# Convert wavelet coefficients for two time-varying functions into two functions with respect to time.

### Description

In much of the costationarity code the combination functions are represented in terms of wavelet coefficients. At certain points the actual combination functions themselves are required (in the time domain) for purposes such as actually forming the linear combination. This function turns the coefficients, for the two combination functions, into their time domain functional representation.

### Usage

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### Arguments

`alpha` |
One set of coefficients for one of the combination functions |

`beta` |
The other set of coefficients |

`n` |
The length of resulting function that you require |

`filter.number` |
The type of wavelet (the number of vanishing moments) |

`family` |
The type of wavelet (the wavelet family) |

### Details

A degree of efficiency is built into the code. Typically, for forming stationary linear combinations then only a few (or at least a medium number) of coarser scale coefficients need to be manipulated (eg modified in the optimizer). However, the actual length of the function (time series length) is typically much longer (e.g. n=256, n=512, or higher). So, this function pads out the small number of coarse coefficients with zeros before forming the combination functions which end up at the correct length, n.

### Value

An object of class `csBiFunction`

which is
list containing two components:

`alpha` |
A vector, of length n, containing one of the time-varying combination functions |

`beta` |
Same as |

### Author(s)

Guy Nason

### References

Cardinali, A. and Nason, Guy P. (2013) Costationarity of
Locally Stationary Time Series Using costat.
*Journal of Statistical Software*, **55**, Issue 1.

Cardinali, A. and Nason, G.P. (2010) Costationarity of locally stationary
time series. *J. Time Series Econometrics*, **2**, Issue 2, Article 1.

### See Also

`LCTS`

, `LCTSres`

### Examples

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