# shiftPitch

Shift audio pitch

## Syntax

``audioOut = shiftPitch(audioIn,nsemitones)``
``audioOut = shiftPitch(audioIn,nsemitones,Name,Value)``

## Description

example

````audioOut = shiftPitch(audioIn,nsemitones)` shifts the pitch of the audio input by the specified number of semitones, `nsemitones`.```

example

````audioOut = shiftPitch(audioIn,nsemitones,Name,Value)` specifies options using one or more `Name,Value` pair arguments.```

## Examples

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Read in an audio file and listen to it.

```[audioIn,fs] = audioread('Counting-16-44p1-mono-15secs.wav'); sound(audioIn,fs)```

Increase the pitch by 3 semitones and listen to the result.

```nsemitones = 3; audioOut = shiftPitch(audioIn,nsemitones); sound(audioOut,fs)```

Decrease the pitch of the original audio by 3 semitones and listen to the result.

```nsemitones = -3; audioOut = shiftPitch(audioIn,nsemitones); sound(audioOut,fs)```

Read in an audio file and listen to it.

```[audioIn,fs] = audioread("SpeechDFT-16-8-mono-5secs.wav"); sound(audioIn,fs)```

Convert the audio signal to a time-frequency representation using `stft`. Use a 512-point `kbdwin` with 75% overlap.

```win = kbdwin(512); overlapLength = 0.75*numel(win); S = stft(audioIn, ... "Window",win, ... "OverlapLength",overlapLength, ... "Centered",false);```

Increase the pitch by 8 semitones and listen to the result. Specify the window and overlap length you used to compute the STFT.

```nsemitones = 8; lockPhase = false; audioOut = shiftPitch(S,nsemitones, ... "Window",win, ... "OverlapLength",overlapLength, ... "LockPhase",lockPhase); sound(audioOut,fs)```

Decrease the pitch of the original audio by 8 semitones and listen to the result. Specify the window and overlap length you used to compute the STFT.

```nsemitones = -8; lockPhase = false; audioOut = shiftPitch(S,nsemitones, ... "Window",win, ... "OverlapLength",overlapLength, ... "LockPhase",lockPhase); sound(audioOut,fs)```

Read in an audio file and listen to it.

```[audioIn,fs] = audioread('FemaleSpeech-16-8-mono-3secs.wav'); sound(audioIn,fs)```

Increase the pitch by 6 semitones and listen to the result.

```nsemitones = 6; lockPhase = false; audioOut = shiftPitch(audioIn,nsemitones, ... 'LockPhase',lockPhase); sound(audioOut,fs)```

To increase fidelity, set `LockPhase` to `true`. Apply pitch shifting, and listen to the results.

```lockPhase = true; audioOut = shiftPitch(audioIn,nsemitones, ... 'LockPhase',lockPhase); sound(audioOut,fs)```

Read in the first 11.5 seconds of an audio file and listen to it.

```[audioIn,fs] = audioread('Rainbow-16-8-mono-114secs.wav',[1,8e3*11.5]); sound(audioIn,fs)```

Increase the pitch by 4 semitones and apply phase locking. Listen to the results. The resulting audio has a "chipmunk effect" that sounds unnatural.

```nsemitones = 4; lockPhase = true; audioOut = shiftPitch(audioIn,nsemitones, ... "LockPhase",lockPhase); sound(audioOut,fs)```

