What's the best criterion for determining a frequency peak? I'm writing an algorithm that analyzes results of discrete Fourier transform (DFT). The algorithm should detect amplitude peaks in predefined ranges of frequencies. This is an example of such a peak:



Vertical red lines are range boundaries (left and right) and range center (middle).

What are the best criteria for determining the absence of this peak in a specified range?

For now I'm using standard deviation and comparing it to some calibration value. But it can be easily confused with some high amplitude noise like this:
First convolve the FFT sequence in the given range by a fairly wide gaussian window. In case there is only one peak, this will just widen it. In case there are many peaks (as in the second example), this will merge them into a uniform and less spiky mass.

Then you can use one of the following peakedness metrics:


Kurtosis.
Ratio of geometric to arithmetic mean