stftPitchShift

This is a reimplementation of the Stephan M. Bernsee smbPitchShift.cpp, a pitch shifting algorithm using the Short-Time Fourier Transform (STFT), especially for vocal audio signals.

This repository features two analogical algorithm implementations, C++ and Python. Both contain several function blocks of the same name (but different file extension, of course).

In addition to the base algorithm implementation, it also features spectral multi pitch shifting and cepstral formant preservation extensions.

Both sources contain a ready-to-use command line tool as well as a library for custom needs. See more details in the build section.

Modules

Pitch shifting

Single pitch

Since the Vocoder module transforms the original DFT complex values real + j * imag into magnitude + j * frequency representation, the single pitch shifting is a comparatively easy task. Both magnitude and frequency vectors are to be resampled according to the desired pitch shifting factor:

• The factor 1 means no change.
• The factor <1 means downsampling.
• The factor >1 means upsampling.

Any fractional resampling factor such as 0.5 requires interpolation. In the simplest case, linear interpolation will be sufficient. Otherwise, bilinear interpolation can also be applied to smooth values between two consecutive STFT hops.

Due to frequency vector alteration, the resampled frequency values needs also be multiplied by the resampling factor.

Multi pitch

In terms of multi pitch shifting, multiple differently resampled magnitude and frequency vectors are to be combined together. For example, the magnitude vectors can easily be averaged. But what about the frequency vectors?

The basic concept of this algorithm extension is to only keep the frequency value of the strongest magnitude value. So the strongest magnitude will mask the weakest one. Thus, all remaining masked components become inaudible.

In this way, the multi pitch shifting can be performed simultaneously in the same DFT frame. There is no need to build a separate STFT pipeline for different pitch variations to superimpose the synthesized signals in the time domain.

Formant preservation

The pitch shifting also causes distortion of the original vocal formants, leading to a so called Mickey Mouse effect if scaled up. One possibility to reduce this artifact, is to exclude the formant feature from the pitch shifting procedure.

The vocal formants are represented by the spectral envelope, which is given by the smoothed DFT mangitude vector. In this implementation, the smoothing of the DFT mangitude vector takes place in the cepstral domain by low-pass liftering. The extracted envelope is then removed from the original DFT magnitude. The remaining residual or excitation signal goes through the pitch shifting algorithm. After that, the previously extracted envelope is combined with the processed residual.

Build

C++

Use CMake to manually build the C++ library, main and example programs like this:

cmake -S . -B build
cmake --build build

Or alternatively just get the packaged library from:

• Vcpkg repository stftpitchshift or
• Ubuntu repository ppa:jurihock/stftpitchshift.

To include this library in your C++ audio project, study the minimal C++ example in the examples folder:

#include <StftPitchShift/StftPitchShift.h>

using namespace stftpitchshift;

StftPitchShift pitchshifter(1024, 256, 44100);

std::vector<float> x(44100);
std::vector<float> y(x.size());

pitchshifter.shiftpitch(x, y, 1);

Optionally specify following CMake options for custom builds:

• -DBUILD_SHARED_LIBS=ON to enable a shared library build,
• -DVCPKG=ON to enable the vcpkg compatible library only build without executables,
• -DDEB=ON to enable the deb package build for library and main executable.

Python

The Python program stftpitchshift can be installed via pip install stftpitchshift.

Also feel free to explore the Python class StftPitchShift in your personal audio project:

from stftpitchshift import StftPitchShift

pitchshifter = StftPitchShift(1024, 256, 44100)

x = [0] * 44100
y = pitchshifter.shiftpitch(x, 1)

Usage

Both programs C++ and Python provides a similar set of command line options:

-h  --help       print this help
    --version    print version number

-i  --input      input .wav file name
-o  --output     output .wav file name

-p  --pitch      fractional pitch shifting factors separated by comma
                 (default 1.0)

-q  --quefrency  optional formant lifter quefrency in milliseconds
                 (default 0.0)

-r  --rms        enable spectral rms normalization

-w  --window     sfft window size
                 (default 1024)

-v  --overlap    stft window overlap
                 (default 32)

-c  --chrono     enable runtime measurements
                 (only available in the C++ version)

-d  --debug      plot spectrograms before and after processing
                 (only available in the Python version)

Currently only .wav files are supported. Please use e.g. Audacity or SoX to prepare your audio files for pitch shifting.

To apply multiple pitch shifts at once, separate each factor by a comma, e.g. -p 0.5,1,2. Alternatively specify pitch shifting factors as semitones denoted by the + or - prefix, e.g. -p -12,0,+12. For precise pitch corrections append the number of cents after semitones, e.g. -p -11-100,0,+11+100.

To enable the formant preservation feature specify a suitable quefrency value in milliseconds. Depending on the source signal, begin with a small value like -q 1. Generally, the quefrency value has to be smaller than the fundamental period, as reciprocal of the fundamental frequency, of the source signal.

At the moment the formant preservation doesn't seem to work well along with the multi pitch shifting and smaller pitch shifting factors. Further investigation is therefore necessary...

Further reading

Instantaneous frequency estimation

• Fundamentals of Music Processing by Meinard Müller (section 8.2.1 in the second edition or online)
• Digital Audio Effects by Udo Zölzer (sections 7.3.1 and 7.3.5 in the second edition)

Cepstrum analysis and formant changing

• Digital Audio Effects by Udo Zölzer (sections 8.2.3 and 8.3.2 in the second edition)
• Discrete-Time Signal Processing by Oppenheim & Schafer (chapter 13 in the third edition)

Credits

• cxxopts by Jarryd Beck
• dr_libs by David Reid

License

stftPitchShift is licensed under the terms of the MIT license. For details please refer to the accompanying LICENSE file distributed with stftPitchShift.