Fred Marshall
Guest
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 Posted:
Thu Dec 29, 2005 9:16 am Post subject:
Re: Sinusoidal Chirp signal |
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"Lilian" <zarchi_7@yahoo.com> wrote in message
news:YeSdnTDHCvzDCS_eRVn-uw@giganews.com...
| Quote: | Hi,
For Linear FM, I have used
i(n)=Aexp(-jpi(cot(angle))*(n2/256))=Aexp(-j*theta).
But I am not sure for sinsoidal chirp signal.I think it cant be used
as i(n)= A cos(theta). Because instantaneous frequency, w(n)=d/dn(theta)
and I cant get sinusoidal for instantaneous frequency signal after
differentiated theta.
Any suggestion for the sinusoidal chirp signal equation?? thanks.
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Your notation leaves much to be desired. So, clarify please and perhaps
someone can help you.
You use, "angle", "theta", "i(n)", "n2" all without definition. So,
attempting to address your concern is risky. But, here goes:
Start with:
wi = instantaneous radian frequency which is a derivative of an angle as a
function of time:
fc(t)=cos(theta(t))
wi=d(theta)/dt
Angle modulation, in particular if:
theta(t) = wc*t + theta0 + K1*f(t)
where K1 is a system parameter or constant.
f(t) is the modulating signal.
This is a phase modulation system.
If we vary the instantaneous frequency linearly with the modulating signal:
wi = wc + K2*f(t)
then
theta(t) = wc*t + theta0 + K2*int[f(t)dt]
where "int" is the integral of:
This is a frequency modulation system.
Both systems are types of angle modulation systems and is often just called
frequency modulation.
So, it appears for a linear chirp you need f(t) to be a ramp, the integral
to be a scaled ramp squared which will add to theta.
Fred |
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