fastgoertzel 
A Python implementation of the Goertzel algorithm built using C++ for improved run time and efficiency on large datasets and loops.
Status and roadmap
-
Improved speed.(Significantly increased speed by using numpy arrays). - Benchmarking for speed comparison. See Performance for measured, reproducible numbers. The earlier "~75x faster than native Python" figure was measured against a Python loop that indexes a NumPy array one element at a time; against an idiomatic pure-Python loop the speed-up is 10-15x, and against a vectorised NumPy single-bin DFT it is 5-8x.
- Batch processing for multiple frequencies (
goertzel_batch,goertzel_sliding_batch). -
Add IIR and k-th FFT implementation of Goertzel.This is what the library already does:goertzelruns the second-order IIR Goertzel filter and evaluates the k-th DFT bin, withk = floor(frequency * len(x)). The two things that are genuinely missing are listed separately below. - Generalized Goertzel for non-integer bins: evaluate the DTFT at exactly
frequencyinstead of at the nearest-below DFT bin. Planned for 2.0. - Streaming (stateful) filter API that keeps the IIR state between calls, for sample-by-sample or chunked input. Planned for 2.0.
- Sampling-rate support (
fs=keyword, frequencies in Hz). Deliberately deferred until the generalized Goertzel lands: with the current bin truncation, asking for 440 Hz atfs=44100with 4096 samples would silently evaluate bin 40, which is 430.7 Hz.
Important semantics of the current release
frequencyis a normalized frequency in cycles per sample, in[0, 1). It is quantized to a DFT bin:k = floor(frequency * len(x)). A frequency that does not fall exactly on a bin is evaluated at the bin below it, andfrequency < 1/len(x)is evaluated at DC. Passk / len(x)and checkint((k / N) * N) == kif an exact bin is required; floating-point rounding makes a few percent ofk / Nvalues truncate tok - 1for non-power-of-twoN.- Phase is cosine-referenced, as with
numpy.fft:cos(w*n + p)gives phasep, andsin(w*n + p)givesp - pi/2. - Amplitude is
2 * |X[k]| / N, which recovers the amplitude of a sinusoid at any interior bin. At DC (k = 0) and Nyquist (k = N/2) this is twice the true amplitude. - All three functions validate their inputs and raise
ValueErrorfor an empty or non-1-D signal, a frequency outside[0, 1), or awindow_sizeoutside[1, len(x)]. Nothing you pass can crash the interpreter (fixed in 1.0.3; earlier releases aborted the process on an invalid frequency ingoertzel_sliding_batch). goertzel_batchandgoertzel_sliding_batchuse OpenMP threads when the build supports it (Linux and Windows wheels; macOS wheels are single-threaded) and the work is large enough. SetOMP_NUM_THREADSto control the thread count. The GIL is released in every function.
Installation
From PyPI (wheels for Linux, macOS, and Windows, plus a source distribution):
pip install fastgoertzel
From source (needs a C++17 compiler):
git clone https://github.com/0zean/fastgoertzel.git
cd fastgoertzel
pip install .
Published wheels are compiled for baseline x86-64 and arm64 so that they run on any CPU. When building from source for your own machine you can opt in to CPU-specific tuning with FASTGOERTZEL_NATIVE=1 pip install . (not Windows). On macOS, Apple's compiler has no OpenMP; to enable threading install libomp with Homebrew and set FASTGOERTZEL_OPENMP_FLAGS as described at the top of setup.py.
For development, uv sync creates the environment and builds the extension in place; make check runs lint, format check, and tests.
