Efficient implementations of high-resolution wideband FFT-spectrometers and their application to an APEX Galactic Center line survey

Spectroscopy has been a major technique in radioastronomy for decades and spectrometers are used in a wide range of radioastronomical applications. With more stable receivers that are wider in bandwidth, spectrometers are required that possess both wide bandwidth and high spectral resolution. The availability of analog-to-digital converters (ADCs) that sample a signal at rates of multiple GHz allowed the development of a novel type of spectrometer. The fast Fourier transform spectrometer (FFTS) digitizes a radio signal and calculates its power spectrum at high speed. The increased complexity of field-programmable gate arrays (FPGAs) provides the processing power necessary for such high-speed operation at a low price and with high flexibility. However, to fully utilize the speed and flexibility offered by FPGAs and to achieve a bandwidth of 2.5 GHz with up to 65536 channels, it is necessary to develop efficient algorithms that are optimized for FPGA-based implementation. This thesis first explains the basic principles behind an FFTS. Then it describes the requirements of astronomical applications that utilize FFTSs and evaluates their requirements. Besides the main application of wideband spectroscopy, the demands of high resolution spectroscopy, of an incoherent pulsar search, and of a readout for microwave kinetic inductance detectors (MKIDs) are specified. The thesis then presents efficient algorithms, that satisfy these requirements. After defining the components of an FFTS and their purpose, the technical requirements of each component are described, and algorithms or implementations are discussed with respect to their processing speed, hardware utilization, memory occupation, flexibility, or just simplicity. Concepts are developed to partition algorithms between the FPGA and the personal computer (PC) to create simple, hardware-efficient components inside the FPGA. To achieve both, high bandwidth and high spectral resolution, parallel and pipelined algorithms are combined. The hardware utilization and the flexibility of different such fast Fourier transform (FFT) architectures are compared, dependent on the significance of either bandwidth or resolution. Control mechanisms are developed and implemented to function in different time frames, dependent on the application. Two fully functional high-resolution wideband spectrometers, in which such algorithms are implemented, benefit from the optimization of the processing pipeline: the Array Fast Fourier Transform Spectrometer (AFFTS) and the eXtended-bandwidth Fast Fourier Transform Spectrometer (XFFTS). Finally, an astronomical application of the aforementioned spectrometers is presented: two unbiased line surveys of molecular cloud positions near the center of our Galaxy with the First Light APEX Submillimeter Heterodyne receiver (FLASH) in the Atacama Pathfinder EXperiment (APEX) telescope. Containing hundreds of spectral lines, those surveys provide a large amount of information on the physical and chemical conditions of the observed objects and thus work for several years of analysis. We present the basic results that can be extracted from a first iteration with the data: line identification, selection of the best molecular tracers, and analysis of those tracers to obtain the physical properties in the studied regions. Unidentified lines and so far unaccessed information, and the possibility to add this data to unbiased surveys taken with other telescopes are a legacy to future astronomical research and thus demonstrate the benefits of the presented concepts