The interlaced chirp Z transform

In this paper we introduce the interlaced chirp Z transform (Interlaced CZT). It is based on the computation of several carefully staggered CZT that are progressively interlaced to result in a spectrum that has denser frequency samples where needed. This simple modification of the CZT is shown to result in significant computational savings over the regular CZT, as well as the zoom CZT (ZCZT). The CZT computes uniformly spaced frequency samples over a desired range with an efficiency similar to that of the FFT algorithm. In practice, several CZT's over increasingly smaller ranges are required to obtain denser frequency samples where needed. This process is referred to as the ZCZT. The interlaced CZT improves on the ZCZT by interlacing successive CZT's such that, in each step, the previous samples are included with the new ones, resulting in dense frequency sampling with increased computational efficiency. The regular CZT is also compared to the ZCZT based on a typical regimen and the conditions under which either is superior are elucidated.