## Spline interpolation

A cookbook recipe for segmented y=f(x) 3rd-order polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog

Introduction

Splines describe a smooth function with a small number of parameters. They are well-known for example from vector drawing programs, or to define a "natural" movement path through given...

## Signed serial-/parallel multiplication

Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm

Summary
• A detailed discussion of bit-level trickstery in signed-signed multiplication
• Algorithm based on Wikipedia example
• Includes a Verilog implementation with parametrized bit width
Signed serial-/parallel multiplication

A straightforward method to multiply two binary numbers is to repeatedly shift the first argument a, and add to a register if the corresponding bit in the other argument b is set. The...

## DSP Algorithm Implementation: A Comprehensive Approach

As DSP engineers, ultimately we are required to design and implement specific DSP algorithms. The first step is to make a choice on which algorithm to use, e.g. for filtering should we use FIR or IIR. Then we can go a little bit deeper into the,  high level, implementation details, e.g. use the symmetry in FIR filter to reduce complexity. When the algorithm is clear, the first step is to test and simulate the algorithm in a high level language like MATLAB.

After we reach confidence in...

## Half-band filter on Xilinx FPGA

1. DSP48 Slice in Xilinx FPGA

There are many DSP48 Slices in most Xilinx® FPGAs, one DSP48 slice in Spartan6® FPGA is shown in Figure 1, the structure may different depending on the device, but broadly similar.

Figure 1: A whole DSP48A1 Slice in Spartan6 (www.xilinx.com)

2. Symmetric Systolic Half-band FIR

Figure 2: Symmetric Systolic Half-band FIR Filter

3. Two-channel Symmetric Systolic Half-band FIR

Figure 3: 2-Channel...

## Signed serial-/parallel multiplication

Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm

Summary
• A detailed discussion of bit-level trickstery in signed-signed multiplication
• Algorithm based on Wikipedia example
• Includes a Verilog implementation with parametrized bit width
Signed serial-/parallel multiplication

A straightforward method to multiply two binary numbers is to repeatedly shift the first argument a, and add to a register if the corresponding bit in the other argument b is set. The...

## Spline interpolation

A cookbook recipe for segmented y=f(x) 3rd-order polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog

Introduction

Splines describe a smooth function with a small number of parameters. They are well-known for example from vector drawing programs, or to define a "natural" movement path through given...

## Half-band filter on Xilinx FPGA

1. DSP48 Slice in Xilinx FPGA

There are many DSP48 Slices in most Xilinx® FPGAs, one DSP48 slice in Spartan6® FPGA is shown in Figure 1, the structure may different depending on the device, but broadly similar.

Figure 1: A whole DSP48A1 Slice in Spartan6 (www.xilinx.com)

2. Symmetric Systolic Half-band FIR

Figure 2: Symmetric Systolic Half-band FIR Filter

3. Two-channel Symmetric Systolic Half-band FIR

Figure 3: 2-Channel...

## DSP Algorithm Implementation: A Comprehensive Approach

As DSP engineers, ultimately we are required to design and implement specific DSP algorithms. The first step is to make a choice on which algorithm to use, e.g. for filtering should we use FIR or IIR. Then we can go a little bit deeper into the,  high level, implementation details, e.g. use the symmetry in FIR filter to reduce complexity. When the algorithm is clear, the first step is to test and simulate the algorithm in a high level language like MATLAB.

After we reach confidence in...