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Register a new userThe Fast Fourier Transform Telescope
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Max Tegmark
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We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of Fast Fourier Transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moores law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as N log N rather than N^2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large Fast Fourier Transform Telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
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We have developed a digital fast Fourier transform (FFT) spectrometer made of an analog-to-digital converter (ADC) and a field-programmable gate array (FPGA). The base instrument has independent ADC and FPGA modules, which allow us to implement different spectrometers in a relatively easy manner. Two types of spectrometers have been instrumented, one with 4.096 GS/s sampling speed and 2048 frequency channels and the other with 2.048 GS/s sampling speed and 32768 frequency channels. The signal processing in these spectrometers has no dead time and the accumulated spectra are recorded in external media every 8 ms. A direct sampling spectroscopy up to 8 GHz is achieved by a microwave track-and-hold circuit, which can reduce the analog receiver in front of the spectrometer. Highly stable spectroscopy with a wide dynamic range was demonstrated in a series of laboratory experiments and test observations of solar radio bursts.
Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT algorithm, designs the butterfly and scramble kernels and implements 2D FFT on GPU. The experiment result demonstrates the validity and advantage over general CPU, especially in the condition of large input size. The approach can also be generalized to other transforms alike.
We present an overview of SITELLE, an Imaging Fourier Transform Spectrometer (iFTS) available at the 3.6-meter Canada-France-Hawaii Telescope. SITELLE is a Michelson-type interferometer able to reconstruct the spectrum of every light source within its 11 field of view in filter-selected bands of the visible (350 to 900 nm). The spectral resolution can be adjusted up to R = 10 000 and the spatial resolution is seeing-limited and sampled at 0.32 arcsec per pixel. We describe the design of the instrument as well as the data reduction and analysis process. To illustrate SITELLEs capabilities, we present some of the data obtained during and since the August 2015 commissioning run. In particular, we demonstrate its ability to separate the components of the [OII] $lambdalambda$ 3726,29 doublet in Orion and to reach R = 9500 around H-alpha; to detect diffuse emission at a level of 4 x 10e-17 erg/cm2/s/arcsec2; to obtain integrated spectra of stellar absorption lines in galaxies despite the well-known multiplex disadvantage of the iFTS; and to detect emission-line galaxies at different redshifts.
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using fast Fourier transform (FFT); unfortunately, acceleration of the calculation of non-uniform sampled planes is limited due to the property of the FFT that imposes uniform sampling. In addition, it gives rise to wasteful sampling data if we calculate a plane having locally low and high spatial frequencies. In this paper, we developed non-uniform sampled ASM and Fresnel diffraction to improve the problem using the non-uniform FFT.
Orthogonal time frequency space (OTFS) modulation can effectively convert a doubly dispersive channel into an almost non-fading channel in the delay-Doppler domain. However, one critical issue for OTFS is the very high complexity of equalizers. In this letter, we first reveal the doubly block circulant feature of OTFS channel represented in the delay-Doppler domain. By exploiting this unique feature, we further propose zero-forcing (ZF) and minimum mean squared error (MMSE) equalizers that can be efficiently implemented with the two-dimensional fast Fourier transform. The complexity of our proposed equalizers is gracefully reduced from $mathcal{O}left(left(NMright)^{3}right)$ to $mathcal{O}left(NMmathrm{log_{2}}left(NMright)right)$, where $N$ and $M$ are the number of OTFS symbols and subcarriers, respectively. Analysis and simulation results show that compared with other existing linear equalizers for OTFS, our proposed linear equalizers enjoy a much lower computational complexity without any performance loss.
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