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) = 5(x-n.Ax) 112=-00 = {(x-n. 2.Ax) 0 and a 1-D rectangular input signal: f(x) = RECT(). (f) If the sampled function is f(x) = f(x) - Sideal(x, Ax), a. Sketch the discrete sampled function for f (x) and x = [0] at a sampling rate of 2u,. (1 mark) . if x = n. Ax if x #n. Ax b. Sketch the discrete sampled function for f(x) and x = [0] at a sampling rate of u. (1 mark) c. Can f (x) be accurately recovered for either of the sampling rates? (1 mark) Useful formulas: (n = 0, +1, +2, ...) -3 8 The integral of a Gaussian function: (x+b) dx = 12 The Fourier transform of a Gaussian Function: F{e-ax} (u) = sin(x) SINC function definition: SINC(x) = xx 3. Consider a 1-D ideal sampling function defined as +oo Sideal(x, Ax) = 5(x-n.Ax) 112=-00 = {(x-n. 2.Ax) 0 and a 1-D rectangular input signal: f(x) = RECT(). (f) If the sampled function is f(x) = f(x) - Sideal(x, Ax), a. Sketch the discrete sampled function for f (x) and x = [0] at a sampling rate of 2u,. (1 mark) . if x = n. Ax if x #n. Ax b. Sketch the discrete sampled function for f(x) and x = [0] at a sampling rate of u. (1 mark) c. Can f (x) be accurately recovered for either of the sampling rates? (1 mark) Useful formulas: (n = 0, +1, +2, ...) -3 8 The integral of a Gaussian function: (x+b) dx = 12 The Fourier transform of a Gaussian Function: F{e-ax} (u) = sin(x) SINC function definition: SINC(x) = xx