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8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the...
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
Using parsevals theorem and FT to find y(t) and its power (b) (4 pts) Fourier Series The input signal r(t) and impulse...
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) +...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
3. (20 pts) Consider a periodic signal x(t) which can be represented by the first K Fourier Serie...
3. (20 pts) Consider a periodic signal x(t) which can be represented by the first K Fourier Series coefficients. Determine the impulse response of the system that can yield x(t) when it is contaminated by a noise r(t) (i.e., the input to the system is x(t)r(t) and the output is r(t)), assuming that r(t) is composed of only very high-frequency components (namely, Ffr(t)) Rjw)-0 for lul < K2π/T, where T is the period of x(t))
3. (20 pts) Consider a...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396]...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
Hello, Can anyone help me with these questions from signals and systems course? Thank you in...
Hello,
Can anyone help me with these questions from signals and
systems course?
Thank you in advance??♀️
Problem 1 [25 points : Consider the following periodic signal x(t). Determine the Fourier series coefficients, ak nu Problem 2 [25 points : Determine the Fourier series coefficients, ax and the average power for the periodic signal x(t) shown. -2 -1 1 2 Problem 350 points: Let x(t) be the input signal to an LTI system with impulse response h(t) and let y(t)...
LTI Systems. Consider two LTI subsystems that are connected in series
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
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.
3. (20 pts) Consider a periodic signal z(t) which can be represented by the first K Fourier Serie...
Could i get the solution ?
3. (20 pts) Consider a periodic signal z(t) which can be represented by the first K Fourier Series coefficients. Determine the impulse response of the system that can yield z(t) when it is contaminated by a noise r(t) (i.e., the input to the system is a(t) +r(t) and the output is r(t)), assuming that r(t) s composed of only very high-frequency components (namely, F r(t)) = R(ja) = 0 for lav-K2π/T, where T is...
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
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
3. Let the following periodic signal : x(t) = m+0 8(t -- 3m) + 8(t-1-3m) + 8(t – 2 – 3m) be the input to a LTI system with a system function: H(s) = es/4 – e-s/4, Let by represent the Fourier series coefficients of the resulting output signal y(t). Determine bk. (5 points)
3. (20 pts) Consider a periodic signal x(t) which can be represented by the first K Fourier Series coefficients. Determine the impulse response of the system that can yield x(t) when it is contaminated by a noise r(t) (i.e., the input to the system is x(t)r(t) and the output is r(t)), assuming that r(t) is composed of only very high-frequency components (namely, Ffr(t)) Rjw)-0 for lul < K2π/T, where T is the period of x(t))
3. (20 pts) Consider a...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
Hello,
Can anyone help me with these questions from signals and
systems course?
Thank you in advance??♀️
Problem 1 [25 points : Consider the following periodic signal x(t). Determine the Fourier series coefficients, ak nu Problem 2 [25 points : Determine the Fourier series coefficients, ax and the average power for the periodic signal x(t) shown. -2 -1 1 2 Problem 350 points: Let x(t) be the input signal to an LTI system with impulse response h(t) and let y(t)...
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.
Could i get the solution ?
3. (20 pts) Consider a periodic signal z(t) which can be represented by the first K Fourier Series coefficients. Determine the impulse response of the system that can yield z(t) when it is contaminated by a noise r(t) (i.e., the input to the system is a(t) +r(t) and the output is r(t)), assuming that r(t) s composed of only very high-frequency components (namely, F r(t)) = R(ja) = 0 for lav-K2π/T, where T is...
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