Signalsmith Audio DSP Library

https://signalsmith-audio.co.uk/code/dsp
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### Reciprocal and Start Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions_func.html

Methods for reciprocal calculations and starting signal processes.

```APIDOC
## Reciprocal()

### Description
Initializes a reciprocal calculation object.

### Method
Constructor

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Returns a Reciprocal object.

#### Success Response (200)
- **Reciprocal< Sample >** - The initialized Reciprocal object.

#### Response Example
None
```

```APIDOC
## then()

### Description
Chains operations, likely for reciprocal calculations.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Returns a chained Reciprocal object.

#### Success Response (200)
- **Reciprocal< Sample >** - The chained Reciprocal object.

#### Response Example
None
```

```APIDOC
## start()

### Description
Starts a cubic interpolation process.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Starts the cubic interpolation.

#### Success Response (200)
- **Cubic< Sample >** - The cubic interpolation object.

#### Response Example
None
```

--------------------------------

### Example Usage of Version Check

Source: https://signalsmith-audio.co.uk/code/dsp/html/group___common.html

An example demonstrating how to use the `signalsmith::versionCheck` function or the `SIGNALSMITH_DSP_VERSION_CHECK` macro to assert version compatibility.

```c++
static_assert(signalsmith::version(1, 4, 1), "version check");
... or use the equivalent `SIGNALSMITH_DSP_VERSION_CHECK`.
```

--------------------------------

### Start and STFT Functions

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions.html

Functions for starting curve operations and Short-Time Fourier Transform.

```APIDOC
## start()

### Description
Starts a cubic curve operation.

### Method
N/A (Method within a class)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
N/A

### Response
Starts the operation on `signalsmith::curves::Cubic< Sample >`.

## STFT()

### Description
Constructs an `STFT` object for spectral analysis.

### Method
N/A (Constructor)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
N/A

### Response
Returns a `signalsmith::spectral::STFT< Sample >` object.
```

--------------------------------

### Get Cubic Curve Start Point

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1curves_1_1_cubic.html

The `start()` method returns the reference x-value, which is used as the center of the cubic expansion. This value is fundamental to how the curve is defined and evaluated.

```cpp
Sample | start () const
```

```cpp
template<typename Sample = double>
| Sample signalsmith::curves::Cubic< Sample >::start  | ( | __| ) |  const
inline
```

--------------------------------

### Include and Use Delay Class in C++

Source: https://signalsmith-audio.co.uk/code/dsp

Include the delay header and instantiate a delay line. This example shows basic usage of the delay tools within the library.

```cpp
#include "dsp/delay.h";

using Delay = signalsmith::delay::Delay<float>;
Delay delayLine(1024);
```

--------------------------------

### Cubic::hermite() Static Method

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1curves_1_1_cubic.html

Details on how to create a cubic curve segment using start and end values along with their gradients.

```APIDOC
## Static Method signalsmith::curves::Cubic::hermite()

### Description

Cubic segment based on start/end values and gradients.

### Signature

```cpp
template<typename Sample = double>
static Cubic signalsmith::curves::Cubic< Sample >::hermite(Sample x0, Sample x1, Sample y0, Sample y1, Sample g0, Sample g1)
```

### Parameters

* **x0** (Sample) - The starting x-coordinate.
* **x1** (Sample) - The ending x-coordinate.
* **y0** (Sample) - The starting y-coordinate.
* **y1** (Sample) - The ending y-coordinate.
* **g0** (Sample) - The gradient at the starting point.
* **g1** (Sample) - The gradient at the ending point.

### Returns

A `Cubic` segment representing the defined curve.
```

--------------------------------

### Set FFT Size and Get Window

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Sets the FFT size and returns a reference to the window vector for modification. The window is initially filled with ones.

```cpp
std::vector< Sample > & setSizeWindow (int size, int rotateSamples=0)
```

--------------------------------

### Run All Tests using Make

Source: https://signalsmith-audio.co.uk/code/dsp

Execute all tests for the DSP library using the 'make test' command. This is the standard way to run the test suite.

```bash
make test
```

--------------------------------

### Differentiate Cubic Curve

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1curves_1_1_cubic.html

The `dx()` method differentiates the cubic curve. This can be called without arguments to get the derivative of the curve at its reference start point, or with an x-value to get the derivative at that specific point.

```cpp
Cubic | dx () const
```

```cpp
Sample | dx (Sample x) const
```

```cpp
template<typename Sample = double>
| Cubic signalsmith::curves::Cubic< Sample >::dx  | ( | __| ) |  const
inline
```

```cpp
template<typename Sample = double>
| Sample signalsmith::curves::Cubic< Sample >::dx  | ( | Sample | _x_ ) |  const
inline
```

--------------------------------

### Cubic::start() Method

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1curves_1_1_cubic.html

Retrieves the reference x-value used as the center of the cubic expansion.

```APIDOC
## Method signalsmith::curves::Cubic::start()

### Description

The reference x-value, used as the centre of the cubic expansion.

### Signature

