Question

Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?

(a) y(n)=\(\sum_{k=0}^{M+1} b_k x(n+k)\)

(b) y(n)=\(\sum_{k=0}^{M+1} b_k x(n-k)\)

(c) y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)

(d) None of the mentioned

The question was posed to me in homework.

Origin of the question is Design of IIR Filters from Analog Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (c) y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)

For explanation I would say: An FIR filter of length M with input x(n) and output y(n) is described by the difference equation

y(n)=\(\sum_{k=0}^{M-1} b_k x(n-k)\)

where {bk} is the set of filter coefficients.