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Unformatted text preview: Chapter 8 - The Discrete Fourier Transform / Polar Nuisances Chapter 8: The Discrete Fourier Transform Polar Nuisances There are many nuisances associated with using polar notation. None of these are overwhelming, just really annoying! Table 8-3 shows a computer program for converting between rectangular and polar notation, and provides solutions for some of these pests. Nuisance 1: Radians vs. Degrees It is possible to express the phase in either degrees or radians . When expressed in degrees, the values in the phase signal are between -180 and 180. Using radians, each of the values will be between -π and π, that is, -3.141592 to 3.141592. Most computer languages require the use radians for their trigonometric functions, such as cosine, sine, arctangent, etc. It can be irritating to work with these long decimal numbers, and difficult to interpret the data you receive. For example, if you want to introduce a 90 degree phase shift into a signal, you need to add 1.570796 to the phase. While it isn't going to kill you to type this into your program, it does become tiresome. The best way to handle this problem is to define the constant, P I = 3.141592, at the beginning of your program. A 90 degree phase shift can then be written as . Degrees and radians are both widely used in DSP and you need to become comfortable with both. 1 Nuisance 2: Divide by zero error When converting from rectangular to polar notation, it is very common to find frequencies where the real part is zero and the imaginary part is some nonzero value. This simply means that the phase is exactly 90 or -90 degrees. Try to tell your computer this! When your program tries to calculate the phase from: Phase X [ k ] = arctan( ImX [ k ]/ ReX [ k ]), a divide by zero error occurs. Even if the program execution doesn't halt, the phase you obtain for this frequency won't be correct. To avoid this doesn't halt, the phase you obtain for this frequency won't be correct....
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This note was uploaded on 10/29/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- Signal Processing