An algorithm is introduced which performs real time, high-resolution Fourier transforms of large amounts of input data over an adjustable output band. The algorithm combines recent Fast Fourier and Chirp z-Transform developments to segment input data and boost output spectrum resolution. The target application is in test and measurement, where large numbers of input samples must be processed in real time, and a given frequency range of interest is usually involved. Because the application often runs on embedded hardware with limited resources, the algorithm dynamically attempts to optimize performance for available memory. Results are evaluated on hardware and resource requirements for achieving high resolution and real time operation. The feasibility of the algorithm's implementation in DSP hardware due to these requirements is discussed, along with its usefulness based on performance. Felder A Real-Time Variable Resolution Chirp z-Transform Table of

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A real-time variable resolution Chirp z-Transform

A fast Fourier transform (FT) algorithm using Hadamard transform (HT) is introduced, which is called HFT (Hadamard Fourier Transform). In the algorithm proposed here, a HT is used as mid-transform and the redundant calculation in the original fast FT algorithm is reduced by double transformation. The results of theoretical analysis show that the number of multiplications and additions of HFT are both decreased by 60% compared with that of traditional FFT and the executed result shows the computing speed of HFT is 1.6 to 1.7 times faster than FFT. Comparing with the similar algorithms such as WFT-II1, RFT2, it has a market improvement in computing speed and eliminates the limitatiom on the length of transform.

C. Fan

Papers

A fast Fourier transform algorithm using Hadamard transform