Unwanted frequency shift in DA-converted signal

Phase must be continuous and can be done as follows (DDS structure):

LUT to contain one full cycle:

data=round(32767*sin(2*pi*(0:255)/256)); --for 256 points, 16 bits signed

or data = round(32767*exp(j*2*pi*(0:255)/256))); --for sin/cos

then you address the LUT with 8 MSB of large n bit accumulator then the increment value decides the frequency:

incr = 2^n *f/125,000,000

As such you keep phase continuity even when you change frequencies.