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8. Calculate all of the Discrete-Time Fourier Series coefficients, a, for the signal below. -8 6...
Consider the discrete-time periodic signal n- 2 (a) Determine the Discrete-Time Fourier Series (DTFS) coefficients ak...
Consider the discrete-time periodic signal n- 2 (a) Determine the Discrete-Time Fourier Series (DTFS) coefficients ak of X[n]. (b) Suppose that x[n] is the input to a discrete-time LTI system with impulse response hnuln - ]. Determine the Fourier series coefficients of the output yn. Hint: Recall that ejIn s an eigenfunction of an LTI system and that the response of the system to it is H(Q)ejfhn, where H(Q)-? h[n]e-jin
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the...
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the analysis equation to determine the discrete-time Fourier Series (DTFS) coefficients, a. Express the a in terms of cosines [72] -2 N= -3 (b) Sketch the spectrum, as vs. k for -5Sk s5. Please note each value. ak 2 5 Prob. 2 (cont.) -Discrete-Time Fourier Series (CTFS) (c) A periodic signal rafnl is given below. a2In] 2 1 E -3 what is the fundamental period...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients o...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0,...
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
2- In cach of the following, we specify the Fourier series coefficients of a CT signal...
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
f) Calculate the coefficients of the trigonometric form of the Fourier series numerically in MATLAB and...
f) Calculate the coefficients of the trigonometric form of the Fourier series
numerically in MATLAB and graphically represent the one-sided spectrum
(width and phase) frequency for n up to 10 compared to the analytics results.
g) From the coefficients of the trigonometric form of the Fourier series ,
calculate the coefficients of the exposure series and present the two-sided spectrum (width and phase) frequency.
h) Find the average and active value of the signal from the Fourier expansion.
i) Check...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks]
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
Use the method of inspection (or any method) to determine the Discrete Time Fourier Series coefficients...
Use the method of inspection (or any method) to determine the Discrete Time Fourier Series coefficients for the following signal Xin1= 2 +sing Yanitiniz: OX[k] for k-1, 2 fork-0, for k=1,0 for k=2, 2 2) 2) e OX[k)- for k=-1.2 for k=0 for k-1.0 for 2-2 2) 2j OX[K) fork-1.2 for k0 for k-1,0 for k-2,-2 2 2 - e 2j OXIK) for k.1, 1 for kr. for k=1.0 for k-2,2 21 e X[k] for k=- 1, 2 fork-0. for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
Consider the discrete-time periodic signal n- 2 (a) Determine the Discrete-Time Fourier Series (DTFS) coefficients ak of X[n]. (b) Suppose that x[n] is the input to a discrete-time LTI system with impulse response hnuln - ]. Determine the Fourier series coefficients of the output yn. Hint: Recall that ejIn s an eigenfunction of an LTI system and that the response of the system to it is H(Q)ejfhn, where H(Q)-? h[n]e-jin
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the analysis equation to determine the discrete-time Fourier Series (DTFS) coefficients, a. Express the a in terms of cosines [72] -2 N= -3 (b) Sketch the spectrum, as vs. k for -5Sk s5. Please note each value. ak 2 5 Prob. 2 (cont.) -Discrete-Time Fourier Series (CTFS) (c) A periodic signal rafnl is given below. a2In] 2 1 E -3 what is the fundamental period...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
f) Calculate the coefficients of the trigonometric form of the Fourier series
numerically in MATLAB and graphically represent the one-sided spectrum
(width and phase) frequency for n up to 10 compared to the analytics results.
g) From the coefficients of the trigonometric form of the Fourier series ,
calculate the coefficients of the exposure series and present the two-sided spectrum (width and phase) frequency.
h) Find the average and active value of the signal from the Fourier expansion.
i) Check...
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks]
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
Use the method of inspection (or any method) to determine the Discrete Time Fourier Series coefficients for the following signal Xin1= 2 +sing Yanitiniz: OX[k] for k-1, 2 fork-0, for k=1,0 for k=2, 2 2) 2) e OX[k)- for k=-1.2 for k=0 for k-1.0 for 2-2 2) 2j OX[K) fork-1.2 for k0 for k-1,0 for k-2,-2 2 2 - e 2j OXIK) for k.1, 1 for kr. for k=1.0 for k-2,2 21 e X[k] for k=- 1, 2 fork-0. for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
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