hirp is a signal of the form x(t) = A sin(2πϕ(t)) where A is the amplitude and the function ϕ(t) is the phase of the chirp. If the phase has the form ϕ(t) = f0 ((t1 − t0) / ln ( f1/ f0 )) * ((f1/ f0)^( t−t0/ t1−t0 ) − 1 ) + ϕ0, Then the signal is called a logarithmic chirp, exponential chirp, or exponentially swept sine. Here, f0 is the frequency at time t0, f1 is the frequency at time t1, and ϕ0 is the phase at time t0, where t1 > t0, f1 ̸= f0, and f1f0 > 0 The frequency of a chirp at time t is f(t) = dϕ/ dt . What would the frequency of a logarithmic chirp as a function of time t and show that the frequency strictly increases for t0 < t < t1 when f1 > f0 and strictly decreases for t0 < t < t1 when f1 < f0.? Thank you for the help.
A chirp is a signal of the form
x(t) = A sin(2πϕ(t))
where A is the amplitude and the function ϕ(t) is the phase of the chirp. If the phase has the form
ϕ(t) = f0 ((t1 − t0) / ln ( f1/ f0 )) * ((f1/ f0)^( t−t0/ t1−t0 ) − 1 ) + ϕ0,
Then the signal is called a logarithmic chirp, exponential chirp, or exponentially swept sine.
Here, f0 is the frequency at time t0, f1 is the frequency at time t1, and ϕ0 is the phase at time t0, where
t1 > t0, f1 ̸= f0, and f1f0 > 0
The frequency of a chirp at time t is f(t) = dϕ/ dt .
What would the frequency of a logarithmic chirp as a function of time t and show that the frequency strictly increases for t0 < t < t1 when f1 > f0 and strictly decreases for t0 < t < t1 when f1 < f0.?
Thank you for the help.
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