Consider two expressions of a Fourier transform
syms t omega real
HU(omega) = -(exp(-omega*1i)*(exp(omega*1i) – 1)*(omega + 1i))/(omega*(omega^2 + 1))
Y(omega) = (exp(-omega*1i)*1i – 1i)/(omega*(1 + omega*1i))
The transforms are equivalent
simplify(HU(omega)-Y(omega))
so I would expect the inverse transforms to be equivalent.
Inverse transform of Y(omega)
y(t) = ifourier(Y(omega),omega,t)
Inverse transform of HU(omega)
hu(t) = ifourier(HU(omega),omega,t)
hu(t) looks complicated, but the primary concern is that Dirac delta in the first term in the numerator.
Simplify both expressions
s = @(z) simplify(rewrite(simplify(z),’heaviside’));
y(t) = s(y(t))
hu(t) = s(hu(t))
Sure enough, both time domain signals are the same with the exception that hu(t) includes that Dirac delta term.
Show that they are the same, except for the Dirac delta, by subtracting and using fplot that ignores Dirac delta terms:
figure
fplot(y(t)-hu(t),[-10,10]),ylim([-1e-16,1e-16])
Is this a bug, or is there a problem in the code, or am I misunderstanding what the results should be?Consider two expressions of a Fourier transform
syms t omega real
HU(omega) = -(exp(-omega*1i)*(exp(omega*1i) – 1)*(omega + 1i))/(omega*(omega^2 + 1))
Y(omega) = (exp(-omega*1i)*1i – 1i)/(omega*(1 + omega*1i))
The transforms are equivalent
simplify(HU(omega)-Y(omega))
so I would expect the inverse transforms to be equivalent.
Inverse transform of Y(omega)
y(t) = ifourier(Y(omega),omega,t)
Inverse transform of HU(omega)
hu(t) = ifourier(HU(omega),omega,t)
hu(t) looks complicated, but the primary concern is that Dirac delta in the first term in the numerator.
Simplify both expressions
s = @(z) simplify(rewrite(simplify(z),’heaviside’));
y(t) = s(y(t))
hu(t) = s(hu(t))
Sure enough, both time domain signals are the same with the exception that hu(t) includes that Dirac delta term.
Show that they are the same, except for the Dirac delta, by subtracting and using fplot that ignores Dirac delta terms:
figure
fplot(y(t)-hu(t),[-10,10]),ylim([-1e-16,1e-16])
Is this a bug, or is there a problem in the code, or am I misunderstanding what the results should be? Consider two expressions of a Fourier transform
syms t omega real
HU(omega) = -(exp(-omega*1i)*(exp(omega*1i) – 1)*(omega + 1i))/(omega*(omega^2 + 1))
Y(omega) = (exp(-omega*1i)*1i – 1i)/(omega*(1 + omega*1i))
The transforms are equivalent
simplify(HU(omega)-Y(omega))
so I would expect the inverse transforms to be equivalent.
Inverse transform of Y(omega)
y(t) = ifourier(Y(omega),omega,t)
Inverse transform of HU(omega)
hu(t) = ifourier(HU(omega),omega,t)
hu(t) looks complicated, but the primary concern is that Dirac delta in the first term in the numerator.
Simplify both expressions
s = @(z) simplify(rewrite(simplify(z),’heaviside’));
y(t) = s(y(t))
hu(t) = s(hu(t))
Sure enough, both time domain signals are the same with the exception that hu(t) includes that Dirac delta term.
Show that they are the same, except for the Dirac delta, by subtracting and using fplot that ignores Dirac delta terms:
figure
fplot(y(t)-hu(t),[-10,10]),ylim([-1e-16,1e-16])
Is this a bug, or is there a problem in the code, or am I misunderstanding what the results should be? ifourier, inconsistent results MATLAB Answers — New Questions

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