Understanding Fft Windows
APPLICATION NOTE AN014
Understanding FFT Windows
The Fast Fourier Transform (FFT) is the Fourier Transform of a block of time data points. It represents the frequency composition of the time signal. Figure 2 shows a 10 Hz sine waveform (top) and the FFT of the sine waveform (bottom). A sine wave is composed of one pure tone indicated by the single discrete peak in the FFT with height of 1.0 at 10 Hz.
Introduction
FFT based measurements are subject to errors from an effect known as leakage. This effect occurs when the FFT is computed from of a block of data which is not periodic. To correct this problem appropriate windowing functions must be applied. The user must choose the appropriate window function for the specific application. When windowing is not applied correctly, then errors may be introduced in the FFT amplitude, frequency or overall shape of the spectrum. This application note describes the phenomenon of leakage, the various windowing functions and their strengths and weaknesses, and examples are given for various applications.
FFT Background
Most dynamic signal analyzers (Figure 1) compute time and frequency measurements. Time measurements include capturing time traces of measured sig-
Figure 1. Dactron FocusTM (left) and the Dactron PhotonTM (right) Dynamic Signal Analyzers Figure 2. Time waveform of sine function (top) and FFT (bottom).
nals, including filtering and statistical measures. Frequency measurements that are computed by most DSAs include Fast Fourier Transform, Power Spectral Density, Frequency Response Functions, Coherence and many more. These signals are computed in the DSP from the digitized time data. Time data is digitized and sampled into the DSP block by block. A block is a fixed number of data points in the digital time record. Most frequency functions are computed from one block of data at a time. A block of data is also called a time record or time window.
Leakage
The FFT computation assumes that a signal is
Understanding FFT Windows
The Fast Fourier Transform (FFT) is the Fourier Transform of a block of time data points. It represents the frequency composition of the time signal. Figure 2 shows a 10 Hz sine waveform (top) and the FFT of the sine waveform (bottom). A sine wave is composed of one pure tone indicated by the single discrete peak in the FFT with height of 1.0 at 10 Hz.
Introduction
FFT based measurements are subject to errors from an effect known as leakage. This effect occurs when the FFT is computed from of a block of data which is not periodic. To correct this problem appropriate windowing functions must be applied. The user must choose the appropriate window function for the specific application. When windowing is not applied correctly, then errors may be introduced in the FFT amplitude, frequency or overall shape of the spectrum. This application note describes the phenomenon of leakage, the various windowing functions and their strengths and weaknesses, and examples are given for various applications.
FFT Background
Most dynamic signal analyzers (Figure 1) compute time and frequency measurements. Time measurements include capturing time traces of measured sig-
Figure 1. Dactron FocusTM (left) and the Dactron PhotonTM (right) Dynamic Signal Analyzers Figure 2. Time waveform of sine function (top) and FFT (bottom).
nals, including filtering and statistical measures. Frequency measurements that are computed by most DSAs include Fast Fourier Transform, Power Spectral Density, Frequency Response Functions, Coherence and many more. These signals are computed in the DSP from the digitized time data. Time data is digitized and sampled into the DSP block by block. A block is a fixed number of data points in the digital time record. Most frequency functions are computed from one block of data at a time. A block of data is also called a time record or time window.
Leakage
The FFT computation assumes that a signal is
References: Hartmann, William M., "Signals, Sound, and Sensation," American Institute of Physics, New York, 1997. Ramirez, Robert W., "The FFT, Fundamentals and Concepts," Prentice-Hall, New Jersey, 1985. Ziemer, Rodger E., et. al., "Signals & Systems," Prentice Hall, New Jersey, 1998. Copyright © 2003 LDS AN014 1203 Focus and Photon are trademarks of LDS. UK USA FRANCE GERMANY LDS LDS LDS LDS Ltd. Inc. SARL GmbH Tel: Tel: Tel: Tel: +44 (0) 1763 242424 +1 203 265 7966 +33 (0) 1 69 11 21 30 +49 (0) 89 969 89 180 Send all E-mail inquiries to: sales@lds-group.com www.lds-group.com