Copyright	(c) Alexander Vivian Hugh McPhail 2010 2014 2015 2016
License	BSD3
Maintainer	haskell.vivian.mcphail <at> gmail <dot> com
Stability	provisional
Portability	uses FFI
Safe Haskell	None
Language	Haskell98

Numeric.Signal

Contents

Filtering
Analytic Signal
Statistics
Preprocessing

Description

Signal processing functions

Synopsis

class Convolvable a where
- convolve :: a -> a -> a
class (Storable a, Container Vector a, Num (Vector a), Convert a, Floating (Vector a), RealElement a, Num a) => Filterable a
hamming :: Filterable a => Int -> Vector a
pwelch :: Int -> Int -> Vector Double -> (Vector Double, Vector Double)
fir :: (Filterable a, Convert (Complex a), Double ~ DoubleOf a) => Int -> [(a, a)] -> Int -> Int -> Vector a -> Vector a
standard_fir :: (Filterable a, Double ~ DoubleOf a, Convert (Complex a)) => Int -> [(a, a)] -> Vector a
broadband_fir :: (Filterable a, Double ~ DoubleOf a, Convert (Complex a)) => Int -> (Int, Int) -> Vector a
freqzF :: (Filterable a, Double ~ DoubleOf a, Filterable (DoubleOf a)) => Vector a -> Vector a -> Int -> Vector a -> Vector a
freqzN :: (Filterable a, Double ~ DoubleOf a) => Vector a -> Vector a -> Int -> Int -> (Vector a, Vector a)
filter :: Filterable a => Vector a -> Vector a -> Int -> Vector a -> Vector a
broadband_filter :: (Filterable a, Double ~ DoubleOf a) => Int -> (Int, Int) -> Vector a -> Vector a
analytic_signal :: Vector Double -> Vector (Complex Double)
analytic_power :: Filterable a => Vector (Complex Double) -> Vector a
analytic_phase :: Filterable a => Vector (Complex a) -> Vector a
unwrap :: Filterable a => Vector a -> Vector a
cross_covariance :: Filterable a => Int -> Vector a -> Vector a -> (a, a, Vector a)
cross_correlation :: Filterable a => Int -> Vector a -> Vector a -> Vector a
cross_spectrum :: (Filterable a, Double ~ DoubleOf a) => Int -> Vector a -> Vector a -> Vector (Complex Double)
auto_covariance :: Filterable a => Int -> Vector a -> (a, Vector a)
auto_correlation :: Filterable a => Int -> Vector a -> Vector a
detrend :: Int -> Vector Double -> Vector Double
resize :: Filterable a => Int -> Vector a -> Vector a
downsample :: Filterable a => Int -> Vector a -> Vector a
deriv :: Filterable a => Vector a -> Vector a
cumulative_sum :: Filterable a => Vector a -> Vector a

Documentation

class Convolvable a where Source #

Methods

convolve :: a -> a -> a Source #

convolve two containers, output is the size of the second argument, no zero padding

Instances

Instances details

Convolvable (Vector (Complex Double)) Source #
Instance details Defined in Numeric.Signal.Internal Methods convolve :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) Source #
Convolvable (Vector (Complex Float)) Source #
Instance details Defined in Numeric.Signal.Internal Methods convolve :: Vector (Complex Float) -> Vector (Complex Float) -> Vector (Complex Float) Source #
Convolvable (Vector Double) Source #
Instance details Defined in Numeric.Signal.Internal Methods convolve :: Vector Double -> Vector Double -> Vector Double Source #
Convolvable (Vector Float) Source #
Instance details Defined in Numeric.Signal.Internal Methods convolve :: Vector Float -> Vector Float -> Vector Float Source #

class (Storable a, Container Vector a, Num (Vector a), Convert a, Floating (Vector a), RealElement a, Num a) => Filterable a Source #

Minimal complete definition

fromDouble, filter_, hamming_, complex_power_, downsample_, deriv_, unwrap_, polyEval_, cross_covariance_, cumulative_sum_

Instances

Instances details

Filterable Double Source #
Instance details Defined in Numeric.Signal.Internal Methods fromDouble :: Vector Double -> Vector Double filter_ :: Vector Double -> Vector Double -> Vector Double -> Vector Double hamming_ :: Int -> Vector Double complex_power_ :: Vector (Complex Double) -> Vector Double downsample_ :: Int -> Vector Double -> Vector Double deriv_ :: Vector Double -> Vector Double unwrap_ :: Vector Double -> Vector Double polyEval_ :: Vector Double -> Vector (Complex Double) -> Vector (Complex Double) cross_covariance_ :: Int -> Vector Double -> Vector Double -> (Double, Double, Vector Double) cumulative_sum_ :: Vector Double -> Vector Double
Filterable Float Source #
Instance details Defined in Numeric.Signal.Internal Methods fromDouble :: Vector Double -> Vector Float filter_ :: Vector Float -> Vector Float -> Vector Float -> Vector Float hamming_ :: Int -> Vector Float complex_power_ :: Vector (Complex Double) -> Vector Float downsample_ :: Int -> Vector Float -> Vector Float deriv_ :: Vector Float -> Vector Float unwrap_ :: Vector Float -> Vector Float polyEval_ :: Vector Float -> Vector (Complex Double) -> Vector (Complex Double) cross_covariance_ :: Int -> Vector Float -> Vector Float -> (Float, Float, Vector Float) cumulative_sum_ :: Vector Float -> Vector Float

