Homework Answers
MATLAB Code:
close all
clear
clc
t = -1:0.001:10;
f = exp(-t).*cos(9*t).*heaviside(t);
plot(t,f), xlabel('t'), ylabel('f(t)')
disp('The signal is not time limited, even though it appears so
in the graph.')
disp('f(t) -> 0 only when t -> infinity.')
Plot:
Output:
The signal is not time limited, even though it appears so in the
graph.
f(t) -> 0 only when t -> infinity.
Add Answer to:
1. Consider the signal 12 t < 0; 0, f(t)=(e-t cos(9t), t20. (a) Plot a picture of this signal over the range -1t10. Use MATLAB, and include your code. (b) Is this signal time-limited? Explain....
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in thi...
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
Please include code Use Matlab (or octave) to plot a direction field for the differential equation 3. sin(t) y'...
Please include code
Use Matlab (or octave) to plot a direction field for the differential equation 3. sin(t) y'cos(t) y = e Use a plot that allows t to range from 0 to T (not including the end points) One way to offset values a little bit is to add a small number to the endpoint or subtract a small number, so consider setting a 0+1E- 8 and b = m-1E-8
Use Matlab (or octave) to plot a direction field...
Need MatLab code Exercise: Use MATLAB to generate the sinusoidal waveform: x(t) = 3 cos(1200) Consider...
Need MatLab code
Exercise: Use MATLAB to generate the sinusoidal waveform: x(t) = 3 cos(1200) Consider the frequency of this sinusoid and use this information to select an appropriate time-step and time array that will allow this signal to be correctly represented and displayed on a new MATLAB figure window (display 4 periods of this wave only). Now set up an appropriate frequency array and use the fft() and fftshift() functions to generate and plot the Fourier Transform (magnitude spectra)...
Please include your matlab code and plot, as well as the derivation of the expressions for...
Please include your matlab code and plot, as well as the
derivation of the expressions for voltages across both the resistor
and inductor themselves. Really need help understanding this!
5. Consider the RL Circuit shown below. Assume the excitation is a 10 kHz sine wave with amplitude of 1 volt. Derive expressions for the voltages across the resistor and the inductor as time functions. Plot the voltages across the resistor and the inductor over two periods using MATLAB and a...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t<...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t...
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t). Subsequently, COS y(t) is low-pass filtered with a system having frequency response H(w) = 4recG ) to produce q(t). Sketch F(w),Y(w), Q(u), and determine q(t) 2. If signal f(t) is not band-limited, would it be possible to reconstruct f(t) exactly from its samples f(nT) taken with some finite sampling interval T> 0? Explain your reasoning
1. Signal f(t) : (5 +...
Now use MATLAB to generate and plot 15seconds of this signal in the time-domain.Use the fft()...
Now use MATLAB to generate and plot 15seconds of this signal
in the time-domain.Use the fft() function to find the fourier
transform of this signal and plot its magnitude spectrum
School of Engineering Task 3 - The Fourier Transform: Scaling property Exercise: Let's take a look now at using the Fourier transform on aperiodic signals. Consider the real exponential signal from the discharging capacitor in tas 3 of laboratory 1 which was found to be: You(t)=e"u(t) Begin by calculating manually...
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...
Its related to MATLAB Generate a continuous-time signal z(t)-cos(2π 10t + 5) + cos(2π30t + 5). You may use the part of...
Its related to MATLAB
Generate a continuous-time signal z(t)-cos(2π 10t + 5) + cos(2π30t + 5). You may use the part of the followings. a >>t0:0.001:1; >plot (t, x_t) b. Generate a discrete-time signal x[n] = (1/4)(u[n]-u[n-4). You may use the part of the followings >>a_n-ones (1, 4) s> b_nzeros (1, 7) >> stem(n, x n)
Generate a continuous-time signal z(t)-cos(2π 10t + 5) + cos(2π30t + 5). You may use the part of the followings. a >>t0:0.001:1; >plot (t,...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot F(w). Express the x-axis in [Hz]. Plot for f = -8Hz to 8Hz. f(t) = cos(27 (34))e-**" 0.8 0.6 0.4 0.2 f(t) appears to oscillate at 3 cycles/sec 0 -0.2 -0.4 -0.6 0.8 -1 2 -1.5 -0.5 0 0.5 1 1.5 2
2. Consider the signal f(t) = 20 cos(5t) + cos(9t) sin(5t) - 7 (a) What is the highest angular frequency present in this signal? What is the highest numerical frequency present in this signal? (b) What is the Nyquist frequency? rate for this signal? Did you use the angular or the numerical (c) If you sample this signal with sampling period T, which values of T may you choose to be in accordance with the Nyquist rate? Choose and fix...
