I am testing the frequency response as a filter as below, what should be the sample rate of the chirp signals, someone told me it should be at least 2 times of the input signals frequency, someone said it should be at least 10 times? Why?
2 times is the minimal sampling rate to ensure the signal can be possibly measured. This is called the Nyquist frequency. It shows that if your sampling rate is twice the frequency of the signal, you measure at least 2 different values per period. If you would only measure 1 value, a lower frequent signal or even a constant value could fit your measurement.
10, or even 20 times is what you should use if you desire to filter the signal (or for that fact, control it). This allows to fit your response so smooth, continuous-time filters can be properly applied without to many sampling issues.