Objective: Provide introduction to DSP and FPGA. Understand general FPGA architecture and why FPGAs are uniquely suited to the implementation of DSP algorithms.

• From discrete logic to FPGAs -some history!
• The generic DSP system
• DSP cores and processors review
• Custom and semi-custom ASICs
• System-on-chip (SOC)
• FPGA flexibility and functionality
• FPGAs vs Programmable DSPs

Objective: Review fundamental concepts of sampling theorem, quantization, Fourier analysis and digital filter design.

• Aliasing and reconstruction filters
• Sampling rates and wordlengths
• Z-domain notation and fundamental analysis
• FIR and IIR filters
• Digital filter design and specification
• Oversampling techniques (sigma delta)

Objective: Explore different Xilinx FPGA families and architectures. Provide introduction to Spartan 3 and Virtex-5 FPGAs.

• The FPGA technology roadmap
• Clocking rates, data rates and sample rates
• FPGA memory and registers
• Input/output blocks and requirements
• Bits, Slices and Configurable Logic Blocks
• Comparable MIPs Performance Ratings
• FPGA Families and Sources

Objective: Understand DSP slices, clocking resources and power consumption.

• Building delay lines and Shift Registers
• Use of RAM (memory) on FPGAs
• Serial to Parallel and Parallel to serial
• Multiplexors for channel selection
• Full adders, carry logic, and adder trees
• Multipliers: Shift and Add; ROM based
• Efficient multiplier implementation

Objective: Understand fixed point binary arithmetic. Map arithmetic operations to Xilinx FPGA hardware.

• 2's complement fixed point arithmetic
• Fundamental adders and multiplier arrays
• Division and square root arrays….not so easy!
• Wordlength issues and Fixed point arithmetic
• Saturate and wraparound
• Overflow and underflow

Objective: Review the representation of DSP algorithms using signal flow graph. Use the Cut Set method to improve timing performance. Implement parallel and serial FIR filters.

• DSP/Digital Filter Signal Flow Graphs
• Latency, delays and "anti-delays"!
• Re-timing: Cut-set and delay scaling
• The transpose FIR
• Pipelining and multichannel architectures
• SFG topologies for FPGAs

Objective: Discuss the theory and FPGA implementation of the Fast Fourier Transform.

• DFT, FFT and IFFT
• FFT FPGA architectures
• FFT wordlength growth and accuracy

Objective: Develop polyphase structure for efficient implementation of multirate filters. Use CIC filter for interpolation and decimation.

• Upsampling and interpolation filters
• Downsampling and decimation filters
• Efficient arithmetic for FIR implementation
• Integrators and differentiators
• Half-band, moving average and comb filters
• Cascade Integrator Comb (CIC) Filters (Hogenauer)
• Efficient arithmetic for IIR Filtering

Objective: Introduce CORDIC algorithm for calculation of various trigonometric functions.

• CORDIC rotation mode and vector mode
• Compute cosine and sine function
• Compute vector magnitude and angle
• Architecture for FPGA implementation

Objective: Introduce LMS algorithm in adaptive signal processing. Illustrate QR algorithm as a Recursive Least Squares (RLS) technique and why it is particularly suited to FPGA implementation.

• Adaptive applications (equalisation, beamforming)
• LMS Algorithms and parallel implementation
• Non-canonical LMS algorithms
• Linear algebra; solving linear systems of equations
• The QR algorithm for adaptive signal processing
• QR processing requirements and numerical issues

Objective: Review quadrature modulation and pulse-shaping. Discuss implementation of numerically controlled oscillators.

• Quaternary Phase Shift Keying (QPSK)
• Transmit/Receive Filters - Root Raised Cosine
• Undersampling and Digital Downconversion
• Direct digital upconversion
• Digital IF stages (and fs/4 Systems)
• Numerically controlled oscillators (NCO)
• Design partitioning for FPGAs

Objective: Cover symbol timing recovery, carrier phase recovery, carrier frequency recovery and frame synchronization.

• Carrier recovery, squaring and Costas loops, PLLs
• Phase rotations; Sampling rate conversions
• Symbol timing recovery, early/late gate detection
• Delay locked loop timing and synchronisation