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ArrayFuncs.jl
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ArrayFuncs.jl
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export detrend, detrend!, demean, demean!, bandpass, bandpass!, bandstop, bandstop!,
lowpass, lowpass!, highpass, highpass!, phase!, phase
import Statistics.mean
import LinearAlgebra.pinv
using DSP
# Signal processing functions for arrays (rather than SeisData or SeisChannel)
"""
lstsq(A,X)
Least-squares regression of array `A` using the pseudo-inverse.
Solves the equation `A X = B` by computing a vector `X` that
minimizes the Euclidean 2-norm `|| B - A X ||^2`.
# Arguments
- `A::AbstractArray`: Coefficient matrix.
- `X::AbstractArray`: Dependent variable.
"""
function lstsq(A::AbstractArray,X::AbstractArray)
coeff = pinv(A' * A) * A' * X
end
"""
detrend!(X::AbstractArray{<:Union{Float32,Float64},1})
Remove linear trend from array `X` using least-squares regression.
"""
function detrend!(X::AbstractArray{<:Union{Float32,Float64},1})
N = length(X)
A = ones(N,2)
A[:,1] = Array(1:N) ./ N
coeff = lstsq(A,X)
X[:] = X .- A *coeff
return nothing
end
detrend(A::AbstractArray{<:Union{Float32,Float64},1}) = (U = deepcopy(A);
detrend!(U);return U)
"""
detrend!(X::AbstractArray{<:Union{Float32,Float64},2})
Remove linear trend from columns of `X` using least-squares regression.
"""
function detrend!(X::AbstractArray{<:Union{Float32,Float64},2})
M,N = size(X)
A = ones(M,2)
A[:,1] = Array(1:M) ./ M
for ii = 1:N
coeff = lstsq(A,X[:,ii])
X[:,ii] = X[:,ii] .- A *coeff
end
return nothing
end
detrend(A::AbstractArray{<:Union{Float32,Float64},2}) = (U = deepcopy(A);
detrend!(U);return U)
"""
demean!(A::AbstractArray{<:Union{Float32,Float64},1})
Remove mean from array `A`.
"""
function demean!(A::AbstractArray{<:Union{Float32,Float64},1})
μ = mean(A)
for ii = 1:length(A)
A[ii] -= μ
end
return nothing
end
demean(A::AbstractArray{<:Union{Float32,Float64},1}) = (U = deepcopy(A);
demean!(U);return U)
"""
demean!(A::AbstractArray{<:Union{Float32,Float64},2})
Remove mean from columns of array `A`.
"""
function demean!(A::AbstractArray{<:Union{Float32,Float64},2})
M,N = size(A)
for ii = 1:N
μ = mean(A[:,ii])
for jj = 1:M
A[jj,ii] -= μ
end
end
return nothing
end
demean(A::AbstractArray{<:Union{Float32,Float64},2}) = (U = deepcopy(A);
demean!(U);return U)
"""
taper!(A,fs; max_percentage=0.05, max_length=20.)
Taper a time series `A` with sampling_rate `fs`.
Defaults to 'hann' window. Uses smallest of `max_percentage` * `fs`
or `max_length`.
# Arguments
- `A::AbstractArray`: Time series.
- `fs::Float64`: Sampling rate of time series `A`.
- `max_percentage::float`: Decimal percentage of taper at one end (ranging
from 0. to 0.5).
- `max_length::Float64`: Length of taper at one end in seconds.
"""
function taper!(A::AbstractArray{<:Union{Float32,Float64},1}, fs::Float64;
max_percentage::Float64=0.05, max_length::Float64=20.)
N = length(A)
wlen = min(Int(floor(N * max_percentage)), Int(floor(max_length * fs)), Int(
floor(N/2)))
taper_sides = [-hanning(2 * wlen -1, zerophase=true) .+ 1;0]
A[1:wlen] .= A[1:wlen] .* taper_sides[1:wlen]
A[end-wlen+1:end] .= A[end-wlen+1:end] .* taper_sides[wlen+1:end]
return nothing
end
taper(A::AbstractArray{<:Union{Float32,Float64},1}, fs::Float64;
max_percentage::Float64=0.05, max_length::Float64=20.) = (U = deepcopy(A);
taper!(U,fs,max_percentage=max_percentage,max_length=max_length);return U)
function taper!(A::AbstractArray{<:Union{Float32,Float64},2}, fs::Float64;
max_percentage::Float64=0.05, max_length::Float64=20.)
