Discrete time sine wave generation near nyquist I'm trying to wrap my head around how to generate sine-waves out of a DAC near the Nyquist frequency (or determining how close I can get for reliable results). So if I want to generate a 499 Hz sine wave using a 1 kSPS DAC, I will calculate each sample:
$$y(t) = \sin(2 \pi 499 \ t) $$
Converting this to discrete time:
$$ y[k] = y\left( \tfrac{k}{1000} \right) = \sin \left(2 \pi 499 \frac{k}{1000} \right)$$
I end up with something like this:

The red line shows the 499 Hz signal, while the blue dots show the DAC sample. I get these large amplitude fluctuations. I know it's common to use a reconstruction filter to get rid of DAC images, which I always thought of as a low-pass filter from DC to Nyquist, which wouldn't really help get rid of the amplitude fluctuations...or would it?
Is there a better approach for generating sine waves? Or is there just simply a limit I cannot exceed (and what is the limit)?
There's nothing wrong about this – it's absolutely what you should be seeing.
The sine wave is intact, if you applied a reconstruction filter – there's no amplitude fluctuation of the wave, as soon as you limit its bandwidth to the nyquist bandwidth, the analog signal &quot;has&quot; to follow the full sines.