To increase fidelity, set `PreserveFormants` to `true`. Use the default cepstral order of `30`. Listen to the result.

```cepstralOrder = 30; audioOut = shiftPitch(audioIn,nsemitones, ... "LockPhase",lockPhase, ... "PreserveFormants",true, ... "CepstralOrder",cepstralOrder); sound(audioOut,fs)```

## Input Arguments

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Input signal, specified as a column vector, matrix, or 3-D array. How the function interprets `audioIn` depends on the complexity of `audioIn`:

• If `audioIn` is real, `audioIn` is interpreted as a time-domain signal. In this case, `audioIn` must be a column vector or matrix. Columns are interpreted as individual channels.

• If `audioIn` is complex, `audioIn` is interpreted as a frequency-domain signal. In this case, `audioIn` must be an L-by-M-by-N array, where L is the FFT length, M is the number of individual spectrums, and N is the number of channels.

Data Types: `single` | `double`
Complex Number Support: Yes

Number of semitones to shift the audio by, specified as a real scalar.

The range of `nsemitones` depends on the window length (`numel(Window)`) and the overlap length (`OverlapLength`):

`-12*log2(numel(Window)-OverlapLength)``nsemitones``-12*log2((numel(Window)-OverlapLength)/numel(Window))`

Data Types: `single` | `double`

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `'Window',kbdwin(512)`

Window applied in the time domain, specified as the comma-separated pair consisting of `'Window'` and a real vector. The number of elements in the vector must be in the range [1, `size(audioIn,1)`]. The number of elements in the vector must also be greater than `OverlapLength`.

Note

If using `shiftPitch` with frequency-domain input, you must specify `Window` as the same window used to transform `audioIn` to the frequency domain.

Data Types: `single` | `double`

Number of samples overlapped between adjacent windows, specified as the comma-separated pair consisting of `'OverlapLength'` and an integer in the range [0, `numel(Window)`).

Note

If using `shiftPitch` with frequency-domain input, you must specify `OverlapLength` as the same overlap length used to transform `audioIn` to a time-frequency representation.

Data Types: `single` | `double`

Apply identity phase locking, specified as the comma-separated pair consisting of `'LockPhase'` and `false` or `true`.

Data Types: `logical`

Preserves formants, specified as the comma-separated pair consisting of `'PreserveFormants'` and `true` or `false`. Formant preservation is attempted using spectral envelope estimation with cepstral analysis.

Data Types: `logical`

Cepstral order used for formant preservation, specified as the comma-separated pair consisting of `'CepstralOrder'` and a nonnegative integer.

#### Dependencies

To enable this name-value pair argument, set `PreserveFormants` to `true`.

Data Types: `single` | `double`

## Output Arguments

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Pitch-shifted audio, returned as a column vector or matrix of independent channels.

## Algorithms

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To apply pitch shifting, `shiftPitch` modifies the time-scale of audio using a phase vocoder and then resamples the modified audio. The time scale modification algorithm is based on [1] and [2] and is implemented as in `stretchAudio`.

After time-scale modification, `shiftPitch` performs sample rate conversion using an interpolation factor equal to the analysis hop length and a decimation factor equal to the synthesis hop length. The interpolation and decimation factors of the resampling stage are selected as follows: The analysis hop length is determined as ```analysisHopLength = numel(Window)-OverlapLength```. The `shiftPitch` function assumes that there are 12 semitones in an octave, so the speedup factor used to stretch the audio is ```speedupFactor = 2^(-nsemitones/12)```. The speedup factor and analysis hop length determine the synthesis hop length for time-scale modification as `synthesisHopLength = round((1/SpeedupFactor)*analysisHopLength)`.

The achievable pitch shift is determined by the window length (`numel(Window)`) and `OverlapLength`. To see the relationship, note that the equation for speedup factor can be rewritten as: ```nsemitones = -12*log2(speedupFactor)```, and the equation for synthesis hop length can be rewritten as `speedupFactor = analysisHopLengh/synthesisHopLength`. Using simple substitution, ```nsemitones = -12*log2(analysisHopLength/synthesisHopLength)```. The practical range of a synthesis hop length is [1, `numel(Window)`]. The range of achievable pitch shifts is:

• Max number of semitones lowered: `-12*log2(numel(Window)-OverlapLength)`

• Max number of semitones raised: `-12*log2((numel(Window)-OverlapLength)/numel(Window))`

### Formant Preservation

Pitch shifting can alter the spectral envelope of the pitch-shifted signal. To diminish this effect, you can set `PreserveFormants` to `true`. If `PreserveFormants` is set to `true`, the algorithm attempts to estimate the spectral envelope using an iterative procedure in the cepstral domain, as described in [3] and [4]. For both the original spectrum, X, and the pitch-shifted spectrum, Y, the algorithm estimates the spectral envelope as follows.

For the first iteration, EnvXa is set to X. Then, the algorithm repeats these two steps in a loop:

1. Lowpass filters the cepstral representation of EnvXa to get a new estimate, EnvXb. The `CepstralOrder` parameter controls the quefrency bandwidth.

2. To update the current best fit, the algorithm takes the element-by-element maximum of the current spectral envelope estimate and the previous spectral envelope estimate:

`$Env{X}_{\text{a}}=\mathrm{max}\left(Env{X}_{\text{a}},Env{X}_{\text{b}}\right).$`

The loop ends if either a maximum number of iterations (`100`) is reached, or if all bins of the estimated log envelope are within a given tolerance of the original log spectrum. The tolerance is set to `log(10^(1/20))`.

Finally, the algorithm scales the spectrum of the pitch-shifted audio by the ratio of estimated envelopes, element-wise:

`$Y=Y×\left(\frac{Env{X}_{\text{b}}}{Env{Y}_{\text{b}}}\right).$`

## References

[1] Driedger, Johnathan, and Meinard Müller. "A Review of Time-Scale Modification of Music Signals." Applied Sciences. Vol. 6, Issue 2, 2016.

[2] Driedger, Johnathan. "Time-Scale Modification Algorithms for Music Audio Signals." Master's Thesis. Saarland University, Saarbrücken, Germany, 2011.

[3] Axel Roebel, and Xavier Rodet. "Efficient Spectral Envelope Estimation and its application to pitch shifting and envelope preservation." International Conference on Digital Audio Effects, pp. 30–35. Madrid, Spain, September 2005. hal-01161334

[4] S. Imai, and Y. Abe. "Spectral envelope extraction by improved cepstral method." Electron. and Commun. in Japan. Vol. 62-A, Issue 4, 1997, pp. 10–17.

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