Sampling and reconstruction are two of the most essential and widely used operations in signal-processing systems. In this lesson you will be introduced to the roles of sampling and reconstruction in signal processing and the questions that will be addressed in subsequent lessons. All signals in the physical world, e.g., sound or light intensity, have […]

# Sampling and Reconstruction

## Aliasing and the Sampling Theorem Simplified

In this lesson you will learn why aliasing occurs when sampling a signal. Aliasing is when a continuous-time sinusoid appears as a discrete-time sinusoid with multiple frequencies. The sampling theorem establishes conditions that prevent aliasing so that a continuous-time signal can be uniquely reconstructed from its samples. The sampling theorem is very important in signal […]

## Fourier Transform Interpretation of Sampling

In the Fourier Transform Interpretation of Sampling lesson you will learn how the Fourier transform of the sampled signal depends on the Fourier transform of the original continuous-time signal. This relationship provides the basis for understanding the sampling theorem, how to reconstruct a continuous-time signal from samples, and how aliasing can distort the frequency content of […]

## Reconstruction and the Sampling Theorem

In this lesson you will learn when a continuous-time signal can be reconstructed from its samples and how to do the reconstruction. These insights are easy to obtain using the frequency domain representation for sampling that is derived in the preceding lesson. The condition for unique reconstruction is that the sampling theorem be satisfied. The […]

## Reconstruction and the Sampling Theorem Examples

This lesson presents several examples of sampling to illustrate aliasing and the conditions of the sampling theorem.

## Two-Dimensional Sampling Theorem

The principles that govern sampling of signals in time are easily extended to sampling of two- and higher-dimensional signals. In this lesson the conditions required to satisfy the sampling theorem in two dimensions. Sampling is with respect to space in this case. You will learn how the highest spatial frequency of interest determines the required spacing between […]