# FIR Filter Type - MATLAB

A question about using fir1/fir2/firpm to design FIR filters in MATLAB. The first parameter is the 'filter order'. For my filter design I pass in 250 as this argument. However, when looking at the impulse response of the filter, it is a type 1 FIR filter. So my question is, is the filter order not the same as the number of taps? Is the number of taps one less, so 249 in this case, which gives the type 1 symmetry?

Cheers

The filter order equals the number of taps minus $$1$$. The filter order is the order of the polynomial corresponding to the filter's transfer function. E.g.,

$$H(z)=h[0]+h[1]z^{-1}+h[2]z^{-2}\tag{1}$$

has $$3$$ coefficients (taps) but it is a second order polynomial (in $$z^{-1}$$), so the filter order equals $$2$$ (i.e., it has $$2$$ zeros and $$2$$ poles).

For type I and type III linear phase FIR filters, the filter order is even, i.e., they have an odd number of taps, whereas types II and IV have an odd filter order (even number of taps).