```cpp
template<typename Sample = double>
Sample signalsmith::curves::Cubic< Sample >::start() const
```

### Returns

The reference x-value (`Sample` type).
```

--------------------------------

### Initialize WindowedFFT with Size

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Constructs a WindowedFFT object with a specified size and rotation samples.

```cpp
WindowedFFT (int size, int rotateSamples=0)
```

--------------------------------

### Get FFT Size

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Returns the current size of the FFT.

```cpp
int size () const
```

--------------------------------

### Initialize WindowedFFT with Custom Window Function

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Constructs a WindowedFFT object with a specified size, a custom window function, window offset, and rotation samples.

```cpp
template<class WindowFn>
WindowedFFT (int size, WindowFn fn, Sample windowOffset=0.5, int rotateSamples=0)
```

--------------------------------

### Get Window Vector

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Returns a constant reference to the window vector used by the FFT.

```cpp
const std::vector< Sample > & window () const
```

--------------------------------

### BiquadStatic Response Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1filters_1_1_biquad_static-members.html

Provides details on how to get the frequency response and decibel response of a Biquad filter.

```APIDOC
## BiquadStatic Response Methods

### Description
These methods calculate the frequency response of the Biquad filter.

### Methods

#### `response(Sample scaledFreq) const`
Calculates the frequency response of the Biquad filter.

- **`scaledFreq`** (Sample) - The scaled frequency to evaluate.

#### `responseDb(Sample scaledFreq) const`
Calculates the frequency response of the Biquad filter in decibels (dB).

- **`scaledFreq`** (Sample) - The scaled frequency to evaluate.

### Defined In
signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
```

--------------------------------

### RealFFT Static Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1fft_1_1_real_f_f_t.html

Static methods for determining appropriate FFT sizes. Use `fastSizeAbove` to find the next suitable size greater than or equal to the input, and `fastSizeBelow` for the largest suitable size less than or equal to the input.

```cpp
static size_t | **fastSizeAbove** (size_t size)
static size_t | **fastSizeBelow** (size_t size)
```

--------------------------------

### Class Members Documentation

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions.html

This section lists all documented class members, categorized by their starting letter, with links to their respective class documentation.

```APIDOC
## Class Members Documentation

This section lists all documented class members, categorized by their starting letter, with links to their respective class documentation.

### - a -

*   **add()** : `signalsmith::curves::CubicSegmentCurve< Sample >`
*   **analyse()** : `signalsmith::spectral::STFT< Sample >`
*   **analyseRaw()** : `signalsmith::spectral::STFT< Sample >`

### - b -

*   **bandpass()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **bandStop()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **bandwidthToBeta()** : `signalsmith::windows::Kaiser`
*   **bandwidthToEnbw()** : `signalsmith::windows::Kaiser`
*   **bandwidthToEnergyDb()** : `signalsmith::windows::Kaiser`
*   **bandwidthToPeakDb()** : `signalsmith::windows::Kaiser`
*   **bandwidthToSigma()** : `signalsmith::windows::ApproximateConfinedGaussian`
*   **barkRange()** : `signalsmith::curves::Reciprocal< Sample >`
*   **barkScale()** : `signalsmith::curves::Reciprocal< Sample >`

### - c -

*   **clear()** : `signalsmith::curves::CubicSegmentCurve< Sample >`

### - d -

*   **Delay()** : `signalsmith::delay::Delay< Sample, Interpolator >`
*   **down()** : `signalsmith::rates::Oversampler2xFIR< Sample >`
*   **downChannel()** : `signalsmith::rates::Oversampler2xFIR< Sample >`
*   **dx()** : `signalsmith::curves::Cubic< Sample >`

### - e -

*   **ensureValid()** : `signalsmith::spectral::STFT< Sample >`

### - f -

*   **fastSizeAbove()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **fastSizeBelow()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **fft()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **fftRaw()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **fill()** : `signalsmith::windows::ApproximateConfinedGaussian`, `signalsmith::windows::Kaiser`

### - g -

*   **get()** : `signalsmith::delay::MultiBuffer< Sample >::Stride< isConst >`

### - h -

*   **hermite()** : `signalsmith::curves::Cubic< Sample >`
*   **highpass()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **highShelf()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **highShelfDb()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`

### - i -

*   **ifft()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **ifftRaw()** : `signalsmith::spectral::WindowedFFT< Sample >`
*   **inPlace()** : `signalsmith::mix::Hadamard< Sample, size >`, `signalsmith::mix::Hadamard< Sample, -1 >`, `signalsmith::mix::Householder< Sample, size >`, `signalsmith::mix::Householder< Sample, -1 >`
*   **inverse()** : `signalsmith::curves::Linear< Sample >`

### - k -

*   **Kaiser()** : `signalsmith::windows::Kaiser`

### - l -

*   **latency()** : `signalsmith::rates::Oversampler2xFIR< Sample >`, `signalsmith::spectral::ProcessSTFT< Sample >`, `signalsmith::spectral::STFT< Sample >`
*   **layersToBandwidth()** : `signalsmith::envelopes::BoxStackFilter< Sample >`
*   **layersToPeakDb()** : `signalsmith::envelopes::BoxStackFilter< Sample >`
*   **Linear()** : `signalsmith::curves::Linear< Sample >`
*   **lowpass()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **lowShelf()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **lowShelfDb()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`

### - n -

*   **next()** : `signalsmith::envelopes::CubicLfo`
*   **nextInvalid()** : `signalsmith::spectral::STFT< Sample >`
*   **notch()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`

### - o -

*   **operator()()** : `signalsmith::curves::CubicSegmentCurve< Sample >`, `signalsmith::windows::Kaiser`
*   **operator[]()** : `signalsmith::rates::Oversampler2xFIR< Sample >`
*   **optimalRatios()** : `signalsmith::envelopes::BoxStackFilter< Sample >`

### - p -

*   **partialSumWindow()** : `signalsmith::spectral::STFT< Sample >`
*   **peak()** : `signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >`
*   **processSpectrum()** : `signalsmith::spectral::ProcessSTFT< Sample >`
```

