RustFFT | performance FFT library written in pure Rust

Your code is, in a sense, fine; what you are seeing are basic problems with interpreting the FFT, not with computing it.

First, the FFT is naturally a function from complex samples to complex samples. When you start with a real-valued input signal and convert it to complex by adding a zero imaginary component (or any other simple value, even copying the real input_buffer[i]), the output will always be a mirrored spectrum.

(Complex-valued signals can have arbitrarily asymmetric spectra, distinguishing positive frequencies from negative ones. This is not widely useful in audio, but it is fundamental to software-defined radio (SDR) applications of FFT and other DSP operations.)

In order to not get the mirroring, you must discard one half of the output. (It's slightly more efficient — though not 50%, if I recall correctly — to skip computing that half, but it doesn't look like rustfft offers that option.)

If you discard the upper half of the output (in terms of array indices), then you will find that the remaining “frequency bins” are arranged from 0 Hz up to 22.05 kHz. The library documentation notes this:

Output Order

Elements in the output are ordered by ascending frequency, with the first element corresponding to frequency 0.

Applications that do use the second half of the spectrum often swap the two halves, so that instead of a range of 0 Hz to [sampling frequency]/2, they go from −[sampling frequency]/2 to +[sampling frequency]/2. But since you're starting with a real, not complex, signal, this doesn't apply to you; I just mention it since you might have seen it in other plots that have 0 Hz at the center.

The drop-off which is visible in the center of your image corresponds to the high-pass anti-aliasing filter required in any digital signal processing. It should appear at the right edge once you've discarded the right half.

Finally, your code does not appear to have any windowing applied to the input signal. Windowing is a complex topic, but it is necessary to account for the fact that the FFT presumes a periodic signal which exactly repeats over the length of the input buffer, but we're actually feeding it a signal whose period is not an even division of the input buffer; windowing dampens the effects of this by attenuating the beginning and ending portions of the signal.

You should look up a standard window function and apply it to your input data before the FFT; this should reduce the secondary peak you're observing.