Chirp-Z Transform (CZT)

The Chirp-Z Transform (CZT) is an algorithm for computing frequency spectra that performs a z-transform of an input sequence along a spiral contour in the z-domain. Unlike traditional Fourier transforms and z-transforms, CZT can execute transforms on non-unit circles. This makes CZT more flexible in signal processing applications and enables it to handle more complex signals. For example, CZT can be used to analyze non-periodic signals such as impulse signals and short-duration pulses. In implementation, CZT typically utilizes the chirp convolution algorithm which can be efficiently computed using FFT operations, making it computationally efficient despite its increased flexibility. Additionally, CZT finds widespread applications in radar signal processing, communication signal processing, medical image processing, and other fields. Therefore, learning CZT is essential for signal processing engineers working with non-uniform frequency analysis requirements.