# Homework Help: Nyquist Sampling Thm - Question

1. Oct 1, 2006

### cepheid

Staff Emeritus
Here's my question:

Suppose a signal x(t) has a Nyquist sampling frequency $\omega_s$. Compute the Nyquist sampling frequency for the following signal in terms of $\omega_s$:

x(t) + x(t-1)

Well my first thought was, let's see how the spectrum of this new signal compares to that of the original signal. Computing the Fourier transform, an operation I've denoted by script F, I arrived at the result that:

$$\mathcal{F}\{x(t) + x(t-1)\} = (1 + e^{-j\omega})X(j\omega)$$

where X(jw) is the FT of x(t). I'm really not sure how to use this result to proceed.