The FFT technique is subject to many problems due to the finite nature of the data. If the data doesn't 'start' and 'stop' on zero values, then there can be artifacts introduced into the frequency response spectrum that is obtained. Below are shown four versions of the same impulse response. This particular impulse was from the OUTDOOR data, and is for the driver BG28. It was chosen because the data was 'clean' and the start point of the impulse could be adjusted within the analysis window without problems of reflections. The first trace, in red, is the complete 4096 point sample.
The following traces are 512 point sections of the complete data set in which the impulse is positioned (relatively) at the beginning, middle and end of the analysis domain (512 points). Each of the three truncated data sets were then subjected to FFT analysis.
Below is the outcome of the FFT analysis of the three data sets. In these cases the resolution enhancing technique of 'padding with zeros' was used. The 512 point data set was placed at the beginning of a 4096 point domain, with point 513 and beyond set to the last value in the 512 point data set. This gives a resolution of approximately 15Hz, i.e. the FFT 'bin size' is 15Hz. The frequency responses were 1/12 octave smoothed.
We see very large differences in the spectrum. Differences so large, that we might ask, "How can these be from the same data?" Clearly, the position of the impulse in the data set determines much of the shape and linearity of the obtained frequency response. Note the low frequency response of the condition wherein the impulse was set to the beginning of the data set. It is relatively smooth, whereas the other two responses are plagued with rippling. Which is the 'real' response?
Below is a set of overlayed plots that represent an even more esoteric aspect of FFT analysis, i.e. the use of 'windows' on the data set. Windowing in FFT analysis is the multipication of the data set by a predetermined set of 'weights' (for each data point). The general idea is to reduce the effects of the end points of the data set upon the FFT analysis. Windows reduce the resolution of the data by increasing the width of the FFT bin sizes.
Each of the plots is from the same data set, with the impulse set to the beginning of the set. The conditions were NO Window, Half-Blackman, Half-Hamming, and Half-Bingham windows. The frequency responses were 1/12 octave smoothed.
Note that the Half-Bingham window is closest in value to the un-windowed FFT reponse. Often the effect of windowing is much larger than what is shown here. The data set used had relatively clean start and stop points.
The Half-Blackman and Half-Hamming windows reduce the resolution of the data compared to the mild Half-Blackman window. Half windows are used when the impulse starting point is placed at the beginning of the data domain for analysis. The Half-Bingham window was used on the data of this study.
Measurement Issues - Comparison: MLS Averages.
References.
Acoustic Line Source Research - Table of Contents.
