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presec5 - ECE 2200 Section V Problems(Week 6 Spring 2009 1...

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ECE 2200: Section V Problems (Week 6 / Spring 2009) 1. The FIR filter with impulse response h [ n ] = 2 δ [ n - 2] has output y [ n ] = u [ n - 3] - u [ n - 6] 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. A linear time-invariant system is described by the difference equation y [ n ] = x [ n ] - 2 x [ n - 1] + x [ n - 2] (a) Find the frequency response H ( e j ˆ ω ), and then express it as a mathematical formula, in polar form (magnitude and phase). (b) Plot the magnitude and phase of H ( e j ˆ ω ) as a function of ˆ ω for - π ˆ ω π . Do this by hand and with the MATLAB function freqz . (c) Find all frequencies, ω , for which the response to the input e jωn is zero. (d) When the input to the system is x [ n ] = sin( πn/ 100)determine the functional form for the output signal y [ n ]. (e) Impulse Response: Determine the response of this system to a unit impulse input. Plot h [ n ] as a function of n . 4. For each of the following frequency responses determine the corresponding impulse
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