Error "It must be of type 'Type::MATLABOutput"

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James Manns
James Manns 2024-2-1
编辑： Walter Roberson 2024-2-2
I have a signal x(t)=exp(-100t), t>0. I'm trying to plot the ESD against frequency and then find and plot the 35dB bandwidt and the bandwidth that contains 99% of the energy.. The EDS plots fine but I get the following error for the 35dB plot:
"Error using / Invalid return value '[1/(2*abs(100 + w*1i)^2)]'. It must be of type'Type::MATLABOutput'.
Error in untitled3 (line 22) f_3dB = solve(ESD == max(ESD)/2, f);"
The code is below:
clc
clear all
syms t w;
x_t = exp(-100*t)*(heaviside(t));
X_w = fourier(x_t, w);
ESD = abs(X_w)^2;
% Plot ESD against linear frequency
f = linspace(-10, 10, 1000); % frequency range for plotting
ESD_plot = subs(ESD, w, 2*pi*f);
figure;
plot(f, ESD_plot);
title('Energy Spectral Density (ESD)');
xlabel('Frequency (Hz)');
ylabel('ESD');
grid on;
f_35dB = solve(ESD == max(ESD)/3162, f);
disp(['35 dB Bandwidth: ', num2str(2*f_35dB)]);
% Define frequency step size for numerical integration
df = 0.001;
freq_range = -10:df:10;
% Calculate energy in each frequency band
energy_in_band = double(subs(ESD, w, 2*pi*freq_range)) * df;
% Find the bandwidth containing 99% of the energy
cumulative_energy = cumsum(energy_in_band);
desired_energy = 0.99 * max(cumulative_energy);
bandwidth_99percent_energy = 2 * freq_range(find(cumulative_energy >= desired_energy, 1, 'first'));
disp(['Bandwidth containing 99% of the energy: ', num2str(bandwidth_99percent_energy)]);

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采纳的回答

Walter Roberson
Walter Roberson 2024-2-2
编辑：Walter Roberson 2024-2-2
f_35dB = solve(ESD == max(ESD)/3162, f);
max(ESD) returns a max() expression that is incompatible with the result of the calculation. It does not calculate the w for which ESD is the maximum and substitute that w to get the maximum ESD.
And you are asking to also solve f which is a vector of numeric frequencies.
  1 个评论
Walter Roberson
Walter Roberson 2024-2-2
编辑：Walter Roberson 2024-2-2
Ran in:
clc
clear all
syms t w;
x_t = exp(-100*t)*(heaviside(t));
X_w = fourier(x_t, w);
ESD = abs(X_w)^2;
% Plot ESD against linear frequency
f = linspace(-10, 10, 1000); % frequency range for plotting
ESD_plot = subs(ESD, w, 2*pi*f);
figure;
plot(f, ESD_plot);
title('Energy Spectral Density (ESD)');
xlabel('Frequency (Hz)');
ylabel('ESD');
grid on;
best_w = solve(diff(ESD, w),w)
best_w = 
0
max_ESD = subs(ESD, w, best_w)
max_ESD = 
f_35dB = double(solve(ESD == max_ESD/3162))
f_35dB = 0.0000e+00 - 5.5232e+03i
disp(['35 dB Bandwidth: ', num2str(2*f_35dB)]);
35 dB Bandwidth: 0-11046.3327i
% Define frequency step size for numerical integration
df = 0.001;
freq_range = -10:df:10;
% Calculate energy in each frequency band
energy_in_band = double(subs(ESD, w, 2*pi*freq_range)) * df;
% Find the bandwidth containing 99% of the energy
cumulative_energy = cumsum(energy_in_band);
desired_energy = 0.99 * max(cumulative_energy);
bandwidth_99percent_energy = 2 * freq_range(find(cumulative_energy >= desired_energy, 1, 'first'));
disp(['Bandwidth containing 99% of the energy: ', num2str(bandwidth_99percent_energy)]);
Bandwidth containing 99% of the energy: 19.506

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