I'm new to DSP. As I reading the textbook, I cannot understand the formula $X_{s}(f)=\frac{1}{T}\sum_{n=-\infty}^{\infty} X(f-nf_{s})$. Could you please give me some keywords so I can learn the theorem and understand it?
From spectral analysis, the original spectrum (frequency components) $X(f)$ and the sampled signal spectrum $X_s(f)$ in terms of Hz are related as $X_{s}(f)=\frac{1}{T}\sum_{n=-\infty}^{\infty} X(f-nf_{s})$ where $X(f)$ is assumed to be the original baseband spectrum, while $X_s(f)$ is its sampled signal spectrum, consisting of the original baseband spectrum $X(f)$ and its replicas $X(f-nf_s)$. Since Equation (2.2) is a well-known formula, the derivation is omitted here and can be found in well-known texts (Ahmed and Natarajan, 1983; Alkin, 1993; Ambardar, 1999; Oppenheim and Schafer, 1975; Proakis and Manolakis, 1996).