Inverting (spectrogram vertical flip) a signal of WAV file

Question

What I need is to invert a signal (on spectrogram it would look like a vertical flip) of a WAV file. Actually, of a bandpass of a signal - from 500 to 800 Hz, for example.

This image will perfectly explain what I mean:

I am using C#, NWaves and R language (seewave library). But I can consider any language, tool, library or software to achieve it. I just need to find any way to do it.

If it can be done using R, this is a bandpass I am using:

LF.croak <- ffilter(bull, f = [email protected], channel = 1, from = startFreq, to = endFreq, bandpass = TRUE, custom = NULL, wl = 4096, ovlp = 90, wn = "hanning", fftw = FALSE, rescale=FALSE, listen=FALSE, output="Wave")

If it can be done using Nwaves, this is the signal and where we start:

DiscreteSignal signal = waveContainer[Channels.Left];

Any help or hint will be appreciated!

Answer 1

If you have a real signal signal is $x_n$, then $x_n' = (-1)^n \, x_n$, by the convolution theorem $X'(f) = X(f_s/2-f)$, and you also have frequency aliasing, as a result. $X'(f)$ is the complex conjugate of $X(f)$ flipped, in the spectrogram you are looking at the magnitude of the spectrum, so you should have your spectrum flipped.