A common structure for recursive discrete transforms

Software implementation of the Recursive Discrete Fourier Transform

“…The R-DFT realizes the observer-based structure [3], which calculates the DFT values of the incoming signal for every single new input. The observer theory is based on the predictioncorrection scheme, where the observer is a system, which can copy the state variables of the observed system.…”

“…The Recursive DFT (R-DFT) provides an alternative computation method to acquire the DFT components of a signal, which applies the observer-based structure [3] and recalculates the spectral values for every new incoming sample in a sliding manner. This paper presents a possible implementation based on the x86, Streaming SIMD Extension (SSE) and 16-bit architectures and compares the results with an optimized FFT.…”

R–DFT-based Parameter Estimation for WiGig

“…Péceli provides an alternative solution for spectrum calculation according to Hostetter's proposal [3,4], the R-DFT, which is based on the observer theory. This model supposes that the measured signal (x [k]) is a linear combination of the elements of a basis system, as Fig.…”

“…The N points R-DFT calculates the spectrum point by point, where N is the periodicity of the received data because of the convergence properties [4]. The procedure of Moose in Eq.…”

Possibilities for On-line Detector Connectivity Checks in Beam Loss Monitoring Systems

“…In order to detect these frequency components, we implemented a structure based on the resonator-based spectral observer (Fourier analyzer, FA) proposed by Péceli [27], complemented by a frequency adaptation method based on that first suggested by Nagy [28]. As demonstrated in Fig.…”