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1. Discrete Time Signals Plot the following sequences: (a) x[n]...
Signals and Systems: Discrete time Fourier Series: If: 1. Please find the F.S. representation of x[n] 2. Please plot the amplitude spectrum 3. What is the fundamental frequency of x[n]? 4. How many d...
Signals and Systems: Discrete time Fourier Series: If: 1. Please find the F.S. representation of x[n] 2. Please plot the amplitude spectrum 3. What is the fundamental frequency of x[n]? 4. How many distinct harmonics can be present in x[n]?--for this fundamental frequency. 5. How many harmonics are actually in x[n]? Trying to prepare for finals, its crunch time, thank you for your help! r[n] = 2sin(n-) + cos(n-) r[n] = 2sin(n-) + cos(n-)
Question 4. (20 points) Compute the DTFT of the discrete-time signals, 1) x[n] = n(0.5)"u[n]. (opt)...
Question 4. (20 points) Compute the DTFT of the discrete-time signals, 1) x[n] = n(0.5)"u[n]. (opt) 2) x[n] = n(0.5)”cos(4n)u[n]. (opt) 3) x[n] = (0.5)" cos(4n)u[n]. (7pt)
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. ...
Please explain why. Thank you.
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. For each of the given sampling rates in F, Hz or in T period, (i) determine the spectrum x(eM) of x[n]; (ii) plot its magnitude and phase as a function of w in and as a function of sampling frequency Fs in HZ; and (iii explain whether e(t) can be recovered from rn] (a) re(t) 8 +12e-3207e-j0(+), with sampling rate...
Compute the Discrete-Time Fourier Transform analytically for the following signals and plot the absolute values and...
Compute the Discrete-Time Fourier Transform analytically for the following signals and plot the absolute values and the phase of the DTFT from-2π to 2π x[n] αηυ[n] for α-0.7 and 0.3 x[n]-δ[n-r] for τ-2 and 3 xInrk], for r -2 and 3 a. b. C. Please show your work step by step and include the formula for finding the absolute value of DTFT and the phase of DTFT.
4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the...
4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the signal b. Find the Fourier Transform of x[n]
Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: ...
how to calculate the convolution
Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence with u[n] is the sum of all the components (an integrator) 2. x[n]=仁1,-2-3-4) 1 vl n | =.xln|>k 11 | n | = 〈ー1, 2(00.-1,-3.-6.-10-10.
Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence...
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--o...
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3...
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3 2 1 -1 x(n) 6 4 2 a. (15 points) Compute the Fourier transform X(w). b. (5 points) Write down all the characteristics and properties of X(w). c. (5 points) Explain the limitations of X(w) if it should be compute using a microprocessor. What is the solution?
d) Given a discrete time sequence: x[n] 218(n 2) - (n 1) +358 (n) -(n 1)218...
d) Given a discrete time sequence: x[n] 218(n 2) - (n 1) +358 (n) -(n 1)218 (n - 2) where δ(n) is the unit-impulse sequence and the general Discrete Time Fourier Transform (DTFT) X(ej") is: i) ii) iii) Do the following without explicitly finding X(ejo) Determine χ[0]-4x[1] Evaluate DTFT X(ejw) at ω-0. Using one of the DTFT properties, state the value the phase value of X(eM) (ie. φ(u)) . Explain how you get the answer
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists,...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
Question 4. (20 points) Compute the DTFT of the discrete-time signals, 1) x[n] = n(0.5)"u[n]. (opt) 2) x[n] = n(0.5)”cos(4n)u[n]. (opt) 3) x[n] = (0.5)" cos(4n)u[n]. (7pt)
Please explain why. Thank you.
(5%) The following signals r t) is sanpled periodically to obtained the discrete-time signal [n. For each of the given sampling rates in F, Hz or in T period, (i) determine the spectrum x(eM) of x[n]; (ii) plot its magnitude and phase as a function of w in and as a function of sampling frequency Fs in HZ; and (iii explain whether e(t) can be recovered from rn] (a) re(t) 8 +12e-3207e-j0(+), with sampling rate...
Compute the Discrete-Time Fourier Transform analytically for the following signals and plot the absolute values and the phase of the DTFT from-2π to 2π x[n] αηυ[n] for α-0.7 and 0.3 x[n]-δ[n-r] for τ-2 and 3 xInrk], for r -2 and 3 a. b. C. Please show your work step by step and include the formula for finding the absolute value of DTFT and the phase of DTFT.
4. Consider the discrete time signal x[n] = u[n-2] - u[n – 6] a. Plot the signal b. Find the Fourier Transform of x[n]
how to calculate the convolution
Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence with u[n] is the sum of all the components (an integrator) 2. x[n]=仁1,-2-3-4) 1 vl n | =.xln|>k 11 | n | = 〈ー1, 2(00.-1,-3.-6.-10-10.
Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence...
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
a) Find the transform of the following signals and plot the ROC . I x(n)-(0.5)'u(-n-3)+2(0.75) u(n+2) x(n)--on2u(n-2)
3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3 2 1 -1 x(n) 6 4 2 a. (15 points) Compute the Fourier transform X(w). b. (5 points) Write down all the characteristics and properties of X(w). c. (5 points) Explain the limitations of X(w) if it should be compute using a microprocessor. What is the solution?
d) Given a discrete time sequence: x[n] 218(n 2) - (n 1) +358 (n) -(n 1)218 (n - 2) where δ(n) is the unit-impulse sequence and the general Discrete Time Fourier Transform (DTFT) X(ej") is: i) ii) iii) Do the following without explicitly finding X(ejo) Determine χ[0]-4x[1] Evaluate DTFT X(ejw) at ω-0. Using one of the DTFT properties, state the value the phase value of X(eM) (ie. φ(u)) . Explain how you get the answer
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
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