Time and Frequency Domain Analysis: Considerations in Automotive Applications 2001-26-0053
When transferring signals from the analog world to the digital world, it is essential to understand the requirements that must be fulfilled, in order to maintain the integrity of the data and signal information. Both Nyquist and Shannon formulated a sampling theorem that is valid beyond time domain signal sampling. The theorem states that the information must be sampled at twice its bandwidth to keep its information intact. At the same time, a signal can be limited in time and frequency domain. A very short time signal, infinitely short, has an infinite bandwidth. This coupling between time, frequency and bandwidth is very important to fully understand when designing data acquisition systems.
This paper describes the basic requirements needed and illustrates this using examples, and discuss the frequent misconception that sampling twice that maximum frequency is adequate in test and measurement applications. Also, examples are presented were this restriction to the sampling theorem becomes very difficult to handle when performing frequency analysis due its unnecessary high sampling. It turns out, that it is of outmost importance to have a sparse time domain sampling when performing frequency analysis using DFT or FFT. Examples, illustrating this are presented.
It is also important to remember that the FFT is sparsely sampled in frequency domain. This can be handled by interpolation algorithms based on zero-padding or other techniques that interpolates the information between the frequency lines. This increase in sample rate is not an increase in frequency resolution, also a common misconception. This article gives examples and illustrates different interpolation levels and how this interpolation can help understand the data better.
The summary of this paper is to present the proper requirements for sampling of an analog signal when converting it into a digital representation. Different sampling techniques, sparse and not sparse, are presented and applications are given when each technique has its advantages. By not following the guidelines, severe measurement errors can occur, and it might be impossible to restore the data. This paper is thus intended as an eye opener to some common considerations that should be done before performing measurements in automotive applications that require more data points than sparsely sampled systems will deliver.