Description Usage Arguments Details Value See Also Examples

View source: R/RcppExports.R View source: R/functions.R

Reconstructs a function using wavelet coefficients (`waveletCoef`

object) as input.

1 |

`beta` |
A |

`j1` |
The finest resolution to be used in the projection (specifies which resolution that the wavelet expansion is truncated). |

Function that takes an input of wavelet coefficients in the form of a `waveletCoef`

object (see `multiCoef`

for details) and optionally a desired maximum resolution level, `j1`

, to create an inhomogeneous wavelet expansion starting from resolution `j0`

up to resolution `j1`

.
Namely, it creates the wavelet expansion,

*∑_{k = 0}^{2^{j_0} - 1} β_k φ_{j_0,k} + ∑_{j = j_0}^{j_1} ∑_{k = 0}^{2^j - 1} β_{j,k} ψ_{j,k}.*

where *(φ,ψ)* denote the father and mother periodised Meyer wavelet functions and *β_{j,k}* denotes the mother wavelet coefficient at resolution j and location k and *β_{k}* denotes the father wavelet coefficients at resolution *j=j0* and location *k*.
The coefficients `beta`

need to be ordered so that the first *2^\code{j0}* elements correspond to father wavelet coefficients at resolution *j=\code{j0}* and the remaining elements correspond to the mother wavelet coefficients from resolution *j=\code{j0}* to *j = log_2 n - 1*. If the maximum resolution level *j1* is not specified, the full wavelet expansion will be given.

A numeric vector of size n giving the wavelet function expansion.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
library(mwaved)
# Make a noiseless doppler function
n <- 2^8
x <- (1:n)/n
y <- makeDoppler(n)
# Determine the wavelet coefficients
beta <- multiCoef(y)
# plot three raw wavelet expansions truncating in each case at j1 = 3, 4 and 5 respectively
plot(x, y, type = 'l', main = 'Doppler and wavelet projections at three different truncations')
j0 <- 3
j1 <- 5
j <- j0:j1
lcols <- c(1, j - j0 + 2)
ltys <- c(1, 1:length(j))
matlines(x, sapply(j, function(i) multiProj(beta, j1 = i)), type = 'l', col = lcols[-1])
legend("bottomright", legend = c("Signal", paste('j1 =', j)), col = lcols, lty =ltys)
``` |

```
```

mwaved documentation built on July 13, 2017, 5:03 p.m.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.