
Synthesizer.Plain.Filter.NonRecursive  Portability  requires multiparameter type classes  Stability  provisional  Maintainer  synthesizer@henningthielemann.de 





Description 


Synopsis 

amplify :: C a => a > T a > T a   amplifyVector :: C a v => a > T v > T v   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   delay :: C y => Int > T y > T y   delayPad :: y > Int > T y > T y   generic :: C a v => T a > T v > T v   genericAlt :: C a v => T a > T v > T v   propGeneric :: (C a v, Eq v) => T a > T v > Bool   gaussian :: (C a, C a, C a v) => a > a > a > T v > T v   binomial :: (C a, C a, C a v) => a > a > T v > T v   ratioFreqToVariance :: C a => a > a > a   binomial1 :: C v => T v > T v   sums :: C v => Int > T v > T v   sumsDownsample2 :: C v => T v > T v   downsample2 :: T a > T a   sumsUpsampleOdd :: C v => Int > T v > T v > T v   sumsUpsampleEven :: C v => Int > T v > T v > T v   sumsPyramid :: C v => Int > T v > T v   sumRange :: C v => T v > (Int, Int) > v   pyramid :: C v => T v > [T v]   sumRangePrepare :: C v => ((Int, Int) > source > v) > source > (Int, Int) > v   sumRangeFromPyramid :: C v => [T v] > (Int, Int) > v   sumRangeFromPyramidRec :: C v => [T v] > (Int, Int) > v   sumsPosModulated :: C v => T (Int, Int) > T v > T v   sumsPosModulatedPyramid :: C v => Int > T (Int, Int) > T v > T v   movingAverageModulatedPyramid :: (C a, C a v) => a > Int > Int > T Int > T v > T v   differentiate :: C v => T v > T v   differentiateCenter :: C v => T v > T v   differentiate2 :: C v => T v > T v 



Envelope application




amplifyVector :: C a v => a > T v > T v  Source 



:: C a   => T a  the envelope
 > T a  the signal to be enveloped
 > T a  



:: C a v   => T a  the envelope
 > T v  the signal to be enveloped
 > T v  






Shift






Smoothing



Unmodulated nonrecursive filter



Unmodulated nonrecursive filter
Output has same length as the input.
It is elegant but leaks memory.




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.


binomial :: (C a, C a, C a v) => a > a > T v > T v  Source 


ratioFreqToVariance :: C a => a > a > a  Source 

Compute the variance of the Gaussian
such that its Fourier transform has value ratio at frequency freq.





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







Given a list of numbers
and a list of sums of (2*k) of successive summands,
compute a list of the sums of (2*k+1) or (2*k+2) summands.
Example for 2*k+1
[0+1+2+3, 2+3+4+5, 4+5+6+7, ...] >
[0+1+2+3+4, 1+2+3+4+5, 2+3+4+5+6, 3+4+5+6+7, 4+5+6+7+8, ...]
Example for 2*k+2
[0+1+2+3, 2+3+4+5, 4+5+6+7, ...] >
[0+1+2+3+4+5, 1+2+3+4+5+6, 2+3+4+5+6+7, 3+4+5+6+7+8, 4+5+6+7+8+9, ...]







Compute the sum of the values from index l to (r1).
(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.







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.







Moving average, where window bounds must be always nonnegative.
The laziness granularity is 2^height.



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.


Filter operators from calculus



Forward difference quotient.
Shortens the signal by one.
Inverts Synthesizer.Plain.Filter.Recursive.Integration.run in the sense that
differentiate (zero : integrate x) == x.
The signal is shifted by a half time unit.


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



Second derivative.
It is differentiate2 == differentiate . differentiate
but differentiate2 should be faster.


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