# Low-pass filtering of on-line handwriting signals

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.

## An interactive demo of low-pass filtering of on-line handwriting.

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.

## Other interesting material:

Handwriting Recognition and Document Analysis Conferences

Pen & Mobile Computing