Please forgive my bad drawing.
The two pic in the attachments illustrates one of my doubts. Two signals with different frequencies are sampled with the same sample rate with a sampling interval of Ts and a size of 8 FFT.
For the higher frequency case, about 2.5 cycles signal is passed to fft to process. Then recall from above, passing more cycles ("sampled data") to fft can have a better "Bandwidth of frequency bins" and more "number of bins".
My doubt is in the lower frequency case. As the pic shows, with the same Ts and "size of fft". The fft cannot process the entire cycle of the lower frequency signal. It has to either lower the "sampling rate" or increase "fft size" to fit the entire signal.
If this is true, then it means "sampling rate" and "fft size" is dynamic. I understand both "sampling rate" and "fft size" can be changed as wanted like the oscilloscope we use in lab. However, this circumstance only suitable if we know the frequency of the signal. How to dynamically change "sampling rate" and "fft size" without knowing the signal frequency??
