AN2182

Digital filtering principles

5/18

The output signal frequency response is given by the following expression:

where H(f), X(f) and Y(f) are the respective Fourier transforms of h(k), x(k) and y(k).

2.3

Finite impulse response filters

The FIR (Finite Impulse Response) are non-recursive filters, meaning that the output signal y(i)

is a linear combination of N input samples x(k) in the case of a N–1 order filter. Its equation is

A FIR filter is characterized by its order and its coefficients and can be used to implement any

kinds of filters (low-pass, high-pass, pass-band or cutoff band).

Yf

()

Hf

() Xf

()

⋅

=

yn

()

a

k

xn

k

–

()

k0

=

N1

–

∑

⎝⎠

⎜⎟

⎜⎟

⎛⎞

=