3. Consider a 1-D ideal sampling function defined as +oo Sideal(x, Ax) = 5(x-n.Ax) 112=-00...

 

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3. Consider a 1-D ideal sampling function defined as +oo Sideal(x, Ax) = Σ 5(x-n.Ax) 112=-00 = {(x-n. 0 and a 1-D rectangular input signal: 2.Ax) if x = n. Ax if x #n. Ax f₁(x) = RECT(). (e) Given the following sinusoidal function and its Fourier transform: f₂(x) = cos (2nu₂x) F₂(u) = 8(u+u) + d(u-uo), a. Is F₂ (u) bandlimited? If yes, what is the maximum frequency and Nyquist frequency? (1 mark) Useful formulas: . b. Can f₂ (x) be sampled using Sideal (x, Ax) without aliasing? If yes, under what condition? (1 mark) • The integral of a Gaussian function:fa(x+b)² dx = The Fourier transform of a Gaussian Function: F{e-ux³}(u): SINC function definition: SINC(x) = sin(xx) XX (n = 0, +1, +2, ...) = n²u² 3. Consider a 1-D ideal sampling function defined as +oo Sideal(x, Ax) = Σ 5(x-n.Ax) 112=-00 = {(x-n. 0 and a 1-D rectangular input signal: 2.Ax) if x = n. Ax if x #n. Ax f₁(x) = RECT(). (e) Given the following sinusoidal function and its Fourier transform: f₂(x) = cos (2nu₂x) F₂(u) = 8(u+u) + d(u-uo), a. Is F₂ (u) bandlimited? If yes, what is the maximum frequency and Nyquist frequency? (1 mark) Useful formulas: . b. Can f₂ (x) be sampled using Sideal (x, Ax) without aliasing? If yes, under what condition? (1 mark) • The integral of a Gaussian function:fa(x+b)² dx = The Fourier transform of a Gaussian Function: F{e-ux³}(u): SINC function definition: SINC(x) = sin(xx) XX (n = 0, +1, +2, ...) = n²u²

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a Yes F2u is bandlimited The maximum frequency is ... View the full answer