predicting the charcteristics of Filters
A limited word length in a DSP causes excess quantization (i.e., a large quantization step size) of data samples, raising the noise floor, and of filter coefficients, which can make the actual response of the filter deviate from its theoretical value. The latter effect is most visible in the area of reduced stop-band attenuation.

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For example, in an FIR filter, the coefficients also define the filter's impulse response. Also, for any filter, the Fourier transform of its impulse response is its frequency response.

It is an interesting exercise to draw a curve representing the desired frequency response and take its inverse Fourier transform to get the impulse response. In any real implementation, you're going to have to select a finite number of coefficients, and you're going to have to apply a "window" function to those coefficients in order to limit the effects of the truncation on the impulse response.

Take the Fourier transform of these coefficients and see how the resulting frequency response deviates from the ideal response you started with.

Now, quantize those coefficients to the precision they'll actually have on the DSP. Take another Fourier transform and see how this has further modified the frequency response.

In some cases, the effects can be dramatic. Doing this a few times can give you a good sense of the level of filter performance you can expect for various values of filter length and word width.

To address the overflow issues that Olin is alluding to, you would normally scale the coefficients during the design phase so that the maximum gain in the filter's passband is unity. However, this can create additional quantization errors in the coefficients, causing the smaller ones to disappear altogether. If the hardware of the DSP includes, say, an 8-bit overflow field on the MAC accumulator, you might set the coefficient gain to 256 instead, and then shift the output samples right by 8 bits to get an overall gain of unity.