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It is confusing to me that you're clocking it at 12 kHz but getting harmonics of spectral nulls at N*5 kHz instead of N*12 kHz.AFAICT you should have spectral nulls at every integer harmonic of the sample clock rate:http://electronicdesign.com/digital-ics/well-controlled-audio-band-noise-source-uses-basic-microcontroller-filteringhttp://pdfserv.maximintegrated.com/en/an/AN3455.pdf