Tutorial 4: Wideband Spectrometer

Introduction

A spectrometer is something that takes a signal in the time domain and converts it to the frequency domain. In digital systems, this is generally achieved by utilising the FFT (Fast Fourier Transform) algorithm.

When designing a spectrometer for astronomical applications, it’s important to consider the science case behind it. For example, pulsar timing searches will need a spectrometer which can dump spectra on short timescales, so the rate of change of the spectra can be observed. In contrast, a deep field HI survey will accumulate multiple spectra to increase the signal to noise ratio. It’s also important to note that “bigger isn’t always better”; the higher your spectral and time resolution are, the more data your computer (and scientist on the other end) will have to deal with. For now, let’s skip the science case and familiarize ourselves with an example spectrometer.

Setup

This tutorial comes with a completed model file, a compiled bitstream, ready for execution on Skarab, as well as a Python script to configure the Skarab and make plots. Here

Spectrometer Basics

When designing a spectrometer there are a few main parameters of note:

  • Bandwidth: The width of your frequency spectrum, in Hz. This depends on the sampling rate; for complex sampled data this is equivalent to:

../../_images/bandwidtheq12.png

In contrast, for real or Nyquist sampled data the rate is half this:

../../_images/bandwidtheq22.png

as two samples are required to reconstruct a given waveform .

  • Frequency resolution: The frequency resolution of a spectrometer, Δf, is given by

../../_images/freq_eq2.png,

and is the width of each frequency bin. Correspondingly, Δf is a measure of how precise you can measure a frequency.

  • Time resolution: Time resolution is simply the spectral dump rate of your instrument. We generally accumulate multiple spectra to average out noise; the more accumulations we do, the lower the time resolution. For looking at short timescale events, such as pulsar bursts, higher time resolution is necessary; conversely, if we want to look at a weak HI signal, a long accumulation time is required, so time resolution is less important.

Configuration and Control

Hardware Configuration

The tutorial comes with a pre-compiled bof file, which is generated from the model you just went through (tut_spec.fpg). All communication and configuration will be done by the python control script called tut_spec.py.

Next, you need to set up your Skarab. Switch it on, making sure that:

• Your tone source is set within the band of the ADC. The default digital downconverter setting is 1 GHz, so signals within 375 MHz of this frequency should pass. In the tut_spec.py script, 1 GHz is mapped to DC. In our setup, we set the tone frequency to 1.054 GHz. If you use a different tone frequency, be sure to update the freq_range_mhz = [0,80] in the Python script so that the plot covers the range of your tone.

The tut_spec.py spectrometer script

Once you’ve got that done, it’s time to run the script. First, check that you’ve connected the ADC to mega-array connector, and that the clock source is connected to clk_i of the ADC. Now, if you’re in linux, browse to where the tut3.py file is in a terminal and at the prompt type

 ./tut_spec.py <skarab IP or hostname> -l <accumulation length> -b <fpgfile name>

replacing with the IP address of your Skarab, is the number of accumulations, and with your fpgfile. You should see a spectrum like this:

../../_images/1p054GHz_sine_10accum.png

Take some time to inspect the tut_spec.py script. It is quite long, but don’t be intimiated. Most of the script is configuration for the ADC. The import lines begin after the #START OF MAIN comment. There, you will see that the script

• Instantiates the casperfpga connection with the Skarab

• Uploads the fpg file

• Sets the ADC

• Records ADC snapshots, interleaves them and writes to a file adcN_data.txt where N is 0..4

• Plots the spectral outputs of the memory blocks

Conclusion

If you have followed this tutorial faithfully, you should now know:

• What a spectrometer is and what the important parameters for astronomy are.

• Which CASPER blocks you might want to use to make a spectrometer, and how to connect them up in Simulink.

• How to connect to and control a Skarab spectrometer using python scripting.