different algorithms implementing
similar noise reduction techniques for time series can be found in
several commercially available software packages. For example, using
the exponential smoothing option available in MATLAB would result
Search WWH ::




Custom Search