Differentiators - Digital Filter Design Solutions - page 330

Low-Pass

First-Order

Band-Pass

Differentiators

Type a

Second-Order LP

Type b

Figure 6.15 Layout of differentiators presented in this chapter.

designed using the Gaussian window technique described in Section 6.4. The seed
filters for the Type a differentiators were the standard low-pass filters again
derived from the window technique. In that regard, second order differentiators
display many properties as their parent filter.

6.7.1 Filter Identifier

The filter identifier is the name given to the differentiating filter. The
differentiator identifier is found at the top of the page and follows the format for
unity gain filters:

DIFF nnn F m.m

DIFF First-Order Differentiator

nnn Number of filter coefficients (i.e., filter length)

F Normalized frequency

Cut-off frequency value

m.m

For example, the identifier DIFF99F0.3 means a differentiating filter of length 99
with normalized cut-off frequency at 0.3. Here, first-order differentiators were
designed exclusively using the window (Fourier) technique. Band-pass
differentiators have the following identifier structure:

DIFF nnn C m.m W p.p

DIFF First-Order Differentiator

nnn Number of filter coefficients (i.e., filter length)

C Center frequency of band

m.m Center frequency value with respect to width

W Width of band measured at half height

Width value m.m

Thus for example, the identifier DIFF255C0.65W0.1 corresponds to a 255-tap, 0.1-
wide, band-pass differentiator with center frequency at 0.65. Note that the width
and center values are in normalized frequency units. For second-order
differentiators the following format is used: