ABSTRACT
Sampling is a frequent operation in radiological applications. Whenever a continuous signal is represented by a discrete signal, it must be sampled. Sampling transforms a continuous signal into a discrete signal. The sampling theorem states that a signal should be sampled at twice the highest frequency in the signal. Misinterpretation of a higher frequency due to sampling is called aliasing. Aliasing is a particularly common cause of artifacts in nuclear magnetic resonance imaging. A comb signal is a sequence of equally spaced delta functions. This chapter examines various components of the comb signal, along with their Fourier transforms. The interpolation is used to mean inserting additional points in between points in a discrete signal. This process can be broken down into two separate processes. The first process involves fitting two or more of the discrete points to a continuous model of the function, such as, a spline function. The second part involves resampling this model at the intervening points.