--------------------------------

### Kaiser Constructor Details

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1windows_1_1_kaiser.html

Detailed documentation for the Kaiser window constructor.

```APIDOC
## Constructor & Destructor Documentation

### `Kaiser()`

**Description:** Set up a Kaiser window with a given shape. `beta` is `pi*alpha` (since there is ambiguity about shape parameters).
```

--------------------------------

### Signalsmith Audio DSP Library Functions

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions_func.html

This section lists the functions available in the Signalsmith Audio DSP Library, categorized by their starting letter.

```APIDOC
## Signalsmith Audio DSP Library Functions

This documentation lists the functions available in the Signalsmith Audio DSP Library.

### Functions by Alphabetical Order

#### - a -
* `add()` : signalsmith::curves::CubicSegmentCurve< Sample >
* `analyse()` : signalsmith::spectral::STFT< Sample >
* `analyseRaw()` : signalsmith::spectral::STFT< Sample >

#### - b -
* `bandpass()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `bandStop()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `bandwidthToBeta()` : signalsmith::windows::Kaiser
* `bandwidthToEnbw()` : signalsmith::windows::Kaiser
* `bandwidthToEnergyDb()` : signalsmith::windows::Kaiser
* `bandwidthToPeakDb()` : signalsmith::windows::Kaiser
* `bandwidthToSigma()` : signalsmith::windows::ApproximateConfinedGaussian
* `barkRange()` : signalsmith::curves::Reciprocal< Sample >
* `barkScale()` : signalsmith::curves::Reciprocal< Sample >

#### - c -
* `clear()` : signalsmith::curves::CubicSegmentCurve< Sample >

#### - d -
* `Delay()` : signalsmith::delay::Delay< Sample, Interpolator >
* `down()` : signalsmith::rates::Oversampler2xFIR< Sample >
* `downChannel()` : signalsmith::rates::Oversampler2xFIR< Sample >
* `dx()` : signalsmith::curves::Cubic< Sample >

#### - e -
* `ensureValid()` : signalsmith::spectral::STFT< Sample >

#### - f -
* `fastSizeAbove()` : signalsmith::spectral::WindowedFFT< Sample >
* `fastSizeBelow()` : signalsmith::spectral::WindowedFFT< Sample >
* `fft()` : signalsmith::spectral::WindowedFFT< Sample >
* `fftRaw()` : signalsmith::spectral::WindowedFFT< Sample >
* `fill()` : signalsmith::windows::ApproximateConfinedGaussian, signalsmith::windows::Kaiser

#### - g -
* `get()` : signalsmith::delay::MultiBuffer< Sample >::Stride< isConst >

#### - h -
* `hermite()` : signalsmith::curves::Cubic< Sample >
* `highpass()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `highShelf()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `highShelfDb()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >

#### - i -
* `ifft()` : signalsmith::spectral::WindowedFFT< Sample >
* `ifftRaw()` : signalsmith::spectral::WindowedFFT< Sample >
* `inPlace()` : signalsmith::mix::Hadamard< Sample, size >, signalsmith::mix::Hadamard< Sample, -1 >, signalsmith::mix::Householder< Sample, size >, signalsmith::mix::Householder< Sample, -1 >
* `inverse()` : signalsmith::curves::Linear< Sample >

#### - k -
* `Kaiser()` : signalsmith::windows::Kaiser

#### - l -
* `latency()` : signalsmith::rates::Oversampler2xFIR< Sample >, signalsmith::spectral::ProcessSTFT< Sample >, signalsmith::spectral::STFT< Sample >
* `layersToBandwidth()` : signalsmith::envelopes::BoxStackFilter< Sample >
* `layersToPeakDb()` : signalsmith::envelopes::BoxStackFilter< Sample >
* `Linear()` : signalsmith::curves::Linear< Sample >
* `lowpass()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `lowShelf()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `lowShelfDb()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >

#### - n -
* `next()` : signalsmith::envelopes::CubicLfo
* `nextInvalid()` : signalsmith::spectral::STFT< Sample >
* `notch()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >

#### - o -
* `operator()`() : signalsmith::curves::CubicSegmentCurve< Sample >, signalsmith::windows::Kaiser
* `operator[]()` : signalsmith::rates::Oversampler2xFIR< Sample >
* `optimalRatios()` : signalsmith::envelopes::BoxStackFilter< Sample >

#### - p -
* `partialSumWindow()` : signalsmith::spectral::STFT< Sample >
* `peak()` : signalsmith::filters::BiquadStatic< Sample, cookbookBandwidth >
* `processSpectrum()` : signalsmith::spectral::ProcessSTFT< Sample >
```

