Question

If h(n) is absolutely summable, i.e., BIBO stable, then the equation for the frequency response H(ω) is given as?

(a) HI(ω)-j HR(ω)

(b) HR(ω)-j HI(ω)

(c) HR(ω)+j HI(ω)

(d) HI(ω)+j HR(ω)

This question was posed to me in class test.

The doubt is from General Considerations for Design of Digital Filters in division Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (c) HR(ω)+j HI(ω)

To explain I would say: If h(n) is absolutely summable, i.e., BIBO stable, then the frequency response H(ω) exists and

H(ω)= HR(ω)+j HI(ω)

where HR(ω) and HI(ω) are the Fourier transforms of he(n) and ho(n) respectively.