University of Twente Student Theses


Multi-rate discrete fourier transform characteristics : results of models, simulations, and measurements

Beuker, W. (2019) Multi-rate discrete fourier transform characteristics : results of models, simulations, and measurements.

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Embargo date:2 December 2023
Abstract:The Discrete Fourier Transform (DFT) is a technique to assess data in a sampled signal from a frequency point of view. This technique is widely used in industry; from wireless communication to mobile devices. A limitation of the DFT is that the highest recoverable frequency component (the so called Nyquist frequency) is limited by the sample frequency of the measurement system. At the Integrated Circuit Design group of the University of Twente, an extension to the DFT is developed. This extension eliminates this limitation on the expense of multiple measurements at different sample frequencies. This extension is called the Multi-Rate Discrete Fourier Transform (MR-DFT). The intended use case of the MR-DFT is in the field of characterising class-E Power Amplifiers to compensate for PVT spread and load impedance mismatch. The MR-DFT is the main focus of this work. In this work a measurement setup to measure the MR-DFT is presented and measurement results of QAM constellations are presented. With the current setup, frequencies of 1.75*f_nyquist are measurable. Also the mathematical background of the MR-DFT is presented. Furthermore, the effect of noise on the MR-DFT is described and a model for the impact of noise is presented. This model is compared to simulations and measurements. As case study, the effect of quantization noise on the noise floor of the output of the MR-DFT is investigated. Although the noise (floor) profiles of the measurements, model, and simulations do not match in an absolute manner, the noise floors have a similar profile. The model is a step into the right direction but it is suspected some of the assumptions are not correct, deviating the model results from simulations. It is suspected that the measurements deviate from the simulation due to a limitation in the measurement setup and since other noise sources are present (like jitter) in the measurement setup. They seem to have a larger impact on the noise floor than the quantization noise, making it impossible to assess the effect of the quantization noise. Although the results on the expected noise floor of the MR-DFT of measurements, simulations, and a model are not (exactly) in line, this work is a great step toward unravelling the mysteries of the MR-DFT.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:53 electrotechnology, 54 computer science
Programme:Embedded Systems MSc (60331)
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