FixedPointDSP

FixedPointDSP is a modern, header-only C++23 library providing
high-performance fixed-point arithmetic and essential DSP building-blocks.
It’s ideal for embedded targets, hardware-aligned simulation, and any context
where floating-point is too heavy or unavailable.

by @aarushgoradia

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Highlights

• Header-only (just include—no linking or external dependencies)
• Templated FixedPoint<TotalBits, FracBits, OverflowPolicy>
  • Arbitrary bit-width, configurable overflow (wrapping, saturation)
• Operator overloads with compile-time safety (C++23 concepts)
• DSP primitives:
  • FIR filter
  • Convolution (linear & circular)
  • DFT & FFT
• Unit-tested with Google Test and benchmarked with Google Benchmark
• Cross-platform via CMake (Windows, Linux, macOS)

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Project Layout

├── include/
│ ├── fixed_point/
│ │ ├── fixed_point.hpp # core class
│ │ ├── arithmetic_policies.hpp # overflow rules
│ │ └── promote.hpp # promotion logic
│ ├── fir/ # FIR filter headers
│ │ ├── fir_filter.hpp # FIR filter implementation
│ │ └── fir_coefficients.hpp # coefficient helpers
│ └── dsp/
│ ├── convolution.hpp # linear & circular conv.
│ ├── dft.hpp # O(N²) DFT
│ └── fft.hpp # O(N log N) FFT
├── tests/ # Google Test unit-tests
│ ├── FixedPointTests.cpp
│ ├── FIRFilterTests.cpp
│ ├── ConvolutionTests.cpp
│ ├── DFTTests.cpp
│ └── FFTTests.cpp
├── benchmarks/ # Google Benchmark performance tests
│ └── fft_benchmark.cpp
├── external/ # third-party (googletest, benchmark)
├── CMakeLists.txt
└── README.md

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Getting Started

Prerequisites

• Compiler: C++23 support (GCC 13+, Clang 16+, MSVC 2022+)
• Build: CMake ≥ 3.20
• Google Test & Google Benchmark (included as external/)
  • Download GoogleTest and GoogleBenchmark
  • Create an external/ folder in the main repo folder
  • Drag googletest-xxx/ and benchmark-xxx/ into the external/ folder
  • Rename to googletest/ and benchmark/ (omit the version)

Build & Test

1. Configure & build

cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build

2. Run unit tests

ctest --output-on-failure

3. (Optional) Run FFT benchmark

./build/FFTBenchmark --benchmark_time_unit=ms

Performance

 ------------------------------------------------------
Benchmark            Time             CPU   Iterations
------------------------------------------------------
BM_DFT/128       0.527 ms        0.516 ms         1120
BM_DFT/256        2.01 ms         2.04 ms          345
BM_DFT/512        8.23 ms         8.33 ms           90
BM_DFT/1024       42.6 ms         42.5 ms           18
BM_FFT/128       0.008 ms        0.008 ms        89600
BM_FFT/256       0.018 ms        0.018 ms        37333
BM_FFT/512       0.041 ms        0.040 ms        17231
BM_FFT/1024      0.092 ms        0.092 ms         7467

Measured on a 2024 Intel i7, FixedPoint <16,8> saturation policy.

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Roadmap

• Core FixedPoint class & arithmetic

• Overflow policies (wrap, saturate)

• FIR filter & convolution + unit tests

• DFT & unit tests

• FFT, unit tests & performance benchmarks

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🙋 Author

Aarush Goradia B.S.E. in ECE, Princeton University — building C++, hardware, and systems.