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If you have a signal $$g(t)=\cos(2\pi \hat{f}(t)t)\tag{1}$$ then the function $\hat{f}(t)$ is not the instantaneous frequency of $g(t)$ (unless $\hat{f}(t)$ is constant). If you want an instantaneous frequency $f(t)$, then the equation $$\frac{\phi'(t)}{2\pi}=f(t)\tag{2}$$ must be satisfied, where $\phi(t)$ is the phase of the signal $g(t)$. So in order ...

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The Python implementation looks almost exactly like the definitions in Wikipedia. One will need to define functions in order to make it work, like this: # necessary imports: import numpy as np # start by defining a function that returns a sine wave with time-dependent frequency # f_func is a function f(t, f0, k) def chirp(t, f_func, f0, k): return np....

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You need to resample the signal to simulate the Doppler induced dilation. The resampling factor is I=Td/Ts where Td = Duration of the signal after dilation Ts = Actual duration of the transmitted signal In Matlab you can use the function resample(), but you need to find the resampling parameters P and Q from I. Also, I=1+v/c for signal expansion and I=1-v/...

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