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Properties <strong>of</strong> the <strong>Frequency</strong> <strong>Response</strong>Properties <strong>of</strong> the <strong>Frequency</strong> <strong>Response</strong>Relation to Impulse <strong>Response</strong> and Difference Equation• In the definition <strong>of</strong> the frequency response, He jˆ , for an<strong>FIR</strong> filter, the coefficients were utilized• Similarly given the frequency response, the impulse responsecan be foundhn • In Chapter 5 we saw that the impulse response and differenceequation are directly related, so in summary given one theother two are easy to obtainExample:• Given sayMwe immediately see that• The difference equation is• The frequency response isb kTime Domain <strong>Frequency</strong> Domain= hk n– kHe jˆ– hk e jˆ k =hn k = 0hn yn He jˆ==He jˆMk = 02n + 3n – 1 – 2n – 2 = 23 – 2b k2xn + 3xn–1 – 2xn–2– ˆ = 2+3e j–2e – j2ˆECE 2610 Signals and Systems 6–14
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