In this demo, the effects of low-pass filtering of on-line handwriting
signals are shown. For speed reasons, we use a digital FIR filter with a
boxcar impulse response. In our on-line handwriting recognizers, we mostly
use the FFT/IFT method. Before applying any filter, it is essential
to know something of the bandwidth of pen-tip movements in handwriting.
Of course, we assume an equidistant-time sampled signal (*Fs=100Hz*).

Figure 1. Average PSDF of pen-tip movement in (mixed) handwriting of 32 writers

There is a peak at about 4 Hz, showing the basic periodicity in handwriting. Figure 1 shows a typical power spectral density function for pen-tip movements in handwriting, averaged over 32 writers, 210 words per writer. The word XY pen-tip displacement time functions were circularized with a cosine transition function and padded with zeros until 512 samples (i.e., about 5s of writing time), and an FFT was calculated for that word. The average power spectrum (power-spectral density function, PSDF) of pen-tip movement over words was calculated by accumulating |FFT|^2. The spectrum shows that from the Nyquist sampling theorem point of view, a sampling frequency of 20 samples/second would be sufficient for reconstruction of the signal. However, it is much cheaper to use higher sampling rates than to reconstruct the trajectory and display it in real time. A sampling frequency of 100 samples/second yields about 10 points per stroke in normal handwriting. Five points per stroke is the (barely) acceptable minimum, for users of pen computers.

Please refer to our **Publications**
when using anything from the shown material.

Notes:

- The initial thick trace shows the width (i.e., duration) of the boxcar impulse response in this piece of the trajectory.
- The width of the smooting rectangular window is expressed in number
of samples. Since the sampling interval is 10ms, and a stroke lasts
about 100ms, a window width of 10 samples covers a whole
stroke. In this case, the first dip of the comb-shaped filter response
will be at
*1/0.1s = 10 Hz*, leaving the essence of the data intact. If larger windows are used, the resulting lower bandwidth leads to a trace which looks as if it were written too fast. In a sense, this is indeed what happens in fast writing. What happens here is that the biomechanical filter is more or less a constant factor, but the excitation of that system is in the frequency range of the down-going slope of its transfer function. - If the width is less than 2 samples, no filtering is applied.
- You may change the amont of noise by changing the value and pressing
**Apply**. On each run, new noise is computed (Math.rand()). The noise is expressed as a percentage of the*Y*-range of the unfiltered input word. - The handwriting XY coordinates are loaded from our server, so please be
patient when clicking
**Next**or**Previous**.

to NICI's Java-based Handwriting Demos page

to NICI's on-line handwriting recognizer description

- Handwriting Recognition and Document Analysis Conferences

- Pen & Mobile Computing

- NICI Handwriting Recognition Group home page

- UNIPEN tools

Copyright Lambert Schomaker (April 1, 1996)

since 1/Mar/1996