experts.
I have a question concern "linear sine sweep".
Here is the equation of linear sine sweep(from Wikipedia Chirp).
$$ x(t) = sin\biggl[ 2\pi( f_0 +\frac{f_1-f_0}{2T}t)t\biggr] $$
where,
$f_0$ is start frequency
$f_1$ is end frequency
$T$ is total length of excitation time.
In my case, I would like to calculate the excited frequency at certain time frame.
Let me calculate it through an example.
$f_0 = 20 \text{ Hz}$ , $f_1=200 \text{ Hz}$, $T = 60\text{ s}$.
In this case, above equation can be written as below,
$$ x(t) = sin\biggl[ 2\pi( 20 +1.5t)t\biggr]. $$
If we estimate the frequency at time 30 s, I think we could calculate as 65 Hz.
For checking this is right or not, I checked the power spectrum by selecting time through 29.5 s - 30.5 s for frequency resolution 1 Hz.
However, from the power spectrum, the frequency was 112 Hz.
There is difference between simulation value and calculated value almost twice.
Also, I just checked 1 second(29.5 s - 30.5 s) Fourier transform absolute value, it also displayed the peak frequency as 112 Hz.
What is the correct value?
If the calculated value, 65 Hz, is wrong, is there any comment for correcting this?
Thank you in advance.
If there is any comment or question, please let me know.