3. Consider a 1-D ideal sampling function defined as Sideal (x, Ax) = +00 8(x-n-Ax) 12=-00...

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3. Consider a 1-D ideal sampling function defined as Sideal (x, Ax) = +00 8(x-n-Ax) 12=-00 (8(x-n Ax) if x = n Ax = {(x - n and a 1-D rectangular input signal: 0 (n = 0,1, 2, ...) if xn. Ax f1(x) = RECT (2) (a) Find the sampling period and sampling frequency for Sideal (x, Ax). (2 mark) (b) Find the Fourier transform of f(x) using the integral definition. Sketch the Fourier transform. (3 marks) (c) Is the Fourier transform of fi(x) bandlimited? If yes, what is the maximum frequency and Nyquist frequency? (2 mark) (d) Can f(x) be sampled using Sideal (x, Ax) without aliasing? If yes, under what condition? (2 mark) Useful formulas: The integral of a Gaussian function: e-a(x+b) dx = The Fourier transform of a Gaussian Function: F{eax}(u) = SINC function definition: SINC(x)= sin(xx) Note: where applicable, report your answer using 3 significant figures. 3. Consider a 1-D ideal sampling function defined as Sideal (x, Ax) = +00 8(x-n-Ax) 12=-00 (8(x-n Ax) if x = n Ax = {(x - n and a 1-D rectangular input signal: 0 (n = 0,1, 2, ...) if xn. Ax f1(x) = RECT (2) (a) Find the sampling period and sampling frequency for Sideal (x, Ax). (2 mark) (b) Find the Fourier transform of f(x) using the integral definition. Sketch the Fourier transform. (3 marks) (c) Is the Fourier transform of fi(x) bandlimited? If yes, what is the maximum frequency and Nyquist frequency? (2 mark) (d) Can f(x) be sampled using Sideal (x, Ax) without aliasing? If yes, under what condition? (2 mark) Useful formulas: The integral of a Gaussian function: e-a(x+b) dx = The Fourier transform of a Gaussian Function: F{eax}(u) = SINC function definition: SINC(x)= sin(xx) Note: where applicable, report your answer using 3 significant figures.