- #1
ace1719
- 23
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I have an evil TA (who makes the assignments) who likes to give us torturously difficult assignments on stuff we haven't been taught (and in many cases don't even understand conceptually).
The input signal, x(t) is a real-valued bandlimited signal with bandwidth W. Find y(t).
I'm using mathematica notation here, so I'm not sure whether it will come out properly or not.
a. y(t)=x(t)p(t)
b. p(t)=[itex]\sum\delta'(t-kT)[/itex] where k goes from -∞ to ∞
and [itex]\delta'(t)=\frac{d}{dt}\delta(t)[/itex]
x(t) is not explicitly given in the question, but it's spectrum is, however the real issue here is finding p(t). I know the integral of the delta function is 1, so does that mean the derivative of the delta function is 0, therefore making the summation (essentially an integral) a constant in discrete time?
Homework Statement
The input signal, x(t) is a real-valued bandlimited signal with bandwidth W. Find y(t).
Homework Equations
I'm using mathematica notation here, so I'm not sure whether it will come out properly or not.
a. y(t)=x(t)p(t)
b. p(t)=[itex]\sum\delta'(t-kT)[/itex] where k goes from -∞ to ∞
and [itex]\delta'(t)=\frac{d}{dt}\delta(t)[/itex]
The Attempt at a Solution
x(t) is not explicitly given in the question, but it's spectrum is, however the real issue here is finding p(t). I know the integral of the delta function is 1, so does that mean the derivative of the delta function is 0, therefore making the summation (essentially an integral) a constant in discrete time?