--------------------------------

### Static Methods for Fast FFT Size Calculation

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Details on static methods for determining appropriate FFT sizes.

```APIDOC
## Static Methods

### `fastSizeAbove(int size, int divisor=1)`

**Description**: Returns a fast FFT size less than or equal to `size`.

**Parameters**:
- `size` (int) - The maximum size for the FFT.
- `divisor` (int, optional) - A divisor to consider for fast sizes. Defaults to 1.

### `fastSizeBelow(int size, int divisor=1)`

**Description**: Returns a fast FFT size greater than or equal to `size`.

**Parameters**:
- `size` (int) - The minimum size for the FFT.
- `divisor` (int, optional) - A divisor to consider for fast sizes. Defaults to 1.
```

--------------------------------

### ProcessSTFT Process Spectrum

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_process_s_t_f_t.html

Allows subclasses to alter the spectrum using input up to the current point for the output block starting from the current point.

```APIDOC
## processSpectrum()

### Description
Alter the spectrum, using input up to this point, for the output block starting from this point. Sub-classes should replace this with whatever processing is desired.

### Method
POST (Implicit, as it modifies state)

### Endpoint
N/A (Class member)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
None

### Response
#### Success Response (200)
None (void return type)

#### Response Example
None
```

--------------------------------

### Kaiser Method Details - bandwidthToBeta

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1windows_1_1_kaiser.html

Detailed explanation of the `bandwidthToBeta` static method.

```APIDOC
## Method Details

### `static double bandwidthToBeta(double bandwidth, bool heuristicOptimal = false)`

**Description:** Returns the Kaiser shape where the main lobe has the specified bandwidth (as a factor of 1/window-length). The main lobe extends to ±bandwidth/2. If `heuristicOptimal` is enabled, the main lobe width is slightly wider, improving both the peak and total energy.

**Parameters:**
- **bandwidth** (double) - The desired main lobe bandwidth.
- **heuristicOptimal** (bool) - Optional. If true, uses a heuristic for optimal performance. Defaults to false.
```

--------------------------------

### Include and Use Delay Line Class

Source: https://signalsmith-audio.co.uk/code/dsp/html/index.html

Include the delay header and instantiate a single-channel delay-line. Ensure you have a compatible version of the library.

```cpp
#include "dsp/delay.h"
using Delay = signalsmith::delay::Delay<float>;
Delay delayLine(1024);
```

--------------------------------

### Get Fast FFT Size Below

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Returns a fast FFT size that is greater than or equal to the specified size. Useful for optimizing FFT operations.

```cpp
static int fastSizeBelow (int size, int divisor=1)
```

--------------------------------

### Get Fast FFT Size Above

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Returns a fast FFT size that is less than or equal to the specified size. Useful for optimizing FFT operations.

```cpp
static int fastSizeAbove (int size, int divisor=1)
```

--------------------------------

### Clone DSP Documentation Repository using Git

Source: https://signalsmith-audio.co.uk/code/dsp

Clone the repository containing tests, plotting scripts, and documentation for the DSP library. This is separate from the main library code.

```bash
git clone https://signalsmith-audio.co.uk/code/dsp-doc.git
```

--------------------------------

### Get Next CubicLfo Sample

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1envelopes_1_1_cubic_lfo.html

Retrieve the next output sample from the CubicLfo. The LFO completes a full oscillation in approximately 1/rate samples.

```cpp
float sample = lfo.next();
```

--------------------------------

### MultiBuffer Stride Get Method

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1delay_1_1_multi_buffer_1_1_stride.html

Reads multi-channel data from the buffer into a provided result structure. Ensure the Data type is compatible for reading.

```cpp
template<typename Sample>
template<bool isConst>
template<class Data>
void
signalsmith::delay::MultiBuffer< Sample >::Stride< isConst >::get
(
Data &&
_result_
)
const
```

--------------------------------

### Clone DSP Library using Git

Source: https://signalsmith-audio.co.uk/code/dsp

Clone the main DSP library repository using Git. This command fetches all necessary header files for the DSP tasks.

```bash
git clone https://signalsmith-audio.co.uk/code/dsp.git
```

--------------------------------

### Cubic Class Constructor

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1curves_1_1_cubic.html

Constructs a Cubic object using the specified start x-value and the coefficients (a0, a1, a2, a3) of the cubic polynomial.

```cpp
Cubic | Cubic (Sample xStart, Sample a0, Sample a1, Sample a2, Sample a3)
```

--------------------------------

### Perform FFT with Windowing and Scaling

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Performs a Fast Fourier Transform on the input data, with optional windowing and rotation enabled. The output is stored in the provided output container.

```cpp
template<bool withWindow = true, bool withScaling = false, class Input, class Output>
void fft (Input &&input, Output &&output)
```

--------------------------------

### Upsample, Modify, and Downsample Audio Data

Source: https://signalsmith-audio.co.uk/code/dsp/html/structsignalsmith_1_1rates_1_1_oversampler2x_f_i_r.html

Demonstrates the usage of the Oversampler2xFIR class for block-based audio processing. It shows how to upsample input buffers, modify the oversampled data, and then downsample it to the output. Ensure input and output channel counts are handled correctly, potentially by sizing to the larger count and using `.upChannel()` and `.downChannel()`.

```cpp
#include <rates.h>

// Upsample from multi-channel input (inputBuffers[c][i] is a sample)
oversampler.up(inputBuffers, bufferLength)
// Modify the contents at the higher rate
for (int c = 0; c < 2; ++c) {
float *channel = oversampler[c];
for (int i = 0; i < bufferLength*2; ++i) {
channel[i] = std::abs(channel[i]);
}
}
// Downsample into the multi-channel output
oversampler.down(outputBuffers, bufferLength);
```

--------------------------------

### Get Hadamard Matrix Scaling Factor

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1mix_1_1_hadamard.html

Retrieves the scaling factor applied to make the Hadamard matrix orthogonal. This is useful for understanding the normalization applied.

```cpp
static Sample scalingFactor ()
```

--------------------------------

### MultiDelay::read() Method

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1delay_1_1_multi_delay.html

Details the `read` method for reading samples into an output structure.

```APIDOC
## ◆ read()

### Description
Reads into the provided output structure.

### Signature
```cpp
template<class Sample, template< typename > class Interpolator = InterpolatorLinear>
template<class Output>
void signalsmith::delay::MultiDelay< Sample, Interpolator >::read(Sample delaySamples, Output &output)
```

### Parameters
- **delaySamples** (Sample): The delay in samples.
- **output** (Output &): The output structure to read into.
```

--------------------------------

### Kaiser Method Details - bandwidthToEnergyDb

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1windows_1_1_kaiser.html

Detailed explanation of the `bandwidthToEnergyDb` static method.

```APIDOC
## Method Details

### `static double bandwidthToEnergyDb(double bandwidth, bool heuristicOptimal = false)`

**Description:** Total energy ratio (in dB) between side-lobes and the main lobe. This function uses an approximation which is accurate to ±0.5dB for 2 ⩽ bandwidth ≤ 10, or 1 ⩽ bandwidth ≤ 10 when `heuristicOptimal` is enabled. The heuristic improves performance for all bandwidth values.

**Parameters:**
- **bandwidth** (double) - The main lobe bandwidth.
- **heuristicOptimal** (bool) - Optional. If true, uses a heuristic for optimal performance. Defaults to false.
```

--------------------------------

### Get Oversampler2xFIR Latency

Source: https://signalsmith-audio.co.uk/code/dsp/html/structsignalsmith_1_1rates_1_1_oversampler2x_f_i_r.html

Returns the round-trip latency of the Oversampler2xFIR, which is equivalent to the upsample latency at the higher rate. This value is twice the half latency specified during construction or resize.

```cpp
int latency() const
```

--------------------------------

### CubicLfo Class Documentation

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1envelopes_1_1_cubic_lfo.html

Detailed documentation for the CubicLfo class, including its constructor, methods, and parameter explanations.

```APIDOC
## Class signalsmith::envelopes::CubicLfo

### Description
An LFO based on cubic segments. You can randomise the rate and/or the depth. Randomising the depth past `0.5` means it no longer neatly alternates sides.

### Methods

- **CubicLfo** (long seed)
- void **reset** ()
  Resets the LFO state, starting with random phase.
- void **set** (float low, float high, float rate, float rateVariation=0, float depthVariation=0)
  Smoothly updates the LFO parameters. If called directly after `.reset()`, oscillation will immediately start within the specified range. Otherwise, it will remain smooth and fit within the new range after at most one cycle. The LFO will complete a full oscillation in (approximately) `1/rate` samples. `rateVariation` can be any number, but 0-1 is a good range. `depthVariation` must be in the range [0, 1], where ≤ 0.5 produces random amplitude but still alternates up/down.
- float **next** ()
  Returns the next output sample.

### Method Details

#### ◆ next()

```cpp
float signalsmith::envelopes::CubicLfo::next() const
```

**Description:** Returns the next output sample.

#### ◆ reset()

```cpp
void signalsmith::envelopes::CubicLfo::reset()
```

**Description:** Resets the LFO state, starting with random phase.

#### ◆ set()

```cpp
void signalsmith::envelopes::CubicLfo::set(float low, float high, float rate, float rateVariation = 0, float depthVariation = 0)
```

**Description:** Smoothly updates the LFO parameters.

**Parameters:**
- **low** (float) - The lower bound of the LFO oscillation.
- **high** (float) - The upper bound of the LFO oscillation.
- **rate** (float) - The base rate of the LFO in cycles per sample.
- **rateVariation** (float, optional) - Variation in the LFO rate. Defaults to 0.
- **depthVariation** (float, optional) - Variation in the LFO depth. Must be in the range [0, 1]. Defaults to 0.
```

--------------------------------

### Ensure Valid Output (from index 0)

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_s_t_f_t.html

Ensures valid output starting from index 0, using a callback function `fn` to generate spectra. This is a convenience overload for ensuring validity from the beginning.

```cpp
template<typename Sample>
template<class AnalysisFn>
inline void signalsmith::spectral::STFT< Sample >::ensureValid(AnalysisFn _fn_)
```

--------------------------------

### STFT Constructor

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_s_t_f_t.html

Initializes the STFT object with specified parameters for audio analysis.

```APIDOC
## STFT Constructor

### Description
Initializes the STFT object with the number of channels, window size, interval, history length, and zero padding.

### Method
`STFT(int _channels, int _windowSize, int _interval, int _historyLength = 0, int _zeroPadding = 0)`

### Parameters
- **_channels** (int) - The number of audio channels.
- **_windowSize** (int) - The size of the analysis window.
- **_interval** (int) - The interval between consecutive analysis windows.
- **_historyLength** (int) - Optional. The length of the history buffer. Defaults to 0.
- **_zeroPadding** (int) - Optional. The amount of zero padding to apply. Defaults to 0.

### Request Example
```json
{
  "_channels": 2,
  "_windowSize": 1024,
  "_interval": 512,
  "_historyLength": 0,
  "_zeroPadding": 0
}
```

### Response
#### Success Response (200)
- **STFT object** - A newly constructed STFT object.

#### Response Example
```json
{
  "message": "STFT object created successfully"
}
```
```

--------------------------------

### Ensure Valid Output (with index)

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_s_t_f_t.html

Generates valid output up to a specified index `i` (or 0). It uses a callback function `fn` to generate spectra as needed. The generated block starts at index `i` plus the `.latency()`.

```cpp
template<typename Sample>
template<class AnalysisFn>
inline void signalsmith::spectral::STFT< Sample >::ensureValid(int _i_, AnalysisFn _fn_)
```

--------------------------------

### Run Specific Tests using Make

Source: https://signalsmith-audio.co.uk/code/dsp

Run tests only for a specific module, such as the delay module, using 'make test-delay'. This allows for targeted testing.

```bash
make test-delay
```

--------------------------------

### Set FFT Size and Get Window for Modification

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Sets the FFT size and returns a reference to the window vector, which is initially filled with 1s, allowing for direct modification. The `_rotateSamples_` parameter controls sample rotation.

```cpp
template<typename Sample>
std::vector< Sample > & signalsmith::spectral::WindowedFFT< Sample >::setSizeWindow(
    int _size_,
    int _rotateSamples_ = 0
) inline
```

--------------------------------

### lowShelfDb()

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1filters_1_1_biquad_static.html

Applies a low-shelf filter with gain in dB and bandwidth.

```APIDOC
## lowShelfDb()

### Description
Applies a low-shelf filter with gain specified in decibels (dB) and bandwidth.

### Method
`BiquadStatic &`

### Endpoint
N/A (C++ function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
None

### Response
#### Success Response (200)
None

#### Response Example
None

**Deprecated**: use `BiquadDesign` instead
```

--------------------------------

### STFT and Window Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions_func.html

Methods related to Short-Time Fourier Transform (STFT) and windowing.

```APIDOC
## STFT()

### Description
Initializes a Short-Time Fourier Transform (STFT) object.

### Method
Constructor

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Returns an STFT object.

#### Success Response (200)
- **STFT< Sample >** - The initialized STFT object.

#### Response Example
None
```

```APIDOC
## window()

### Description
Applies a window function for STFT analysis.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Returns the windowed STFT object.

#### Success Response (200)
- **STFT< Sample >** - The STFT object with applied window.

#### Response Example
None
```

--------------------------------

### Set CubicLfo Parameters

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1envelopes_1_1_cubic_lfo.html

Smoothly update the LFO's low, high, rate, and variation parameters. If called after reset, oscillation starts immediately. Otherwise, it smoothly fits within the new range after at most one cycle.

```cpp
lfo.set(0.0f, 1.0f, 440.0f, 0.1f, 0.2f);
```

