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It depends on what you consider processing. The Op Amp will consider the digital signal as analog one. If the Op Amp receives a 0...5V signal for example, it can amplify it, attenuate it, add another signal to it, subtract another signal, filter it, etc, whatever an Op Amp can do to a signal.
If, by processing, you mean Digital Signal Processing, as in data processing, no, it cannot do it.
I only consider use op amp to process digital clock signal.
I am wondering if the processed digital clocks still can drive digital chip, such as the output current of opamp can meet the input current requirements of digital chip?
I think that most op amps have slew rate limitations that
a digital input buffer may not like, or be able to chatter
against (slow dV/dt, time in linear window and ambient
/ self-switching noise).
You would have to criticize the candidate op amp in this
respect as well as its supply and drive attributes.
OPA4658 output is bipolar, while the input of 74HCT04 is unipolar. So, make sure you limit the op amp output voltage to the positive region.
Even so, you cannot just power the opamp between 0 and 5V, because the opa4658 output low level is about 2.3V from rail so the HCT04 will not be able to "see" a VOL level in its input. You will need to drop the op amp negative power supply input below ground by 2V to be able to drive the input of HCT04.
Another solution is to use a different op amp like a rail to rail one, that can drive its output close to the rails. Make sure it has a good slew rate as previously stated.
I can imagine many ways to interface an OP output to a digital circuit, first of all, it should serve a purpose.
But I don't hear it from your considerations yet. What's the use of it?
Some points, e.g. regarding relation of slew-rate, output current and latch-up sound simply wrong.
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