FL10quiz21 - in a table Is there an integration formula for inverse transformation for the Fourier transform e The Fourier transform F θ of a

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ESE 351 Quiz 21 Name: 11/18/10 Section 12.1–12.8 a. If the bilateral Laplace transform of a continuous-time function f ( t ) is F II ( s ), what is the Fourier transform F ( ω ) of f ( t )? You may assume that the imaginary axis is in the region of convergence for the Laplace transform. b. If the bilateral z transform of a discrete-time function f ( k ) is F II ( z ), what is the Fourier transform F ( θ ) of f ( k )? You may assume that the unit circle e is in the region of convergence for the z transform. c. What is the continuous-time Fourier transform ∆( ω ) of the unit impulse δ ( t )? Hint: Do you remember the two-sided Laplace transform ∆ II ( s ) of the unit impulse δ ( t )? d. In this class, inverse transformation for both the Laplace and z transforms is carried out by expanding the transform in partial fractions and then looking up each fraction
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Unformatted text preview: in a table. Is there an integration formula for inverse transformation for the Fourier transform? e. The Fourier transform F ( θ ) of a discrete-time function f ( k ) is periodic and sym-metric. So if we know the transform values F ( θ ) for 0 ≤ θ ≤ θ max , we can construct the rest of the transform values: F ( θ ) for θ < 0 and θ ≥ θ max . What is the value of this θ max ? If you find multiple answers, please pick the smallest positive value. Hint: The answer would be the same if the question is about the frequency response H ( e iθ ) of a discrete-time system....
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