stftpitchshift 1.2

STFT based multi pitch shifting with optional formant preservation.

stftPitchShift

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

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

Vocoder

The Vocoder module transforms the DFT spectral data according to the original algorithm, which is actually the instantaneous frequency estimation technique. See also further reading for more details.

The particular encode function replaces the input DFT values by the magnitude + j * frequency complex numbers, representing the phase error based frequency estimation in the imaginary part.

The decode function does an inverse transformation back to the original DFT complex numbers, by replacing eventually modified frequency value by the reconstructed phase value.

Pitcher

The Pitcher module performs single or multi pitch shifting of the encoded DFT frame depending on the specified fractional factors.

Resampler

The Resampler module provides linear and bilinear interpolation routines, to actually perform pitch shifting, based on the Vocoder DFT transform.

Cepstrum

The Cepstrum module estimates a spectral envelope of the DFT magnitude vector, representing the vocal tract resonances. This computation takes place in the cepstral domain by applying a low-pass filter. The cutoff value of the low-pass filter or lifter is the quefrency value to be specified in seconds or milliseconds.

STFT

As the name of this module already implies, it performs the comprehensive STFT analysis and synthesis steps.

IO

The IO module provides a simple possibility to read and write .wav audio files.

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

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. Since the strongest magnitude will mask the weakest one. Thus, all remaining masked frequency values would be inaudible and can therefore be omitted.

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

Will soon appear...

Build

C++

Use CMake to build the C++ program and library like so:

mkdir build
cd build
cmake ..
cmake --build .

To include this library in your C++ audio project, check the LibStftPitchShift.cmake file and the following minimal example:

#include <StftPitchShift/StftPitchShift.h>

StftPitchShift pitchshifter(1024, 256, 44100);

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

pitchshifter.shiftpitch(x, y, 1);

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)

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

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

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

    --smb        enable original smb algorithm
                 (only available in the C++ version)

To apply multiple pitch shifts at once, separate each factor by a comma, e.g. -p 0.5,1,2.

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

• anyoption by Kishan Thomas
• dr_libs by David Reid
• pocketfft by Martin Reinecke
• smbPitchShift.cpp by Stephan M. Bernsee