Digital Signal Processing Basics and AO Back-Ends

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Digital Signal Processing Basics and AO Back-Ends

• Luis A. Quintero
• Digital Section Head
• Electronics Department
• Arecibo Observatory

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Introduction to Digital Signal Processing
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Continuous Signal Acquisition - Transducers
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Sampling
Continuous-time Signal (real signal)
Amplitude
time
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Signal Storage in Computers
time
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Analog to Digital Converter Quantization
time
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Analog to Digital Converter Quantization
time
2
5
2
1
4
4
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http//www.iusb.edu/

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Digital Signal Processing System
Computer
A/D
D/A


Analog-to-Digital Converter
Digital-to-Analog Converter
Computer (Digital System) - Micro Processor
- DSP (MAC) - Logic Circuit - ASIC -
PAL/CPLD - FPGA
Data Storage Data Processing - Math
Operations - Filters - Fourier Transform
- Data Format
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Sampling Rate Analog to Digital
Fs 9 samples/second 9Hz
Fs 19 samples/second 19Hz
Better signal reconstruction More computer memory
/ BW and
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Analog to Digital Converter - Clock Input
ANALOG
DIGITAL
A/D

Clock for digital circuit
Stable jitter
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Resolution
Resolution 3bits, 23 8 combinations
7
Values from 0 to 7
0
Resolution 4bits, 24 16 combinations
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Values from 0 to 15
time
0
Better signal quantization More computer memory
and
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Saturation

• Resolution 3bits, 23 8 combinations
• Too much power to the ADC
• Saturation caused by interference (RFI)

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Sampling FT, Nyquist and Aliasing
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Sampling FT, Nyquist and Aliasing
Fs 200Hz, Ts 5ms, Fs/2 100Hz
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Signal Processing Adder
4bit adder
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5

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1bit adder
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Signal Processing Multiplier
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8
4

• Multiplication by a Constant Gain
• Multiplication by -1, Sign change
• Multiplication by a function e.g. sin/cos -
  up/down conv.

• Things to consider
• Bit growing
• Precision Approximation Errors

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Signal Processing Functions, e.g. sin/cos
xn
xn sinn
sinn
DDS
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Signal Processing Synchronization
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Filtering e.g. Finite Impulse Response (FIR)
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Auto Correlation
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Discrete Fourier Transform - DFT
Xk FNxn
FFT Fast Fourier Transform, optimized DFT
(butterflies)
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Examples with Signals

• Fourier Transform
• Saturation
• Averaging
• Clock Jitter

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Fourier Transform, one tone
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Fourier Transform, two tones
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Fourier Transform, noise effect
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Fourier Transform, averaging
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Fourier Transform, longer transf.
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Fourier Transform, Saturation
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Fourier Transform, Clock Jitter
0 Jitter
40 Jitter
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Applications in Radio Astronomy
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Gregorian Dome Receivers
Ganesan, R. Telescope Electronics, May 2006
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Radio Frequency Signal Path
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Signal Transport Intermediate Freq.
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Final Stage Data Acquisition
Data Sampling and Storage
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Bandpass Signals in IF
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Sampling - Nyquist Zones Analog BW
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Wideband Arecibo Pulsar Processor (WAPP)

• 4 WAPPs
• 1 WAPP 2 IF Channels
• 2 Correlators
• 1 Multiplexer
• 50/100 MHz BW
• auto / crosscorrelations
• Step attenuators
• Technical issues
• Difficult to troubleshoot
• Obsolete parts

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Wideband Arecibo Pulsar Processor (WAPP)
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WAPP Correlators (1995)
High Performance CMOS Correlator Chip (ASIC)

• 16 Chips per board
• Autocorrelation / Crosscorrelation
• 1024 Lags / chip
• 100MSPS each
• Low Power
• TTL compatible

http//www.naic.edu/astro/general_info/correlator
/cmos.html
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Complex Sampling
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Arecibo L-band Feed Array

• 7 Receivers
• Dual Polarization
• 14 analog signals
• 1225 1525MHz
• 300MHz BW
• Designed by Germán Cortés Medellín (Cornell)

Ganesan, R. Telescope Electronics, May 2006
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Complex Sampling Example ALFA
1225
1525
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Mock Spectrometer / PDEV (2007)

• Designed and developed by Jeff Mock
• 8 x AD9430, 12bits ADCs
• 2 x Xilinx Virtex II Pro FPGA
• 2 QDR Mem, 2M x 36
• 1x PowerPC Processor
• Flash SRAM mems
• 2 x GbE, 2 x RS232
• 5 x SMA (clk, PPS, etc)
• LCD 128x64 pixels

Digitizers
Digital Board
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PDEV Architecture
QDR 2Mx36
Flash / SRAM
PCIe x8 MGT
ADC
GX 2VP70
ADC
ADC
ADC
2 x GbE
PPC 440GX
2 x RS232
ADC
GX 2VP70
ADC
ADC
ADC
4 x SMA
PCIe x8 MGT
QDR 2Mx36
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PDEV Mock Spectrometer
TEST SIGNAL
CW, Noise, CW Noise
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ADC0
12
ADC0
SWITCH
PROC. INT.
STOKES
ACCUMULATOR
PACKETIZE
GAIN/OFFSET
PFB/FFT 16-8k
DDC (DDS, LPF)
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ADC0
12
ADC0
CONFIGURATION REGISTERS
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EALFA / PALFA Backend
14 PDEVs 7 for 7 ALFA pixels (primary) 7
for 7 ALFA pixels (commensal) 14 File servers
(4TB) We own in total 24 PDEVs DDC (DDS, Mixer,
DLPF) PFB (up to 8192 channels) Stokes
parameters Accumulation, Packing
http//www.naic.edu/phil/talks/vc09/tel_Perf_da
tatking_09.ppt
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GALFA Spectrometer / GALSPECT (2004)

• Backend for the
• Arecibo L-band Feed Array (ALFA) multibeam
  receiver
• 7 beams, dual polarization
• Outputs
• Narrowband 8192channels,
• 7MHz BW
• Wideband 512 channels,
• 100MHz BW

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PR Ultimate Pulsar Processing Instrument ( PUPPI)

• 100/200/400/800MHz BW
• Polyphase Filter Bank
• Dual Pol. 8 bit ADC
• Full Stokes
• 200MB per second recording (10GbE)
• 0-15.5dB Level Control
• PSRFITS data format
• 1xBee2 2xiBOB

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Recording Systems Mark IV / 5A / 5C / RDBE

• Mark IV Mark 5A 1Gbps (125MB every second)
• RDBE Mark5C 4Gbps (500MB every second)
• eVLBI, AO-UPR-Centenial link 155Mbps all
  time512Mbps 24h-6h

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Roach Radar Backend RRB

• Complex Baseband - Digital Down Converter (DDC)
• 50MHz bandwidth max.
• 2 x IF channels (polA/polB)
• Bit selection, 8/4bits
• 1.6Gbps max. data rate
• Doppler correction
• Programmable digital filter
• Hardware (three systems)ROACH Signal
  Proc.katADC 2x1.5Gsps_at_8bitRAID Server, dual
  10GbE
• Fixed parameters Summer 2012

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Analog v.s. Digital
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Down Conversion
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Digital Down Conversion
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Questions?