logistic_guy
Full Member
- Joined
- Apr 17, 2024
- Messages
- 424
here is the question
If \(\displaystyle x[n] = \cos(\frac{\pi}{4}n + \phi_0)\) with \(\displaystyle 0 \leq \phi_0 < 2\pi\) and \(\displaystyle g[n] = x[n]\sum_{k=-\infty}^{\infty}\delta[n - 4k]\),
what additional constraints must be imposed on \(\displaystyle \phi_0\) to ensure that \(\displaystyle g[n]*\frac{\sin\frac{\pi}{4}n}{\frac{\pi}{4}n} = x[n]\)?
my attemb
the question look complicated and i don't understand convolution
but i understand the idea of convolution, they want to recover the signal \(\displaystyle x[n]\) from \(\displaystyle g[n]\)
if \(\displaystyle \frac{\sin\frac{\pi}{4}n}{\frac{\pi}{4}n} = \) sinc\(\displaystyle \frac{\pi}{4}n\), can i replace it to simplify the convolution further or it effect the solution?
If \(\displaystyle x[n] = \cos(\frac{\pi}{4}n + \phi_0)\) with \(\displaystyle 0 \leq \phi_0 < 2\pi\) and \(\displaystyle g[n] = x[n]\sum_{k=-\infty}^{\infty}\delta[n - 4k]\),
what additional constraints must be imposed on \(\displaystyle \phi_0\) to ensure that \(\displaystyle g[n]*\frac{\sin\frac{\pi}{4}n}{\frac{\pi}{4}n} = x[n]\)?
my attemb
the question look complicated and i don't understand convolution
but i understand the idea of convolution, they want to recover the signal \(\displaystyle x[n]\) from \(\displaystyle g[n]\)
if \(\displaystyle \frac{\sin\frac{\pi}{4}n}{\frac{\pi}{4}n} = \) sinc\(\displaystyle \frac{\pi}{4}n\), can i replace it to simplify the convolution further or it effect the solution?