Question

The following diagram represents the unit sample response of which of the following filters?

(a) Ideal high pass filter

(b) Ideal low pass filter

(c) Ideal high pass filter at ω=π/4

(d) Ideal low pass filter at ω=π/4

I had been asked this question in final exam.

I'm obligated to ask this question of General Considerations for Design of Digital Filters in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (d) Ideal low pass filter at ω=π/4

To elaborate: At n=0, the equation for ideal low pass filter is given as h(n)=ω/π.

From the given figure, h(0)=0.25=>ω=π/4.

Thus the given figure represents the unit sample response of an ideal low pass filter at ω=π/4.