The use of DFT windows in signaltonoise ratio and harmonic distortion computations
Abstract
The discrete Fourier transform (DFT) is frequently used in the computation of the signaltonoise ratio (SNR) and harmonic distortion. To estimate the SNR or harmonic distortion, a sine wave is applied to the digitizing system under test. When the data record contains an integer number of cycles of the sine wave, energy from the sine wave and its harmonics does not leak into adjacent DFT frequency bins. Each harmonic occupies one and only one DFT frequency bin. To find the rootmeansquare (RMS) value of a harmonic from its DFT, one computes the magnitude of the DFT value at the single frequency of the harmonic. When the DFT's of the fundamental and its harmonics are single lines, the SNR and harmonic distortion are easy to compute. When the data record contains a noninteger number of cycles of the sine wave, energy leaks from the sine wave and its harmonics to adjacent frequencies. The literature contains several approaches to the problem of determining which DFT components correspond to a sine wave harmonic. This paper describes how to estimate the RMS value of a sine wave from its DFT with special attention to the selection of the DFT window. The set of DFT frequencies which comprise a harmonic depends on the DFT window, the length of the DFT, and the number of bits of the digitizer. Criteria are developed for choosing the DFT frequencies that correspond to a sine wave. These criteria lead to better choices of DFT windows for SNR and harmonic distortion calculations.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1993
 Bibcode:
 1993STIN...9330655S
 Keywords:

 Analog To Digital Converters;
 Fourier Transformation;
 Harmonics;
 Signal Processing;
 Signal To Noise Ratios;
 Sine Waves;
 Waveforms;
 Computerized Simulation;
 Cycles;
 Frequencies;
 Mean Square Values;
 RootMeanSquare Errors;
 Instrumentation and Photography