Copyright | (c) Henning Thielemann 2006-2009 |
---|---|

License | GPL |

Maintainer | synthesizer@henning-thielemann.de |

Stability | provisional |

Portability | requires multi-parameter type classes |

Safe Haskell | None |

Language | Haskell2010 |

## Synopsis

- amplify :: C a => a -> T a -> T a
- amplifyVector :: C a v => a -> T v -> T v
- binomial :: (C a, C a, C a v) => a -> a -> T v -> T v
- binomial1 :: C v => T v -> T v
- delay :: C y => Int -> T y -> T y
- delayPad :: y -> Int -> T y -> T y
- differentiate :: C v => T v -> T v
- differentiate2 :: C v => T v -> T v
- differentiateCenter :: C v => T v -> T v
- downsample2 :: T a -> T a
- envelope :: C a => T a -> T a -> T a
- envelopeVector :: C a v => T a -> T v -> T v
- fadeInOut :: C a => Int -> Int -> Int -> T a -> T a
- fadeInOutAlt :: C a => Int -> Int -> Int -> T a -> T a
- gaussian :: (C a, C a, C a v) => a -> a -> a -> T v -> T v
- generic :: C a v => T a -> T v -> T v
- genericAlt :: C a v => T a -> T v -> T v
- minRange :: Ord v => T v -> (Int, Int) -> v
- movingAverageModulatedPyramid :: (C a, C a v) => a -> Int -> Int -> T Int -> T v -> T v
- sumRange :: C v => T v -> (Int, Int) -> v
- sumRangeFromPyramid :: C v => [T v] -> (Int, Int) -> v
- sums :: C v => Int -> T v -> T v
- sumsDownsample2 :: C v => T v -> T v
- sumsPosModulated :: C v => T (Int, Int) -> T v -> T v
- sumsPosModulatedPyramid :: C v => Int -> T (Int, Int) -> T v -> T v
- sumsPyramid :: C v => Int -> T v -> T v
- propGeneric :: (C a v, Eq v) => T a -> T v -> Bool
- sumRangeFromPyramidFoldr :: C v => [T v] -> (Int, Int) -> v
- sumRangeFromPyramidRec :: C v => [T v] -> (Int, Int) -> v
- getRangeFromPyramid :: [T v] -> (Int, Int) -> [v]
- pyramid :: C v => T v -> [T v]

# Documentation

differentiate :: C v => T v -> T v Source #

Forward difference quotient.
Shortens the signal by one.
Inverts `run`

in the sense that
`differentiate (zero : integrate x) == x`

.
The signal is shifted by a half time unit.

differentiate2 :: C v => T v -> T v Source #

Second derivative.
It is `differentiate2 == differentiate . differentiate`

but `differentiate2`

should be faster.

differentiateCenter :: C v => T v -> T v Source #

Central difference quotient.
Shortens the signal by two elements,
and shifts the signal by one element.
(Which can be fixed by prepending an appropriate value.)
For linear functions this will yield
essentially the same result as `differentiate`

.
You obtain the result of `differentiateCenter`

if you smooth the one of `differentiate`

by averaging pairs of adjacent values.

ToDo: Vector variant

downsample2 :: T a -> T a Source #

gaussian :: (C a, C a, C a v) => a -> a -> a -> T v -> T v Source #

`eps`

is the threshold relatively to the maximum.
That is, if the gaussian falls below `eps * gaussian 0`

,
then the function truncated.

genericAlt :: C a v => T a -> T v -> T v Source #

Unmodulated non-recursive filter Output has same length as the input.

It is elegant but leaks memory.

movingAverageModulatedPyramid :: (C a, C a v) => a -> Int -> Int -> T Int -> T v -> T v Source #

The first argument is the amplification. The main reason to introduce it, was to have only a Module constraint instead of Field. This way we can also filter stereo signals.

A control value `n`

corresponds to filter window size `2*n+1`

.

sumRange :: C v => T v -> (Int, Int) -> v Source #

Compute the sum of the values from index l to (r-1).
(I.e. somehow a right open interval.)
This can be used for implementation of a moving average filter.
However, its counterpart `sumRangeFromPyramid`

is much faster for large windows.

sumRangeFromPyramid :: C v => [T v] -> (Int, Int) -> v Source #

This function should be much faster than `sumRange`

but slower than the recursively implemented `movingAverage`

.
However in contrast to `movingAverage`

it should not suffer from cancelation.

sums :: C v => Int -> T v -> T v Source #

Moving (uniformly weighted) average in the most trivial form.
This is very slow and needs about `n * length x`

operations.