An ideal lowpass filter with zero delay has impulse response h_1p[n] and frequency response

(a) A new filter is defined by the equation h₁[n] = (?1)ⁿh_1p?[n] = e^j?n h_1p[n]. Determine an equation for the frequency response of H₁(e^j?), and plot the equation for |?|

(b) A second filter is defined by the equation h2[n] = h_1p[n] cos(0.5?n). Determine the equation for the frequency response of?H₁(e^j?), and plot the equation for |?|

(c) A third filter is defined by the equation. Determine the equation for the frequency response H₃(e^j?), and plot the equation for |?|

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1. lw < 0.2n, 0, 0.2n < lwl