Re: Those frequencies are too high
The 15kHz came from FM broadcast radio… in particular, stereo FM which used ~DC-15kHz for the base-band mono, plonked a pilot tone at 19kHz then used DSB-SC at 38kHz (2×19kHz) for the differential channel.
Mono reception was achieved by using a low-pass filter with cut-off at 15kHz.
Stereo reception was achieved by taking the signal, passing one copy of it through a 15kHz LPF just like a mono set would. A band-pass filter grabbed 30kHz of spectrum around 38kHz and passed that as the input to a mixer. A band-pass filter snatched the 19kHz pilot, fed it to a frequency doubler which then was fed into the LO input on that mixer, giving us the differential signal.
It was then simple analogue arithmetic (L=Left, R=Right, n=noise):
(L+R+n) - (L-R+n) = 2L + 2n
(L+R+n) + (L-R+n) = 2R + 2n
n is usually fairly small. It'll be higher in the L-R component though because FM has a triangular noise profile.