# S5 - EE 2200 Spring 2010 Section FIVE 1 ECE 2200 Spring...

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EE 2200 / Spring 2010: Section FIVE 1 ECE 2200 / Spring 2010 SECTION Five (Week 6: Mar 1-4) 1. The FIR ﬁlter with impulse response h [ n ] = 2 δ [ n - 2] where δ [ k ] is 1 for k = 0 and 0 otherwise, has output y [ n ] = u [ n - 3] - u [ n - 6] where u [ k ] is 1 for k 0 and 0 otherwise. Determine the input x [ n ]. 2. The FIR ﬁlter has a step starting at sample zero as its input, i.e. x [ n ] = u [ n ], and the output is the Kronecker delta function, i.e. y [ n ] = δ [ n ]. Determine the impulse response of the ﬁlter. 3. Consider the linear, time-invariant system described by the diﬀerence equation y [ n ] = 21 x [ n ] - 37 x [ n - 1] + 21 x [ n - 2] (i) Find the frequency response H ( e j ˆ ω ) as a mathematical formula in polar form. (ii) Determine the period of H ( e j ˆ ω ) which is a periodic function of ˆ ω . (iii) Plot the magnitude and phase of H ( e j ˆ ω ) as a function of ˆ ω for - π < ˆ ω < 5 π . Check your answer using the Matlab function

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S5 - EE 2200 Spring 2010 Section FIVE 1 ECE 2200 Spring...

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