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Vout Figure 2: RC Circuit 2. (15pts) Derive...
(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?...
Please answer all parts thank you 6. [15 POINTS] Consider a passive low-pass filter as shown...
Please answer all parts thank
you
6. [15 POINTS] Consider a passive low-pass filter as shown below. 1k2 + - m - + Vin(t) 1 mF Vout(t) a) Derive a transfer function for the above circuit. b) Derive a time-domain expression for the unit impulse response of the circuit. Also, plot the impulse response as a function of time. c) Derive a time-domain expression for the unit step response of the circuit. Also, plot the step response as a function...
Please answer the following fully with detailed justification/explanation. Thank you. Consider the signal e(t) (60m sin...
Please answer the following fully with detailed
justification/explanation. Thank you.
Consider the signal e(t) (60m sin (50t) (a) Determine Xc(jw), the Fourier transform of e(t). Plot (and label) Xe(ju) b) What is the Nyquist rate for re(t)? (c) Consider processing the signal re(t) using the system shown below: Conversion to a Ideal to an e(t) y(t) impulse train Filter H-(ju) The sampling rate for this system is f DT filter is shown below 150 Hz. The frequency response of the...
A filtering circuit is given in Figure1 v¡(t) uo(t) R2 Figure 1: Filter circuit for Problem...
A filtering circuit is given in Figure1 v¡(t) uo(t) R2 Figure 1: Filter circuit for Problem 1 (1.a) Derive the transfer function H(s) = V(s)/V(s) for this filter network. (5 marks) (1.b) Determine the magnitude |H(ju) and phase (jw) of the frequency response of the filter network. (2 marks) (1.c) What type of filter is this? What might it be used for? Justify your answer. (3 marks)
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge...
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge Vout to the input voltage vin. What is the transfer function? What is the time constant of the system? Vout Figure 1: RC Circuit What is the analytical step response solution in terms of vin, Rand C? For assumed values of R 1 K, and C 6.8 uF, perform a simulation using Matlab/Simulink assuming an input square wave signal of 5Vpp,...
Can you please answer in simple steps: e to Question 2. (2a) Show that a filter...
Can you please answer in simple steps:
e to Question 2. (2a) Show that a filter with the frequency response 2 x (104) HW) = w2 + 108 is physcially unrealizable. 2a Hint. Use the basic Fourier transform e-altl # for a > 0 and then the a2 +w2 time shifting property to obtain the inverse Fourier transform h(t) of H(w). Show that h(t) is noncausal. (2b) Can this filter be made approximately realizable by choosing a sufficiently large to?...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts)...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Signal And System Build a first order LPF with cut-off frequency at 10 kHz. A simple...
Signal And System
Build a first order LPF with cut-off frequency at 10 kHz. A simple low pass filter (first order) circuit is shown in Figure 1. V = gain 0.7 (a) RC low Pass Filter Circuit Figure 1 (b) Frequency ResponseCurve show that the impulse response for a first order low-pass filter in Figure 1 is given by 1 H(f) = 1+j295RC The cut-off frequency for a low-pass filter is fcutoff ZRC Generate a rectangular pulse with frequency of...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +j2 exp(-j10t) +3 -j2 exp^10t)+ (2-j2) expG300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t) d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part oft(t) by at least 50%. Write down its H(0) and plot its spectrum. e. Plot the spectrum...
(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?...
Please answer all parts thank
you
6. [15 POINTS] Consider a passive low-pass filter as shown below. 1k2 + - m - + Vin(t) 1 mF Vout(t) a) Derive a transfer function for the above circuit. b) Derive a time-domain expression for the unit impulse response of the circuit. Also, plot the impulse response as a function of time. c) Derive a time-domain expression for the unit step response of the circuit. Also, plot the step response as a function...
Please answer the following fully with detailed
justification/explanation. Thank you.
Consider the signal e(t) (60m sin (50t) (a) Determine Xc(jw), the Fourier transform of e(t). Plot (and label) Xe(ju) b) What is the Nyquist rate for re(t)? (c) Consider processing the signal re(t) using the system shown below: Conversion to a Ideal to an e(t) y(t) impulse train Filter H-(ju) The sampling rate for this system is f DT filter is shown below 150 Hz. The frequency response of the...
A filtering circuit is given in Figure1 v¡(t) uo(t) R2 Figure 1: Filter circuit for Problem 1 (1.a) Derive the transfer function H(s) = V(s)/V(s) for this filter network. (5 marks) (1.b) Determine the magnitude |H(ju) and phase (jw) of the frequency response of the filter network. (2 marks) (1.c) What type of filter is this? What might it be used for? Justify your answer. (3 marks)
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
Prelab Preparation: For the RC circuit shown in Figure 1, derive the modeling equation relating the output volta ge Vout to the input voltage vin. What is the transfer function? What is the time constant of the system? Vout Figure 1: RC Circuit What is the analytical step response solution in terms of vin, Rand C? For assumed values of R 1 K, and C 6.8 uF, perform a simulation using Matlab/Simulink assuming an input square wave signal of 5Vpp,...
Can you please answer in simple steps:
e to Question 2. (2a) Show that a filter with the frequency response 2 x (104) HW) = w2 + 108 is physcially unrealizable. 2a Hint. Use the basic Fourier transform e-altl # for a > 0 and then the a2 +w2 time shifting property to obtain the inverse Fourier transform h(t) of H(w). Show that h(t) is noncausal. (2b) Can this filter be made approximately realizable by choosing a sufficiently large to?...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
Signal And System
Build a first order LPF with cut-off frequency at 10 kHz. A simple low pass filter (first order) circuit is shown in Figure 1. V = gain 0.7 (a) RC low Pass Filter Circuit Figure 1 (b) Frequency ResponseCurve show that the impulse response for a first order low-pass filter in Figure 1 is given by 1 H(f) = 1+j295RC The cut-off frequency for a low-pass filter is fcutoff ZRC Generate a rectangular pulse with frequency of...
The exponential Fourier series of a certain periodic signal is given as f(t) (2+j2) exp(-j300t) +j2 exp(-j10t) +3 -j2 exp^10t)+ (2-j2) expG300t) a. Find the compact trigonometric Fourier series of f(t). b. Find the bandwidth of the signal c. Find the Fourier Transform of f(t) d. Design a simple low pass filter (RC circuit) that reduces the amplitude of the highest frequency part oft(t) by at least 50%. Write down its H(0) and plot its spectrum. e. Plot the spectrum...
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