Consider an ideal lowpass filter with impulse response h1p[n] and frequency response...

Consider an ideal lowpass filter with impulse response h_1p[n] and frequency response

(a) A new filter is defined by the equation Determine an equation for the frequency response of H₁(e^jω), and plot the equation for |ω| < π. What kind of filter is this?

(b) A second filter is defined by the equation h₂[n] = 2h_1p[n] cos(0.5πn). Determine the equation for the frequency response H2(e^jω), and plot the equation for |ω| < π.What kind of filter is this?

(c) A third filter is defined by the equation

Determine the equation for the frequency response H₃(e^jω), and plot the equation for |ω| < π.What kind of filter is this?