Using Excel, plot the function f(t)=3*cos(500*π*t) + 5*cos(800*π*t) from 00025 to .1s at .0025s intervals. Connect...
Using Excel, plot the function f(t)=3*cos(500*π*t) + 5*cos(800*π*t) from 00025 to .1s at .0025s intervals. Connect the points with straight lines. Explain the shape of the resulting plot. Find the FFT using Microsoft Excel.
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Using Excel, plot the function f(t)=3*cos(500*π*t) +
5*cos(800*π*t) from 00025 to .1s at .0025s intervals. Connect...
5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1...
5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1 500). Its spectrum X1c" consists of a pair of spectral lines at positive and negative frequencies. Use the MATLAB command fft to find and plot the signal's spectrum using various values of N.
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling...
Plot the signal s(t) = cos(2πt), and then illustrate the resulting samples with the following sampling intervals: [30 points] • Ts= 0.5 sec. • Ts= 0.75 sec • Ts =1 sec. (a) For each case, also sketch the reconstructed continuous time signal from the samples using linear interpolation (i.e. connecting samples by straight lines). (b) In which case the sampled signal has aliasing distortion? What is the minimal sampling frequency and the corresponding sampling interval needed to avoid aliasing? 3....
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...
In matlab please 3. (15 Points) Consider the following function. f(t) = 5e(-31) cos(20) a. Plot...
In matlab please
3. (15 Points) Consider the following function. f(t) = 5e(-31) cos(20) a. Plot the function for t = 0 to 1 b. Analytically calculate the derivative. C. Calculate the derivative using the diff function d. Calculate the derivative using the gradient function e. In a separate figure, plot the derivatives obtained above in a single new figure (not subplot) using (i) solid blue line for part b, (ii) red dots for part c, and (iii) green o's...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 point...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 points of this function: 10.5403 2 -0.4161 6 0.9602 (a) (2 points) Calculate the quadratic Lagrange interpolating polynomial as the sum of the Lo(x), L1(x), L2(x) polynomials we defined in class. The final answer should be in the form P)a2 bx c, but with a, b, c known. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand...
Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization size N 10,40 and 70. Plot the resulting approximations on the same graph as...
Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization size N 10,40 and 70. Plot the resulting approximations on the same graph as the exact derivative. Find the maximum of the error for each of the three N values.
Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization size N 10,40 and 70. Plot the resulting approximations on the same graph as the exact...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using the inner product 1. In finding coefficients you will need to compute the integral By symmetry, an 0 for odd n, so we need only consider even n. (a) Make a change of variables and use appropriate identities to transform the integral for a to cos (Bcos 8)cos (ne) de (b) The Bessel function of even order, (x), can be defined by the...
please explain and do in matlab Problem 3. Consider the function f(x) e cos(2r). (1) Sketch its graph over the interval [0, m) by the following commands: (2) Using h = 0.01 π/6 in [0, π]. The comm...
please explain and do in matlab
Problem 3. Consider the function f(x) e cos(2r). (1) Sketch its graph over the interval [0, m) by the following commands: (2) Using h = 0.01 π/6 in [0, π]. The commands are: to compute the difference quotient for z And the difference quotient is: ( 6 (3) Using h-0.01 to approximate the second derivative by computing the difdifquo for in [0, π). The commands are: And the difdifquo is:
Problem 3. Consider the...
The function x = (2.5 m) cos[(5π rad/s)t + π/5 rad] gives the simple harmonic motion...
The function x = (2.5 m) cos[(5π rad/s)t + π/5 rad] gives the simple harmonic motion of a body. Find the following values at t = 7.0 s. (a) the displacement m (b) the velocity (Include the sign of the value in your answer.) m/s (c) the acceleration (Include the sign of the value in your answer.) m/s2 (d) the phase of the motion rad (e) the frequency of the motion Hz (f) the period of the motion s
(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t)...
(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t) + c2 cos(t) to the data points (0, -1), (,7), (n, 5), co Co = C1 C2
(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t) + c2 cos(t) to the data points (0, -1), (,7), (n, 5), co Co = C1 C2
5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1 500). Its spectrum X1c" consists of a pair of spectral lines at positive and negative frequencies. Use the MATLAB command fft to find and plot the signal's spectrum using various values of N.
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...
In matlab please
3. (15 Points) Consider the following function. f(t) = 5e(-31) cos(20) a. Plot the function for t = 0 to 1 b. Analytically calculate the derivative. C. Calculate the derivative using the diff function d. Calculate the derivative using the gradient function e. In a separate figure, plot the derivatives obtained above in a single new figure (not subplot) using (i) solid blue line for part b, (ii) red dots for part c, and (iii) green o's...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 points of this function: 10.5403 2 -0.4161 6 0.9602 (a) (2 points) Calculate the quadratic Lagrange interpolating polynomial as the sum of the Lo(x), L1(x), L2(x) polynomials we defined in class. The final answer should be in the form P)a2 bx c, but with a, b, c known. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand...
Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization size N 10,40 and 70. Plot the resulting approximations on the same graph as the exact derivative. Find the maximum of the error for each of the three N values.
Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization size N 10,40 and 70. Plot the resulting approximations on the same graph as the exact...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using the inner product 1. In finding coefficients you will need to compute the integral By symmetry, an 0 for odd n, so we need only consider even n. (a) Make a change of variables and use appropriate identities to transform the integral for a to cos (Bcos 8)cos (ne) de (b) The Bessel function of even order, (x), can be defined by the...
please explain and do in matlab
Problem 3. Consider the function f(x) e cos(2r). (1) Sketch its graph over the interval [0, m) by the following commands: (2) Using h = 0.01 π/6 in [0, π]. The commands are: to compute the difference quotient for z And the difference quotient is: ( 6 (3) Using h-0.01 to approximate the second derivative by computing the difdifquo for in [0, π). The commands are: And the difdifquo is:
Problem 3. Consider the...
(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t) + c2 cos(t) to the data points (0, -1), (,7), (n, 5), co Co = C1 C2
(1 point) Fit a trigonometric function of the form f(t) ,5), using least squares c1 sin(t) + c2 cos(t) to the data points (0, -1), (,7), (n, 5), co Co = C1 C2
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