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10 x(t) = { 1-0. 50.4Sts0.4 0 3.6 < t-0.4 A signal x (t) is defined...
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To...
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To implement Fourier Series (t)---> (ults) -1 1 0 t---> (sec) (ii) To= Wo=- Do- Dn= Sketch D vs nw.. (vi) Sketch <D, (e.) vs nw.. (vii) Power of r(t) = (viii) Express x(t) as sum of Sine Waves, Cosine waves and DC (ix) Show that the expression found in part(viii) is real
Let g(t) be a sawtooth wave shown as follows, 1.0 0.5 0.0 -0.5 0.0 0.2 0.4...
Let g(t) be a sawtooth wave shown as follows, 1.0 0.5 0.0 -0.5 0.0 0.2 0.4 0.6 08 1.0 (i Find its Fourier series. () Sketch IDn I vs nwa.(Magitude Spectrum) Sketch Dn (en) vs nwo. (Phase Spectrum) iv) Find power of g(t) in time domain (v) Find power of g(t) in frequency domain (vi) Write matlab code to sketch g(t) from its Fourier Coefficients, attach the matlab code and the output figure from matlab
c) Consider the following time-domain signal x(t) 2A for -T/2 sts T/2. Assume ()0 otherwise, answer...
c) Consider the following time-domain signal x(t) 2A for -T/2 sts T/2. Assume ()0 otherwise, answer the following i. Sketch the signal showing the major points of interest. Evaluate the Continuous Time Fourier Transform of x(t) as X(ω). ii. Compute the energy spectral density (ESD)X iv. Sketch the ESD of x(t)showing the major features. What can you say about the IV. bandwidth which the signal energy occupies? Is it finite or infinite?
(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...
Don't need to do #1. Please go into detail on how you solved #2 and #3 The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) S...
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d) Sketch IG(Go)
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d)...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T,...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
II. Consider a continuous time signal x(t), containing two windowed sinusoids 0.1 0.2 0.3 0.4 0.5...
II. Consider a continuous time signal x(t), containing two windowed sinusoids 0.1 0.2 0.3 0.4 0.5 0.6 The Fourier transform of the signal is as follows: 15 10 5 -800-_-400 h 200 400 600 The signal x(t) is the input of an LTI filter with frequency response lH(c) shown below 0.5 -&- 400︺-200 0 200 400 600 Shown below are four possible outputs of LTI filter when x(t) is the input. Please select the correct output (a) ya(t) (b) y(t)...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
1. Consider a signal x(t) defined over the interval t =(-1,1]as shown below. X(t) ЛИ (a)...
1. Consider a signal x(t) defined over the interval t =(-1,1]as shown below. X(t) ЛИ (a) Is x(t) an energy signal? Find its energy. (b) Find the Fourier transform X (jo)of x(t).
A signal x(t) is defined as; 3 0 -0.2 <t < 0.2 - 1.8<t< -0.2 To implement Fourier Series (t)---> (ults) -1 1 0 t---> (sec) (ii) To= Wo=- Do- Dn= Sketch D vs nw.. (vi) Sketch <D, (e.) vs nw.. (vii) Power of r(t) = (viii) Express x(t) as sum of Sine Waves, Cosine waves and DC (ix) Show that the expression found in part(viii) is real
Let g(t) be a sawtooth wave shown as follows, 1.0 0.5 0.0 -0.5 0.0 0.2 0.4 0.6 08 1.0 (i Find its Fourier series. () Sketch IDn I vs nwa.(Magitude Spectrum) Sketch Dn (en) vs nwo. (Phase Spectrum) iv) Find power of g(t) in time domain (v) Find power of g(t) in frequency domain (vi) Write matlab code to sketch g(t) from its Fourier Coefficients, attach the matlab code and the output figure from matlab
c) Consider the following time-domain signal x(t) 2A for -T/2 sts T/2. Assume ()0 otherwise, answer the following i. Sketch the signal showing the major points of interest. Evaluate the Continuous Time Fourier Transform of x(t) as X(ω). ii. Compute the energy spectral density (ESD)X iv. Sketch the ESD of x(t)showing the major features. What can you say about the IV. bandwidth which the signal energy occupies? Is it finite or infinite?
(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...
Don't need to do #1. Please go into detail on how you solved #2
and #3
The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d) Sketch IG(Go)
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d)...
For the given rectangular pulse signal shown in figure below, 1 x(1) 1, T 0, T, x) T T1 Find the Fourier transform of the signal and sketch it
II. Consider a continuous time signal x(t), containing two windowed sinusoids 0.1 0.2 0.3 0.4 0.5 0.6 The Fourier transform of the signal is as follows: 15 10 5 -800-_-400 h 200 400 600 The signal x(t) is the input of an LTI filter with frequency response lH(c) shown below 0.5 -&- 400︺-200 0 200 400 600 Shown below are four possible outputs of LTI filter when x(t) is the input. Please select the correct output (a) ya(t) (b) y(t)...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
1. Consider a signal x(t) defined over the interval t =(-1,1]as shown below. X(t) ЛИ (a) Is x(t) an energy signal? Find its energy. (b) Find the Fourier transform X (jo)of x(t).
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