--------------------------------

### Kaiser Window Methods and Constructor

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1windows_1_1_kaiser.html

Details the constructor and core methods for the Kaiser window class.

```APIDOC
## Methods

### `Kaiser(double beta)`

**Description:** Set up a Kaiser window with a given shape parameter `beta`. `beta` is typically `pi * alpha`.

### `double operator()(double unit)`

**Description:** Returns the window's value for a given position in the range [0, 1].

### `template<typename Data> void fill(Data &&data, int size) const`

**Description:** Fills an arbitrary container with Kaiser window values.
```

--------------------------------

### Include Windows Header

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1windows_1_1_approximate_confined_gaussian.html

Include the necessary header file for window functions.

```cpp
#include <windows.h>
```

--------------------------------

### Set and Smooth Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions_func.html

Methods for setting parameters and smoothing signals.

```APIDOC
## set()

### Description
Sets various parameters for signal processing components.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Sets the specified parameters.

#### Success Response (200)
- **MultiBuffer< Sample >::Stride< isConst >** - Sets stride for MultiBuffer.
- **BoxFilter< Sample >** - Sets parameters for BoxFilter.
- **BoxStackFilter< Sample >** - Sets parameters for BoxStackFilter.
- **CubicLfo** - Sets parameters for CubicLfo.
- **PeakHold< Sample >** - Sets parameters for PeakHold.

#### Response Example
None
```

```APIDOC
## smooth()

### Description
Applies smoothing to a signal using a cubic interpolation.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Returns a smoothed signal.

#### Success Response (200)
- **Cubic< Sample >** - Smoothed signal object.

#### Response Example
None
```

--------------------------------

### Perform Inverse FFT with Windowing and Scaling

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Performs an Inverse Fast Fourier Transform on the input data, with optional windowing, 1/N scaling, and rotation enabled. The output is stored in the provided output container.

```cpp
template<bool withWindow = true, bool withScaling = true, class Input, class Output>
void ifft (Input &&input, Output &&output)
```

--------------------------------

### FFT and IFFT Operations

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Documentation for the core FFT and IFFT operations, including raw and windowed versions.

```APIDOC
## Methods

### `fft(Input &&input, Output &&output)`

**Description**: Performs an FFT, with windowing and rotation (if enabled).

**Template Parameters**:
- `withWindow` (bool, optional) - Whether to apply windowing. Defaults to true.
- `withScaling` (bool, optional) - Whether to apply scaling. Defaults to false.
- `Input` - Type of the input.
- `Output` - Type of the output.

### `fftRaw(Input &&input, Output &&output)`

**Description**: Performs an FFT (no windowing or rotation).

**Template Parameters**:
- `Input` - Type of the input.
- `Output` - Type of the output.

### `ifft(Input &&input, Output &&output)`

**Description**: Inverse FFT, with windowing, 1/N scaling and rotation (if enabled).

**Template Parameters**:
- `withWindow` (bool, optional) - Whether to apply windowing. Defaults to true.
- `withScaling` (bool, optional) - Whether to apply 1/N scaling. Defaults to true.
- `Input` - Type of the input.
- `Output` - Type of the output.

### `ifftRaw(Input &&input, Output &&output)`

**Description**: Performs an IFFT (no windowing, scaling or rotation).

**Template Parameters**:
- `Input` - Type of the input.
- `Output` - Type of the output.
```

--------------------------------

### WindowedFFT Constructor and Size Management

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Details on constructing the WindowedFFT object and managing its size and window function.

```APIDOC
## Constructors and Size Management

### `WindowedFFT(int size, int rotateSamples=0)`

**Description**: Constructor for WindowedFFT.

**Parameters**:
- `size` (int) - The size of the FFT.
- `rotateSamples` (int, optional) - Number of samples to rotate. Defaults to 0.

### `WindowedFFT<class WindowFn>(int size, WindowFn fn, Sample windowOffset=0.5, int rotateSamples=0)`

**Description**: Constructor for WindowedFFT with a custom window function.

**Template Parameters**:
- `WindowFn` - The type of the window function functor.

**Parameters**:
- `size` (int) - The size of the FFT.
- `fn` - The window function functor.
- `windowOffset` (Sample, optional) - Offset for the window function. Defaults to 0.5.
- `rotateSamples` (int, optional) - Number of samples to rotate. Defaults to 0.

### `setSizeWindow(int size, int rotateSamples=0)`

**Description**: Sets the size of the FFT and returns the window for modification. The window is initially all 1s.

**Parameters**:
- `size` (int) - The new size for the FFT.
- `rotateSamples` (int, optional) - Number of samples to rotate. Defaults to 0.

**Returns**: A reference to the window vector for modification.

### `setSize(int size, int rotateSamples=0)`

**Description**: Sets the FFT size using the default Blackman-Harris window.

**Parameters**:
- `size` (int) - The new size for the FFT.
- `rotateSamples` (int, optional) - Number of samples to rotate. Defaults to 0.

### `setSize(int size, WindowFn fn, Sample windowOffset=0.5, int rotateSamples=0)`

**Description**: Sets the FFT size with a user-defined functor for the window.

**Template Parameters**:
- `WindowFn` - The type of the window function functor.

**Parameters**:
- `size` (int) - The new size for the FFT.
- `fn` - The window function functor.
- `windowOffset` (Sample, optional) - Offset for the window function. Defaults to 0.5.
- `rotateSamples` (int, optional) - Number of samples to rotate. Defaults to 0.
```

