Efficient frequency determination
Is there any algorithm that tells you the most dominant frequency component, i.e. does argmax(fft(x)) or similar, that's more computationally efficient than argmax(fft(x))?


Mostly no.

The "trouble" is not the argmax, but fft. One alternative to this is to use autocorrelation and then determine whether that function is periodic and where does it crosses zero. The other alternative is to not evaluate the FFT in all 2048 possible points via the use of the Goertzel algorithm.

This covers why the answer is "mostly" no.

But here is a case where the answer might be yes.

Instead of trying to estimate the frequency via the typical "sinusoidal" concept, you can pass your signal through a sign function which will make it look like a square wave and then count its zero-crossings. (For complex $x$, you would have to do it twice). This is an inexpensive way of getting some estimate of "dominant" frequency.

Hope this helps.