- #1
jendrix
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Homework Statement
Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V.
Show that if f(t) and g(t) are members of V then so is f(t) + g(t)
Homework Equations
The Attempt at a Solution
f(t) = e(i*w0*t))
g(t) =e(i*w0*t +φ))
Where W0 = 2*πUsing 'Euler's' I can write these as;
f(t) =cos(w0*t) + i*sin(w0*t)
g(t) =cos(w0*t +φ) + i*sin(w0*t +φ)So for part a) I would plot these functions separating the real and imaginary parts and choosing a value for φ to illustrate the phase shift?Partb) f(t) + g(t) = e(i*w0*t)) + e(i*w0*t +φ))
= (1 + eφ) * ei*w0*t
The signal remains a periodic complex function of t with a period of 1 and is therefore a member of V.Thanks
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