Problem 4: Suppose ?(?) = ? cos(?0?) is applied to a nonlinear system with ?(?) =...
Problem 4: Suppose ?(?) = ? cos(?0?) is applied to a nonlinear system with ?(?) = 2?(?) − 3? 3 (?). Write ?(?) as a sum of cosines. Then evaluate the second-harmonic and third harmonic distortion when ? = 1 and ? = 2.
Problem 5: Repeat Problem 6 with ?(?) = 5?(?) − 2? 2 (?) + 4? 3 (?).
Problems 6: Find and sketch the impulse response of an ideal band-rejection filter having ?(?) = 0 for ?? − ? 2 < |?| < ?? + ? 2 and distortionless transmission for all other frequencies
Homework Answers
In above solution all three
questions are solved with detailed explanation.Add Answer to:
Problem 4: Suppose ?(?) = ? cos(?0?) is applied to a nonlinear
system with ?(?) =...
3. In this problem you will identify the system/transfer function H(e) of a Butterworth digital f...
3. In this problem you will identify the system/transfer function H(e) of a Butterworth digital filter using the impulse invariance approach. Design a Butterworth low pass filter that meets the follow- ing specifications. Passband gain is atleast -2 dB and stopband attenuation is atleast -20 dB, i.e. 0.79433 lH(ejw)I l in the frequency range 0 0.2π and lH(eM)I 0.1 in the frequency range 0.4π-lal T. (a) Sketch the specifications and identify the pass band tolerance, stop band tolerance, transition, passband...
. Problem 1: The signal r(t) = 2 cos(27300t) + cos(27 400t) is sampled with sampling...
. Problem 1: The signal r(t) = 2 cos(27300t) + cos(27 400t) is sampled with sampling frequencies a) 2. = 20007 and b) 2. = 15007. 1) Sketch the amplitude spectra of the sampled signal r(t) in both cases. 2) Sketch the output of the ideal low pass filter with a cut-off frequency 1000m in both cases.
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission...
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(t)+n(t), where nit) is the AWGN with power-spectral density No/2. 1. In a block diagram, give the precise specifications of the optimal receiver. What are the characteristics of the matched filter and the sampler and decision device? 2. Find the error probability of the optimal...
Answer all parts and show all detail please. Problem 4: For the following system uses an...
Answer all parts and show all detail please.
Problem 4: For the following system uses an Ideal Band Pass Filter with a Gain of 1 () X 2(t) h(t) X Cos (2π 3t) 3 (t) BPF fe 30 Hz BW 12 Hz cos (2π 18 t) cos (2π 12 t) A. Write the equation for D1f) and draw an accurate sketch. 10 Points B. Write the equation for D2(f) and draw an accurate sketch 10 Points B. Write the equation...
Please solve problem 4.5-2 ( a,b, and c) and be clear when you write by your hand.
Please solve problem 4.5-2 ( a,b, and c) and be clear when you
write by your hand.
Problems Figure P.4.5-2 HI(f) ed 0.5 f, MHz 1.496 1.499 1.5 1.501 Figure P.4.5-3 Bandpass filter l us shoWn in Hz. Fig. P4.5-1. The carrier frequency is fe 10 kHz and the baseband signal bandwidth is 4k Find the corresponding transfer function of the equalizer filter Ho) shown in the receiver Fig. 4.21. Hint: Use Eq. (4.25). Figure P.4.5-1 H,(o) 0 9 10...
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0) Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
filtering of periodic signals: damental frequency 120 = 1/4 is the Answers: Gk = 0.J, Consider...
filtering of periodic signals: damental frequency 120 = 1/4 is the Answers: Gk = 0.J, Consider the following problems related to filtering of (a) A periodic signal x(t) of fundamental frequen input of an ideal band-pass filter with the following response the following frequency 11312 3 3/2 1 -37% -21 322 5 3/2 ZH(N2) = 2 -3/2 223 - 0 otherwise ero Fourier series coefficients of x(t) are (92)/ = o otherwise The non-zero Fourie X = X-1 = ),...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal ; c. Determine the frequency/frequencies of aliasing noise . Q2)...
