The Fourier Analysis Tool in Microsoft Excel （傅里叶分析工具在Microsoft Excel）.pdf

The Fourier Analysis Tool in Microsoft Excel Douglas A. Kerr Issue 1 March 4, 2009 ABSTRACT AND INTRODUCTION The spreadsheet application Microsoft Excel includes a tool that will calculate the discrete Fourier transform (DFT) or its inverse for a set of data. Users not familiar with digital signal processing may find it difficult to understand the scales used for the input and output data for this process. In this article we review the concept of the discrete Fourier transform, summarize how the Excel tool is used, and explain the meaning of the scales for the data. THE FOURIER TRANSFORM Imagine that we have a function of time that represents a segment of an audio waveform. If we calculate the Fourier Transform of this source function, we get a new function that describes the amplitude frequency spectrum of the waveform. This portrays how the power in the waveform is distributed over frequency.1 The waveform is said to be described in the time domain, while the spectrum is described in the frequency domain. We can have the same concept when the source function occurs “in space” rather than in time, such as a plot of the height variations in a surface as we travel along a line across it, or the variation in the density of a photographic print as we travel along a line across it. In this case, the source function is in the space domain, and the Fourier transform is in the spatial frequency domain. Then, if we have the amplitude spectrum of a waveform we can calculate its i