High-resolution frequency analysis with a small data record

Fast Fourier transform-based implementations of the discrete Fourier transform have proven themselves the workhorses of discrete-time spectral analysis. Although these algorithms find widespread use, they have limitations. One problem is that frequency resolution is dependent on the number of samples available. For a given sampling frequency, the longer the data record, the better the frequency resolution. An alternative approach, model-based spectral analysis, is now being employed, as it derives a higher-resolution spectral detail from fewer samples. This approach was used by National Instruments Corp. in a portion of the design of a portable analyzer for the telephony industry. The analyzer is intended for technicians to use in diagnosing and locating faults on a standard twisted pair copper (plain old telephone system) line. In the software design phase, one option considered and tested for feasibility was employing model-based spectral analysis (MBSA) to decode a calling number delivery signal (better known as Caller ID). Not just applicable in this analyzer example, MBSA works in a variety of circumstances and offers a valuable addition to an engineer's toolbox of software-based methods for spectral analysis. The technique might find an application wherever there is a lack of data, as in the case of analysis of a short time event, or where a restriction is imposed to ensure that the spectral characteristics of a signal do not change over the duration of a data set.