![8) [10 POINTS] Plot the implicitly defined function x2 – y4 = 0 over the domain (-21, 211]. (HINT: Using the ezplot command i](http://img.homeworklib.com/questions/3fcbd760-671f-11eb-a7eb-43d98d6a2abc.png?x-oss-process=image/resize,w_560)
Homework Answers
8)
The code to plot the given function is:
syms x y
ezplot(x^2 == y^4, [-2*pi,2*pi])
Plot is
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8) [10 POINTS] Plot the implicitly defined function x2 – y4 = 0 over the domain...
Matlab Question#1: Determine the discrete-time Fourier transform of x(n) (0.8y'n u(n)+(0.1)'n u(n) Evaluate Xei) at 501 equispaced. points between [0,pi] and plot its magnitude, angle, re...
Matlab Question#1: Determine the discrete-time Fourier transform of x(n) (0.8y'n u(n)+(0.1)'n u(n) Evaluate Xei) at 501 equispaced. points between [0,pi] and plot its magnitude, angle, real, and imaginary parts Matlab Question#2: Determine the discrete-time Fourier transform of Evaluate Xei) at 1001 equispaced points between [0pi] and plot its magnitude, angle, real, and imaginary parts. Matlab Question#3: Compute the FT values at the prescribed frequency points and plot the real and imaginary parts and the magnitude and phase spectrums. The FT...
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300...
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to d...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to determine the frequency response of a signal or system by taking the Fourier Transform empirically (rather than computing it analytically). To do so we make use of the fft and fftshift commands. The fft command is an efficient implementation of the Discrete Fourier Transform (DFT) known as the Fast Fourier Transform (FFT). When the FFT is computed the samples are...
8. [10 points) a. Consider the function f (x1, x2) = x1 - xż. Investigate convexity...
8. [10 points) a. Consider the function f (x1, x2) = x1 - xż. Investigate convexity of this function in R2. What can you say about minimum and maximum values of the function and its behavior at the origin. b. Consider the function f(x1, x2) = x1+xz over the domain C = = {x € R2 : || xt||1 < 1}. Find the maximum of the function f over C.
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 ues...
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 uestion # 1 Use table to find Fourier transform. Sketch the magnitude response and phase response (i) x(t) Cos(1000t) (ii) x(t) 13Cos(100t)- 7Sin(500t) (iv) x(t) rect To (v) xo)-rect ()Cos(10001) (v) x(o) -ret)Cos(000t) Question # 2 Let h(t) be a linear time invariant system, with the following transfer function s + 1 000m (a) Find H(w) (b) Sketch the magnitude and phase response of H(w)...
alpha = 5.0 beta = 7.1 zeta = 6.9 PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the pole...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
1) a) Write MATLAB function that accepts a positive integer parameter n and returns a vector...
1)
a) Write MATLAB function that accepts a positive integer
parameter n and returns a vector containing the values of the
integral (A) for n= 1,2,3,..., n. The function must use the
relation (B) and the value of y(1). Your function must preallocate
the array that it returns. Use for loop when writing your code.
b) Write MATLAB script that uses your function to calculate the
values of the integral (A) using the recurrence relation (B), y(n)
for n=1,2,... 19...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
t0 = 0; tf = 20; y0 = [10;60]; a = .8; b = .01; c...
t0 = 0; tf = 20; y0 = [10;60];
a = .8; b = .01; c = .6; d = .1;
[t,y] = ode45(@f,[t0,tf],y0,[],a,b,c,d);
u1 = y(:,1); u2 = y(:,2); % y in output has 2 columns
corresponding to u1 and u2
figure(1);
subplot(2,1,1); plot(t,u1,'b-+'); ylabel('u1'); subplot(2,1,2);
plot(t,u2,'ro-'); ylabel('u2');
figure(2) plot(u1,u2); axis square; xlabel('u_1');
ylabel('u_2'); % plot the phase plot
%----------------------------------------------------------------------
function dydt = f(t,y,a,b,c,d)
u1 = y(1); u2 = y(2);
dydt = [ a*u1-b*u1*u2 ; -c*u2+d*u1*u2 ];
end
Only...
