A continuous signal $x_a(t)$ is a linear combination of sinusoids of frequency 250 Hz, 450 Hz, 1 kHz, 2.75 kHz and 4.05 kHz. The signal $x_a(t)$ is sampled at $f_s=$1.5 kHz, and the resulting digital signal is converted into analog using a reconstruction filter with a low pass filter with cutoff frequency of 750 Hz. The resulting signals is $y_a(t)$.
The question is, which frequency components will appear in $y_a(t)$'s spectrum? I tried writing a Matlab program where I simulated $x_a(t)$ and then filtered it with a Butterworth low pass filter. I then looked at its frequency spectrum and a component of 500 Hz appeared. I showed this to my professor but he said it was wrong, and he didn't explain why.
So I'm asking you to tell me what is the real answer and why.
Thanks a lot :)