Fourier Transform Operations > DFT

#### Defining the DFT Range Using Limit Cursors

Before generating a DFT, the right limit cursor and left limit cursor should be adjusted to enclose an integer or whole number of cycles on the waveform to be transformed. This is best accomplished by picking a spot on the waveform where the slope is steep and a single points value is well defined, like near the midpoint of a waveform. Also keep in mind that the DFT is generated over the range including those points occupied by the limit cursors. So position the limit cursors accordingly, taking care not to enclose one-too-many points when defining your cycle. To adjust the limit cursors:

Position the mouse pointer in the bottom annotation line underneath the desired limit cursor. Drag with the left mouse button to adjust the position of the limit cursor. Note that when the mouse button is pressed, the limit cursor changes from a dotted line to a solid line in window 1. When the mouse button is released, the limit cursor remains a solid line until a different limit cursor is adjusted.

Choose View Left Limit or View Right Limit (ALT, V, L or ALT, V, R respectively). This changes the desired limit cursor from a dotted line to a solid line in window 1. Adjust the position of the limit cursor by using the ← or → cursor control keys.

Note that the cursors can be moved in either direction, but the right limit cursor cannot be moved to the left of the center cursor and the left limit cursor may not be moved to the right of the center cursor. Note also that the center cursor is ignored, except when it becomes necessary to adjust it to allow the desired placement of the left and right limit cursors.

In cases where compression is enabled, the number of points contained in the resulting DFT is a function of both the compression factor and the number of pixels laying between the right and left limit cursor (or in other words, window size). The relationship of compression to the number of points in the power spectrum is described by the following table. In this table, a random assumption was made about how many pixels were contained between the right and left limit cursors. To demonstrate the math, we randomly assumed 607 pixels were contained between the right and left limit cursors:

 Column A Column B Column C Column D Waveform Compression Factor Highest Power of 2 Number of Points Averaged Points Contained in DFT All odd factors -- Compression factor 607 2 2 1 1214 (607 × 2) 4 4 1 2428 (607 × 4) 6 2 3 1214 8 8 1 4856 (607 × 8) 10 2 5 1214 12 4 3 2428 14 2 7 1214 16* 16 2 4856 18 2 9 1214 20 4 5 2428 22 2 11 1214 24 8 3 4856 26 2 13 1214 28 4 7 2428 30 2 15 1214 32* 32 4 4856 34 2 17 1214 Etc. Etc. Etc. Etc.

*The maximum number of data values that may be transformed is 8191. Any combination of compression factor and pixels contained between the right and left limits that exceeds this value will be automatically transformed by removing as many factors of two as necessary from the highest power and multiplying the number of points averaged by the factor removed.

To illustrate an example from the table above, suppose we need a compression factor of 10 to compress the waveform enough so the area of interest can all be seen on the screen. So we enter 10 as our waveform compression factor and then perform the DFT. The value from column B is derived by evaluating the expression 2x, where the exponent x is the number that appears in the (EX) descriptor field of the analysis reporting area (a direct result of the compression factor). In our example, a 1 appears in the (EX) descriptor field of the analysis reporting area when a compression factor of 10 is used, so 21 = 2. The value in column B is then divided into the waveform compression factor to get the value in column C, which is the number of data points averaged. In our example, 10 ÷ 2 = 5. This means that for every 5 data points on the original waveform, one average value was used as the input to the DFT algorithm. The value in column D is the number of data points contained in the transform, which is derived by multiplying the number of pixels between the left and right limit cursors by the value from column B.

The limit cursor approach has the advantage of displaying all waveform information to be transformed on the screen at once. By adjusting the waveform compression factor, virtually any range of waveform information may be displayed on the screen, isolated by adjusting the limit cursors, then transformed. However, if a compression factor is enabled to bring the desired range on screen, this approach suffers from the disadvantage that each point on a waveform represents multiple acquired points. For example, each displayed point on the waveform represents a combination of 15 acquired points if a compression factor of 15 is enabled, making precise end-point placement difficult. For this reason, a second DFT placement approach is available. This approach defines end-points through use of the time marker and cursor.