"Answer the following questions based on these DT signals x[n]=1+cosā”(2Ļn/6) y[n]=sinā”(4Ļn/6) z[n]=x[n]y[n] What is the DTFS of x[n]? XB06 What is the DTFS of y[n]? Using the properties you learned in class, find the Fourier series of z[n]."
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Use the defining equation for the DTFS coefficients to evaluate the DTFS representation of the following signals. a) x[n] = cos(n+3) b) x[n] = 2sin(n) + cos(1%n) + 1
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Consider the signal s(t) defined as follows: s(t) = {4 - t^2, |t| <= 2; 0, |t| > 2} By direct integration, show that the Fourier transform S(w) of the signal s(t) is: S(w) = -8cos(2w)/w^2 + 4sin(2w)/w^3 Using the result from part (i) of this question, and using the appropriate shift theorem, find the Fourier Transform of s1(t) = {(8 - 2t^2)cos(3t), |t| <= 2; 0, |t| > 2} Determine the Z-transform of the sequence, x(n) = a^(n-1)u(n - 1) Z-transform of the signal x(n) is given by X(z) = log_e(1 - az^-1); |z| > |a| Using the differentiation property of Z-transforms and standards tables, or otherwise, find the signal x(n).
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