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Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(el")...
Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(e)...
Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(e) be the Fourier transform of the discrete-time signal x[n] show below. x[n] -7 -5 -3 -2 2 -1 4 5 a) Find X(e). (5 pts) b) Determine ZX(el), the phase of X(e), (5 pts) c) Evaluate )do. (5 pts) Intel® d) Find X(el). (5 pts) e) Determine and sketch the signal whose Fourier transform is ReX(0)} (5 pts) f) Evaluate xo do. (5 pts)...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,00...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f #...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] =...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier...
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal...
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar. a. Determine the value of an b. Determine ax, k 0, by: 1.first finding the Fourier coefficients of CID II.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part(b) to express the Fourier transform of (t).
(a) Based on the following discrete-time signal x[n], [n] →n -2 -1 0 1 2 3...
(a) Based on the following discrete-time signal x[n], [n] →n -2 -1 0 1 2 3 4 i. [5%] determine the Fourier transform (i.e., X(ein)) and sketch the magnitude spectrum. ii. [4%] Given the following signal Xp[n], which is the periodic version of x[n] with period 4. Derive the Fourier series coefficients of yn], i.e., {ax}. xp[n] -1 1 2 3 4 5 iii. [4%] Hence, derive the Fourier transform of ap[n], i.e., Xp(es"). iv. [5%] Based on the results...
Problem 5. (20 points) a) Given a periodic wave function of S(x) = ax -1 <x<...
Problem 5. (20 points) a) Given a periodic wave function of S(x) = ax -1 <x< n that has a period of 27. Determine if f(x) is an even or odd function b) Find Fourier Sine Transform of f(x)=e
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5)...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(e) be the Fourier transform of the discrete-time signal x[n] show below. x[n] -7 -5 -3 -2 2 -1 4 5 a) Find X(e). (5 pts) b) Determine ZX(el), the phase of X(e), (5 pts) c) Evaluate )do. (5 pts) Intel® d) Find X(el). (5 pts) e) Determine and sketch the signal whose Fourier transform is ReX(0)} (5 pts) f) Evaluate xo do. (5 pts)...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
Problem 3: Find the Fourier series expansion for x(t)- | cos(Ttt/2) Problem 4: Determine the Fourier transform of the signal x(t) shown below which consists of three rectangular pulses. (Note: this is not a periodic function.) x(t) TI Sayfa Sonu Problem 5: Use the duality property of Fourier transform to find the Fourier transform of x(t) - sinc(Wt)
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar. a. Determine the value of an b. Determine ax, k 0, by: 1.first finding the Fourier coefficients of CID II.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part(b) to express the Fourier transform of (t).
(a) Based on the following discrete-time signal x[n], [n] →n -2 -1 0 1 2 3 4 i. [5%] determine the Fourier transform (i.e., X(ein)) and sketch the magnitude spectrum. ii. [4%] Given the following signal Xp[n], which is the periodic version of x[n] with period 4. Derive the Fourier series coefficients of yn], i.e., {ax}. xp[n] -1 1 2 3 4 5 iii. [4%] Hence, derive the Fourier transform of ap[n], i.e., Xp(es"). iv. [5%] Based on the results...
Problem 5. (20 points) a) Given a periodic wave function of S(x) = ax -1 <x< n that has a period of 27. Determine if f(x) is an even or odd function b) Find Fourier Sine Transform of f(x)=e
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
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