Title :
The effects of windowing and quantization error on the amplitude of frequency-domain functions
Author :
Solomon, Otis M., Jr.
Author_Institution :
Sandia Nat. Lab., Albuquerque, NM, USA
fDate :
12/1/1992 12:00:00 AM
Abstract :
The author describes how windows modify the magnitude of a discrete Fourier transform and the level of a power spectral density computed by Welch´s method. For white noise, the magnitude of the discrete Fourier transform at a fixed frequency has a Rayleigh probability distribution. For sine waves with an integer number of cycles and quantization noise, the theoretical values of the amplitude of the discrete Fourier transform and power spectral density are calculated. The authors show the signal-to-noise ratio in a single discrete Fourier transform or power spectral density frequency bin is related to the normal time-domain definition of the signal-to-noise ratio. The answer depends on the discrete Fourier transform length, the window type, and the function averaged
Keywords :
analogue-digital conversion; data analysis; digital simulation; fast Fourier transforms; probability; spectral analysis; white noise; Rayleigh probability distribution; Welch´s method; digital simulation; discrete Fourier transform; frequency-domain functions; integer number of cycles; power spectral density; quantization error; quantization noise; signal-to-noise ratio; sine waves; white noise; windowing; Analog-digital conversion; Data analysis; Discrete Fourier transforms; Frequency domain analysis; Frequency estimation; Quantization; Signal processing algorithms; Signal to noise ratio; Total harmonic distortion; White noise;
Journal_Title :
Instrumentation and Measurement, IEEE Transactions on