Convert between continuous and discrete-time signals. Nyquist-Shannon Sampling Theorem A bandlimited signal with maximum frequency $f_{max}$ can be perfectly reconstructed if: $$ f_s \geq 2f_{max} $$ Reconstruction Ideal (Sinc Interpolation) $$ x(t) = \sum_{n=-\infty}^{\infty} x[n] \cdot \text{sinc}\left(\frac{t - …

Fundamental concepts for understanding and processing signals. Signal Types Continuous-Time vs Discrete-Time Continuous-Time Signal: $x(t)$, defined for all $t \in \mathbb{R}$ Discrete-Time Signal: $x[n]$, defined only at integer values $n \in \mathbb{Z}$ Analog vs Digital Analog: Continuous in both time and amplitude …