This article describes the use of limits in topics that are usually covered in a high school advanced placement chemistry course or a first-year college chemistry course. Such an approach supplements the interpretation of the graph of an equation since it is usually easier to evaluate the limit of a function than to generate its graph. In addition, the evaluation of the limit of an equation provides another viewpoint, which may solidify students' comprehension of concepts in the form of an equation.

In this paper, Fourier transform (FT) is studied under a special situation in which the transform length N is less than the number of input data M. First, the corresponding Fourier transform formula is deduced, and then an implementation example is given as well as performance simulation and implementation analysis. The results show that the mixed radix FT method has less resource consumption and less processing latency compared with fast Fourier transform (FFT) and discrete Fourier transform (DFT) method, respectively. The proposed N < M FT method increases the flexibility of traditional Fourier transform algorithm.