--------------------------------

### Reset and Resize Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/functions_func.html

Methods for resetting and resizing signal processing components.

```APIDOC
## reset()

### Description
Resets various signal processing components to their initial state.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Resets the state of the specified components.

#### Success Response (200)
- **BoxFilter< Sample >** - Reset BoxFilter.
- **BoxStackFilter< Sample >** - Reset BoxStackFilter.
- **BoxSum< Sample >** - Reset BoxSum.
- **CubicLfo** - Reset CubicLfo.
- **STFT< Sample >** - Reset STFT.

#### Response Example
None
```

```APIDOC
## resize()

### Description
Resizes various signal processing components.

### Method
Various (Implied)

### Endpoint
N/A

### Parameters
None explicitly defined in this context.

### Request Example
None

### Response
Resizes the specified components.

#### Success Response (200)
- **BoxFilter< Sample >** - Resized BoxFilter.
- **BoxStackFilter< Sample >** - Resized BoxStackFilter.
- **BoxSum< Sample >** - Resized BoxSum.
- **ProcessSTFT< Sample >** - Resized ProcessSTFT.
- **STFT< Sample >** - Resized STFT.

#### Response Example
None
```

--------------------------------

### Initialize Oversampler2xFIR

Source: https://signalsmith-audio.co.uk/code/dsp/html/structsignalsmith_1_1rates_1_1_oversampler2x_f_i_r.html

Constructor for the Oversampler2xFIR class. Allows setting the number of channels, maximum block size, half latency, and the passband frequency.

```cpp
Oversampler2xFIR(int channels, int maxBlock, int halfLatency=16, double passFreq=0.43)
```

--------------------------------

### MultiDelay Class Overview

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1delay_1_1_multi_delay.html

Provides an overview of the MultiDelay class, its inheritance, and nested structures.

```APIDOC
## Class signalsmith::delay::MultiDelay

### Description
A multi-channel delay-line with its own buffer.

Inherits signalsmith::delay::Reader< Sample, InterpolatorLinear >.

### Nested Classes
- **ChannelView**: A single-channel delay-line view, similar to a `const Delay`.
- **DelayView**: A multi-channel result, lazily calculating samples.

### Static Attributes
- **latency** (Sample): `Super::latency`
```

--------------------------------

### Set FFT Size with Default Window

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1spectral_1_1_windowed_f_f_t.html

Sets the FFT size using the default Blackman-Harris window, with an optional rotation samples parameter.

```cpp
void setSize (int size, int rotateSamples=0)
```

--------------------------------

### RealFFT Class Methods

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1fft_1_1_real_f_f_t.html

Provides methods for setting and retrieving the size of the FFT, and performing forward and inverse FFT operations. Use these methods to manage FFT size and execute transformations.

```cpp
size_t | **setSize** (size_t size)
size_t | **setFastSizeAbove** (size_t size)
size_t | **setFastSizeBelow** (size_t size)
size_t | **size** () const
```

```cpp
template<typename InputIterator, typename OutputIterator>
void | **fft** (InputIterator &&input, OutputIterator &&output)
```

```cpp
template<typename InputIterator, typename OutputIterator>
void | **ifft** (InputIterator &&input, OutputIterator &&output)
```

--------------------------------

### Include Headers for DSP Library

Source: https://signalsmith-audio.co.uk/code/dsp/html/fft_8h.html

Includes necessary headers for common DSP operations, performance monitoring, and standard C++ libraries like vector, complex numbers, and math functions.

```cpp
#include "./common.h"
#include "./perf.h"
#include <vector>
#include <complex>
#include <cmath>
```

--------------------------------

### lowShelf()

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1filters_1_1_biquad_static.html

Applies a low-shelf filter with gain and bandwidth.

```APIDOC
## lowShelf()

### Description
Applies a low-shelf filter with specified gain and bandwidth.

### Method
`BiquadStatic &`

### Endpoint
N/A (C++ function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
None

### Response
#### Success Response (200)
None

#### Response Example
None

**Deprecated**: use `BiquadDesign` instead
```

--------------------------------

### highShelf()

Source: https://signalsmith-audio.co.uk/code/dsp/html/classsignalsmith_1_1filters_1_1_biquad_static.html

Applies a high-shelf filter with gain and bandwidth.

```APIDOC
## highShelf()

### Description
Applies a high-shelf filter with specified gain and bandwidth.

### Method
`BiquadStatic &`

### Endpoint
N/A (C++ function)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
None

### Response
#### Success Response (200)
None

#### Response Example
None

**Deprecated**: use `BiquadDesign` instead
```
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