Filtering

hamming Source #

Arguments

:: Filterable a
=> Int	length
-> Vector a	the Hamming coeffficents

coefficients of a Hamming window

pwelch Source #

Arguments

:: Int	sampling rate
-> Int	window size
-> Vector Double	input signal
-> (Vector Double, Vector Double)	(frequency index,power density)

Welch (1967) power spectrum density using periodogram/FFT method

fir Source #

Arguments

:: (Filterable a, Convert (Complex a), Double ~ DoubleOf a)
=> Int	order (one less than the length of the filter)
-> [(a, a)]	band edge frequency, nondecreasing, [0, f1, ..., f(n-1), 1] ^ band edge magnitude
-> Int	grid spacing
-> Int	transition width
-> Vector a	smoothing window (size is order + 1)
-> Vector a	the filter coefficients

produce an FIR filter

standard_fir :: (Filterable a, Double ~ DoubleOf a, Convert (Complex a)) => Int -> [(a, a)] -> Vector a Source #

standard FIR filter | FIR filter with grid a power of 2 greater than the order, ramp = grid/16, hamming window

broadband_fir Source #

Arguments

:: (Filterable a, Double ~ DoubleOf a, Convert (Complex a))
=> Int	sampling rate
-> (Int, Int)	(lower,upper) frequency cutoff
-> Vector a	filter coefficients

a broadband FIR

freqzF Source #

Arguments

:: (Filterable a, Double ~ DoubleOf a, Filterable (DoubleOf a))
=> Vector a	zero coefficients
-> Vector a	pole coefficients
-> Int	sampling rate
-> Vector a	frequencies
-> Vector a	frequency response

determine the frequency response of a filter, given a vector of frequencies

freqzN Source #

Arguments

:: (Filterable a, Double ~ DoubleOf a)
=> Vector a	zero coefficients
-> Vector a	pole coefficients
-> Int	sampling rate
-> Int	number of points
-> (Vector a, Vector a)	(frequencies,response)

determine the frequency response of a filter, given a number of points and sampling rate

filter Source #

Arguments

:: Filterable a
=> Vector a	zero coefficients
-> Vector a	pole coefficients
-> Int	sampling rate
-> Vector a	input signal
-> Vector a	output signal

filters the signal

broadband_filter Source #

Arguments

:: (Filterable a, Double ~ DoubleOf a)
=> Int	sampling rate
-> (Int, Int)	(lower,upper) frequency cutoff
-> Vector a	input signal
-> Vector a	output signal

a broadband filter

Analytic Signal

analytic_signal :: Vector Double -> Vector (Complex Double) Source #

an analytic signal is the original signal with Hilbert-transformed signal as imaginary component

analytic_power :: Filterable a => Vector (Complex Double) -> Vector a Source #

the power (amplitude^2 = v * (conj c)) of an analytic signal

analytic_phase :: Filterable a => Vector (Complex a) -> Vector a Source #

the phase of an analytic signal

unwrap :: Filterable a => Vector a -> Vector a Source #

unwrap the phase of signal (input expected to be within (-pi,pi))

Statistics

cross_covariance Source #

Arguments

:: Filterable a
=> Int	maximum delay
-> Vector a	time series
-> Vector a	time series
-> (a, a, Vector a)	(sd_x,sd_y,cov_xy)

cross covariance of two signals the cross correlation is computed by dividing the result by the product of the two standard deviations

cross_correlation Source #

Arguments

:: Filterable a
=> Int	maximum delay
-> Vector a	time series
-> Vector a	time series
-> Vector a	result

cross correlation of two signals

cross_spectrum Source #

Arguments

:: (Filterable a, Double ~ DoubleOf a)
=> Int	maximum delay
-> Vector a	time series
-> Vector a	time series
-> Vector (Complex Double)	result

compute the cross spectrum

auto_covariance Source #

Arguments

:: Filterable a
=> Int	maximum delay
-> Vector a	time series
-> (a, Vector a)	(var,cov_xx)

auto covariance of two signals the auto correlation is computed by dividing the result by the variance

auto_correlation Source #

Arguments

:: Filterable a
=> Int	maximum delay
-> Vector a	time series
-> Vector a	result

auto correlation of two signals

Preprocessing

detrend Source #

Arguments

:: Int	window size
-> Vector Double	data to be detrended
-> Vector Double	detrended data

remove a linear trend from data

resize :: Filterable a => Int -> Vector a -> Vector a Source #

resize the vector to length n by resampling

downsample :: Filterable a => Int -> Vector a -> Vector a Source #

resample, take one sample every n samples in the original

deriv :: Filterable a => Vector a -> Vector a Source #

the difference between consecutive elements of a vector

cumulative_sum :: Filterable a => Vector a -> Vector a Source #

cumulative sum of a series