Fourier Transform Operations

#### Discrete Fourier Transform (DFT)

When it is necessary to select a portion of the waveform more accurately than an FFT will allow, or when a non-windowed transform is desired, DFT generation may be used. All the functions available for FFT generation such as scaling, averaging, and smoothing are also available for DFT generation with the exception of windowing. When using DFT's, the need for a windowing function is replaced by the ability to adjust the end-points that define the time series range as discussed in Fourier Transform Operations. With the DFT, there are two ways to define the range of the time series to be transformed. One method allows you to adjust right and left limit cursors so the desired length of time series is enclosed within these limit cursors. This approach allows you to see on window 1 in the Y-T display area precisely what you are transforming. The other method allows you to use the time marker and cursor to specify the DFT range. The location of the time marker on a waveform represents one limit of the transform, while the location of the waveform cursor represents the other limit. This approach does not require that the full range of waveform information to be transformed be viewed on the screen at once. When a DFT is performed, the analysis reporting area is changed to reflect the lack of windowing as shown below:

The window designation is replaced by a C or E (which denotes the DFT approach that was applied) and by the factors of 2 in the compression factor applied to the waveform being transformed. For example, in the middle display shown above, the (C1) descriptor indicates a DFT generated by the time marker and cursor approach with 21 (or 2) as the highest power of 2 used in the DFT calculation. In some cases, an asterisk (C*) will appear in this field. This indicates that the power of 2 used in the DFT calculation is 100 or greater (the field can only accommodate a two digit number). For the same reason, when the power of 2 is greater than 9 but less than 100, the C will be dropped from the display field and only the compression factor will be displayed (i.e., 12). Whichever approach you take, the DFT provides a more accurate power spectrum plot than the FFT at the expense of added time for set-up and calculation. The resulting power spectrum may then be examined in the same manner as the FFT.