Usage
import numpy as np
import pandas as pd
import fastgoertzel as fg
def wave(amp, freq, phase, x):
return amp * np.sin(2*np.pi * freq * x + phase)
x = np.arange(0, 512)
y = wave(1, 1/128, 0, x)
amp, phase = fg.goertzel(y, 1/128)
print(f'Goertzel Amp: {amp:.4f}, phase: {phase:.4f}')
# Compared to max amplitude FFT output
ft = np.fft.fft(y)
FFT = pd.DataFrame()
FFT['amp'] = np.sqrt(ft.real**2 + ft.imag**2) / (len(y) / 2)
FFT['freq'] = np.fft.fftfreq(ft.size, d=1)
FFT['phase'] = np.arctan2(ft.imag, ft.real)
max_ = FFT.iloc[FFT['amp'].idxmax()]
print(f'FFT amp: {max_["amp"]:.4f}, '
f'phase: {max_["phase"]:.4f}, '
f'freq: {max_["freq"]:.4f}')
Performance
Measured with python benchmarks/benchmark.py on an Intel Core i9-14900KF (8P + 16E cores, 32 threads), Windows 11, Python 3.11.9, NumPy 2.4.6, MSVC 19.44 build of fastgoertzel 1.0.2. Each time is the minimum of 7 rounds. Numbers on other machines will differ; re-run the script and quote your own, together with the baseline and thread count.
Single frequency, goertzel(x, 0.1):
| N | fastgoertzel | pure-Python loop | NumPy 2x real dot | np.fft.rfft, one bin |
|---|---|---|---|---|
| 1,000 | 2.3 us | 24 us (10x) | 11 us (4.6x) | 7.3 us (3.1x) |
| 100,000 | 163 us | 2.4 ms (15x) | 0.94 ms (5.8x) | 0.44 ms (2.7x) |
| 1,000,000 | 1.63 ms | 24 ms (15x) | 9.4 ms (5.8x) | 8.6 ms (5.3x) |
| 10,000,000 | 16.3 ms | not run | 116 ms (7.1x) | 126 ms (7.7x) |
The single-frequency path runs at about 600 million samples per second on one core. It is bound by the latency of the Goertzel recurrence, so AVX2 and loop unrolling do not change it.
Per-call latency matters more than throughput in a real-time loop. The same script reports percentiles over 100,000 individual calls (--latency-only). On the machine above, one goertzel call on 64 samples has a p50 of 0.6 us and a p99 of 0.8 us, and on 1,024 samples a p50 of 2.0 us and a p99 of 3.5 us, Python call overhead included. Calls that enter an OpenMP region have a much heavier tail: goertzel_sliding_batch on 1,024 samples with a 256-sample window and 4 frequencies has a p50 of 59 us but a maximum of about 6 ms. Pin OMP_NUM_THREADS=1 for predictable latency on small inputs.
goertzel_batch and goertzel_sliding_batch parallelize over frequencies and windows with OpenMP, so their speed-ups scale with core count. On this 32-thread machine goertzel_batch with N = 1,000,000 and 32 frequencies takes 2.3 ms, against 51 ms on one thread. goertzel_sliding_batch with N = 100,000, window 256 and 8 frequencies takes 17 ms, 5x faster than NumPy's sliding_window_view plus rfft, but 362 ms on one thread, which is 4x slower than NumPy. Pin OMP_NUM_THREADS when comparing.
1 maintainer
Metadata
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Release files for fastgoertzel 1.0.3
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1e23d829d5cfd7b0eb3cc90d613c7eda28b66eee1c645e6ec468c6f5913e0286
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BLAKE2b-256 checksum How to use checksums |
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twine/7.0.0 CPython/3.13.14
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Transparency logRelease files / fastgoertzel-1.0.3-cp310-cp310-macosx_10_9_x86_64.whl
| Download URL | fastgoertzel-1.0.3-cp310-cp310-macosx_10_9_x86_64.whl |
|---|---|
| Size | 97.4 kB |
| Tags | CPython 3.10 macOS 10.9+ x86-64 |
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SHA-256 checksum How to use checksums |
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BLAKE2b-256 checksum How to use checksums |
af2e18f84b53c1636456fea805946978c9a3c97065a58f03895b35a44b004fb7
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Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
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Provenance
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