Modular system for performing the discrete fourier transform via the chirp-Z transform

摘要

Two kinds of apparatus for combining N.sub.2 chirp-Z transform (CZT) modules of length N.sub.1 to perform a discrete Fourier transform (DFT) of length N.sub.1 N.sub.2. The first method uses an auxiliary parallel- input, parallel-output, DFT device of size N.sub.2 and allows the transform of size N.sub.1 N.sub.2 to be performed in the same time as is required for a single CZT module to perform a size N.sub.1 transform. The second method uses an auxiliary parallel-input, serial-output, DFT device of size N.sub.2. If the second method is implemented entirely in a single technology, such as with charge-coupled devices (CCDs), it performs the size N.sub.1 N.sub.2 transform in N.sub.2 times the amount of time required for a single CZT module to perform a size N.sub.1 transform. If N.sub.2 is a composite number, say N.sub.2 = M.sub.1 M.sub. 2, the second method also permits the same hardware to perform M.sub.1 simultaneous transforms of length N.sub.1 M.sub.2.