TE Question 5 (20 marks) An active filter circuit is shown in Fig. 4. The cut-off frequency of this active filter is...
TE Question 5 (20 marks) An active filter circuit is shown in Fig. 4. The cut-off frequency of this active filter is 1590Hz. The Input impedance and voltage gain of this filter are 10k0 and -5VN respectively Vout R1 vin R2 C1 Fig. 4 By assuming the operational amplifier, A is ideal, answer the following questions: (a) () State the type of this active fiter. (i) Explain the characteristic of this active filter. [2 marks] 3 marks] (b) 0) Calculate...
number 2 ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z()...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
3. In this problem you will identify the system/transfer function H(e) of a Butterworth digital filter using the impulse invariance approach. Design a Butterworth low pass filter that meets the follow- ing specifications. Passband gain is atleast -2 dB and stopband attenuation is atleast -20 dB, i.e. 0.79433 lH(ejw)I l in the frequency range 0 0.2π and lH(eM)I 0.1 in the frequency range 0.4π-lal T. (a) Sketch the specifications and identify the pass band tolerance, stop band tolerance, transition, passband...
. Problem 1: The signal r(t) = 2 cos(27300t) + cos(27 400t) is sampled with sampling frequencies a) 2. = 20007 and b) 2. = 15007. 1) Sketch the amplitude spectra of the sampled signal r(t) in both cases. 2) Sketch the output of the ideal low pass filter with a cut-off frequency 1000m in both cases.
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(t)+n(t), where nit) is the AWGN with power-spectral density No/2. 1. In a block diagram, give the precise specifications of the optimal receiver. What are the characteristics of the matched filter and the sampler and decision device? 2. Find the error probability of the optimal...
Answer all parts and show all detail please.
Problem 4: For the following system uses an Ideal Band Pass Filter with a Gain of 1 () X 2(t) h(t) X Cos (2π 3t) 3 (t) BPF fe 30 Hz BW 12 Hz cos (2π 18 t) cos (2π 12 t) A. Write the equation for D1f) and draw an accurate sketch. 10 Points B. Write the equation for D2(f) and draw an accurate sketch 10 Points B. Write the equation...
Please solve problem 4.5-2 ( a,b, and c) and be clear when you
write by your hand.
Problems Figure P.4.5-2 HI(f) ed 0.5 f, MHz 1.496 1.499 1.5 1.501 Figure P.4.5-3 Bandpass filter l us shoWn in Hz. Fig. P4.5-1. The carrier frequency is fe 10 kHz and the baseband signal bandwidth is 4k Find the corresponding transfer function of the equalizer filter Ho) shown in the receiver Fig. 4.21. Hint: Use Eq. (4.25). Figure P.4.5-1 H,(o) 0 9 10...
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
filtering of periodic signals: damental frequency 120 = 1/4 is the Answers: Gk = 0.J, Consider the following problems related to filtering of (a) A periodic signal x(t) of fundamental frequen input of an ideal band-pass filter with the following response the following frequency 11312 3 3/2 1 -37% -21 322 5 3/2 ZH(N2) = 2 -3/2 223 - 0 otherwise ero Fourier series coefficients of x(t) are (92)/ = o otherwise The non-zero Fourie X = X-1 = ),...
TE Question 5 (20 marks) An active filter circuit is shown in Fig. 4. The cut-off frequency of this active filter is 1590Hz. The Input impedance and voltage gain of this filter are 10k0 and -5VN respectively Vout R1 vin R2 C1 Fig. 4 By assuming the operational amplifier, A is ideal, answer the following questions: (a) () State the type of this active fiter. (i) Explain the characteristic of this active filter. [2 marks] 3 marks] (b) 0) Calculate...
number 2
ECE 300 Continuous-Time Signals and Systems H(jø π/2 Plot the spectrum Z (jø) of the filtered input signal z(), the spectrum Z, (jo) of the sampled signal z.(t), and the spectrum Y(ja) of the reconstructed signal y(t). Show clearly how the output spectrum Y (ja) differs from the original spectrum G(jo) C. Which system, A or B, produces less distortion between the input g(t) and the output y(4) or ()? Explain. You can measure distortion by finding the...
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