7 points Question 3. An Unusual Integrable Function (Show Working) Consider the function f : 10, ...
7 points Question 3. An Unusual Integrable Function (Show Working) Consider the function f : 10, 11 → R defined by 1 if r-for some nEN; f(x) = 0 for all other x E [0,1 (1 subpts) (a) Draw a rough diagram of the graph of f. When we study the formal definition of the continuity of a function later in the course, we will be able to prove that this function is discontinuous at those domain values r such...
Matlab Question#1: Determine the discrete-time Fourier transform of x(n) (0.8y'n u(n)+(0.1)'n u(n) Evaluate Xei) at 501 equispaced. points between [0,pi] and plot its magnitude, angle, real, and imaginary parts Matlab Question#2: Determine the discrete-time Fourier transform of Evaluate Xei) at 1001 equispaced points between [0pi] and plot its magnitude, angle, real, and imaginary parts. Matlab Question#3: Compute the FT values at the prescribed frequency points and plot the real and imaginary parts and the magnitude and phase spectrums. The FT...
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from...
Exercise 4. Computing and displaying the Fourier Transform of a signal Later in the semester it will become useful to determine the frequency response of a signal or system by taking the Fourier Transform empirically (rather than computing it analytically). To do so we make use of the fft and fftshift commands. The fft command is an efficient implementation of the Discrete Fourier Transform (DFT) known as the Fast Fourier Transform (FFT). When the FFT is computed the samples are...
8. [10 points) a. Consider the function f (x1, x2) = x1 - xż. Investigate convexity of this function in R2. What can you say about minimum and maximum values of the function and its behavior at the origin. b. Consider the function f(x1, x2) = x1+xz over the domain C = = {x € R2 : || xt||1 < 1}. Find the maximum of the function f over C.
Home-Work 5 All questions carry equal points. Don't forget to highlight your final answers 25 uestion # 1 Use table to find Fourier transform. Sketch the magnitude response and phase response (i) x(t) Cos(1000t) (ii) x(t) 13Cos(100t)- 7Sin(500t) (iv) x(t) rect To (v) xo)-rect ()Cos(10001) (v) x(o) -ret)Cos(000t) Question # 2 Let h(t) be a linear time invariant system, with the following transfer function s + 1 000m (a) Find H(w) (b) Sketch the magnitude and phase response of H(w)...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
1)
a) Write MATLAB function that accepts a positive integer
parameter n and returns a vector containing the values of the
integral (A) for n= 1,2,3,..., n. The function must use the
relation (B) and the value of y(1). Your function must preallocate
the array that it returns. Use for loop when writing your code.
b) Write MATLAB script that uses your function to calculate the
values of the integral (A) using the recurrence relation (B), y(n)
for n=1,2,... 19...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
t0 = 0; tf = 20; y0 = [10;60];
a = .8; b = .01; c = .6; d = .1;
[t,y] = ode45(@f,[t0,tf],y0,[],a,b,c,d);
u1 = y(:,1); u2 = y(:,2); % y in output has 2 columns
corresponding to u1 and u2
figure(1);
subplot(2,1,1); plot(t,u1,'b-+'); ylabel('u1'); subplot(2,1,2);
plot(t,u2,'ro-'); ylabel('u2');
figure(2) plot(u1,u2); axis square; xlabel('u_1');
ylabel('u_2'); % plot the phase plot
%----------------------------------------------------------------------
function dydt = f(t,y,a,b,c,d)
u1 = y(1); u2 = y(2);
dydt = [ a*u1-b*u1*u2 ; -c*u2+d*u1*u2 ];
end
Only...
7 points Question 3. An Unusual Integrable Function (Show Working) Consider the function f : 10, 11 → R defined by 1 if r-for some nEN; f(x) = 0 for all other x E [0,1 (1 subpts) (a) Draw a rough diagram of the graph of f. When we study the formal definition of the continuity of a function later in the course, we will be able to prove that this function is discontinuous at those domain values r such...
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