Numeric.Signal

Signal processing functions

Documentation

class Convolvable a where

Methods

convolve :: a -> a -> a

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

Instances

Convolvable (Vector Double)

Convolvable (Vector Float)

Convolvable (Vector (Complex Double))

Convolvable (Vector (Complex Float))

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

Minimal complete definition

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

Instances

Filterable Double

Filterable Float

Filtering

hamming

Arguments

:: Filterable a

=> Int

length

-> Vector a

the Hamming coeffficents

coefficients of a Hamming window

pwelch

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

Arguments

:: (Filterable a, Container Vector (Complex 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, Container Vector (Complex a), Convert (Complex a)) => Int -> [(a, a)] -> Vector a

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

broadband_fir

Arguments

:: (Filterable a, Double ~ DoubleOf a, Container Vector (Complex a), Convert (Complex a))

=> Int

sampling rate

-> (Int, Int)

(lower,upper) frequency cutoff

-> Vector a

filter coefficients

a broadband FIR

freqzF

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

Arguments

:: (Filterable a, Enum 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

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

Arguments

:: (Filterable a, Double ~ DoubleOf a, Container Vector (Complex a), Convert (Complex 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)

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

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

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

analytic_phase :: (Filterable a, Container Vector a, Double ~ DoubleOf a) => Vector (Complex a) -> Vector a

the phase of an analytic signal

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

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

Statistics

cross_covariance

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

Arguments

:: Filterable a

=> Int

maximum delay

-> Vector a

time series

-> Vector a

time series

-> Vector a

result

cross correlation of two signals

cross_spectrum

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

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

Arguments

:: Filterable a

=> Int

maximum delay

-> Vector a

time series

-> Vector a

result

auto correlation of two signals

Preprocessing

detrend

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

resize the vector to length n by resampling

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

resample, take one sample every n samples in the original

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

the difference between consecutive elements of a vector

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

cumulative sum of a series