Please include code
Use Matlab (or octave) to plot a direction field for the differential equation 3. sin(t) y'cos(t) y = e Use a plot that allows t to range from 0 to T (not including the end points) One way to offset values a little bit is to add a small number to the endpoint or subtract a small number, so consider setting a 0+1E- 8 and b = m-1E-8
Use Matlab (or octave) to plot a direction field...
Need MatLab code
Exercise: Use MATLAB to generate the sinusoidal waveform: x(t) = 3 cos(1200) Consider the frequency of this sinusoid and use this information to select an appropriate time-step and time array that will allow this signal to be correctly represented and displayed on a new MATLAB figure window (display 4 periods of this wave only). Now set up an appropriate frequency array and use the fft() and fftshift() functions to generate and plot the Fourier Transform (magnitude spectra)...
Please include your matlab code and plot, as well as the
derivation of the expressions for voltages across both the resistor
and inductor themselves. Really need help understanding this!
5. Consider the RL Circuit shown below. Assume the excitation is a 10 kHz sine wave with amplitude of 1 volt. Derive expressions for the voltages across the resistor and the inductor as time functions. Plot the voltages across the resistor and the inductor over two periods using MATLAB and a...
4. Consider the periodic function 0, -1<t<- f(t) cos(#(t + 1)), } <t< 0 cos(at), 0<t< 0, }<t<i with f(t) = f(t+2). (a) Determine a general expression for the Fourier series of f. (b) Use MATLAB to plot both f and the sum of the first 5 non-zero terms of the Fourier series for f on the same set of axes for -1<t<3.
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t). Subsequently, COS y(t) is low-pass filtered with a system having frequency response H(w) = 4recG ) to produce q(t). Sketch F(w),Y(w), Q(u), and determine q(t) 2. If signal f(t) is not band-limited, would it be possible to reconstruct f(t) exactly from its samples f(nT) taken with some finite sampling interval T> 0? Explain your reasoning
1. Signal f(t) : (5 +...
Now use MATLAB to generate and plot 15seconds of this signal
in the time-domain.Use the fft() function to find the fourier
transform of this signal and plot its magnitude spectrum
School of Engineering Task 3 - The Fourier Transform: Scaling property Exercise: Let's take a look now at using the Fourier transform on aperiodic signals. Consider the real exponential signal from the discharging capacitor in tas 3 of laboratory 1 which was found to be: You(t)=e"u(t) Begin by calculating manually...
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...
Its related to MATLAB
Generate a continuous-time signal z(t)-cos(2π 10t + 5) + cos(2π30t + 5). You may use the part of the followings. a >>t0:0.001:1; >plot (t, x_t) b. Generate a discrete-time signal x[n] = (1/4)(u[n]-u[n-4). You may use the part of the followings >>a_n-ones (1, 4) s> b_nzeros (1, 7) >> stem(n, x n)
Generate a continuous-time signal z(t)-cos(2π 10t + 5) + cos(2π30t + 5). You may use the part of the followings. a >>t0:0.001:1; >plot (t,...
a) Use MATLAB to find the Fourier Transform F(w) of the following function f(t). b) Plot F(w). Express the x-axis in [Hz]. Plot for f = -8Hz to 8Hz. f(t) = cos(27 (34))e-**" 0.8 0.6 0.4 0.2 f(t) appears to oscillate at 3 cycles/sec 0 -0.2 -0.4 -0.6 0.8 -1 2 -1.5 -0.5 0 0.5 1 1.5 2
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