M,N = size(A)
wlen = min(Int(floor(M * max_percentage)), Int(floor(max_length * fs)), Int(
floor(M/2)))
taper_sides = [-hanning(2 * wlen -1, zerophase=true) .+ 1;0]
for ii = 1:N
A[1:wlen,ii] .= A[1:wlen,ii] .* taper_sides[1:wlen]
A[end-wlen+1:end,ii] .= A[end-wlen+1:end,ii] .* taper_sides[wlen+1:end]
end
return nothing
end
taper(A::AbstractArray{<:Union{Float32,Float64},2}, fs::Float64;
max_percentage::Float64=0.05,max_length::Float64=20.) = (U = deepcopy(A);
taper!(U,fs,max_percentage=max_percentage,max_length=max_length);return U)
"""
phase!(A::AbstractArray)
Extract instantaneous phase from signal A.
For time series `A`, its analytic representation ``S = A + H(A)``, where
``H(A)`` is the Hilbert transform of `A`. The instantaneous phase ``e^{iθ}``
of `A` is given by dividing ``S`` by its modulus: ``e^{iθ} = \\frac{S}{|S|}``
For more information on Phase Cross-Correlation, see:
[Ventosa et al., 2019](https://pubs.geoscienceworld.org/ssa/srl/article-standard/570273/towards-the-processing-of-large-data-volumes-with).
"""
function phase!(A::AbstractArray)
A .= angle.(hilbert(A))
return nothing
end
phase(A::AbstractArray) = (U = deepcopy(A);phase!(U);return U)
"""
bandpass!(A,freqmin,freqmax,fs,corners=4,zerophase=false)
Butterworth-Bandpass Filter.
Filter data `A` from `freqmin` to `freqmax` using `corners` corners.
# Arguments
- `A::AbstractArray`: Data to filter
- `freqmin::Float64`: Pass band low corner frequency.
- `freqmax::Float64`: Pass band high corner frequency.
- `fs::Float64`: Sampling rate in Hz.
- `fs::Int`: Filter corners / order.
- `zerophase::Bool`: If True, apply filter once forwards and once backwards.
This results in twice the filter order but zero phase shift in
the resulting filtered trace.
"""
function bandpass!(A::AbstractArray{<:Union{Float32,Float64},1},
freqmin::Float64, freqmax::Float64, fs::Float64;
corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
low = freqmin / fe
high = freqmax / fe
# warn if above Nyquist frequency
if high - oneunit(high) > -1e-6
@warn "Selected high corner frequency ($freqmax) of bandpass is at or
above Nyquist ($fe). Applying a high-pass instead."
highpass!(A,freqmin,fs,corners=corners,zerophase=zerophase)
return nothing
end
# throw error if low above Nyquist frequency
if low > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Bandpass(freqmin, freqmax; fs=fs)
designmethod = Butterworth(corners)
if zerophase
A[:] = filtfilt(digitalfilter(responsetype, designmethod), A)
else
A[:] = filt(digitalfilter(responsetype, designmethod), A)
end
return nothing
end
bandpass(A::AbstractArray{<:Union{Float32,Float64},1},freqmin::Float64,
freqmax::Float64, fs::Float64; corners::Int=4,zerophase::Bool=false) =
(U = deepcopy(A);bandpass!(U,freqmin,freqmax, fs, corners=corners,
zerophase=zerophase);return U)
function bandpass!(A::AbstractArray{<:Union{Float32,Float64},2},
freqmin::Float64, freqmax::Float64, fs::Float64;
corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
low = freqmin / fe
high = freqmax / fe
M,N = size(A)
# warn if above Nyquist frequency
if high - oneunit(high) > -1e-6
@warn "Selected high corner frequency ($freqmax) of bandpass is at or
above Nyquist ($fe). Applying a high-pass instead."
highpass!(A,freqmin,fs,corners=corners,zerophase=zerophase)
return nothing
end
# throw error if low above Nyquist frequency
if low > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Bandpass(freqmin, freqmax; fs=fs)
designmethod = Butterworth(corners)
if zerophase
for ii = 1:N
A[:,ii] = filtfilt(digitalfilter(responsetype, designmethod), A[:,ii])
end
else
for ii = 1:N
A[:,ii] = filt(digitalfilter(responsetype, designmethod), A[:,ii])
end
end
return nothing
end
bandpass(A::AbstractArray{<:Union{Float32,Float64},2},freqmin::Float64,
freqmax::Float64, fs::Float64; corners::Int=4,zerophase::Bool=false) =
(U = deepcopy(A);bandpass!(U,freqmin,freqmax,fs,corners=corners,
zerophase=zerophase);return U)
"""
bandstop!(A,freqmin,freqmax,fs,corners=4,zerophase=false)
Butterworth-Bandstop Filter.
Filter data `A` removing data between frequencies `freqmin` to `freqmax` using
`corners` corners.
# Arguments
- `A::AbstractArray`: Data to filter
- `freqmin::Float64`: Stop band low corner frequency.
- `freqmax::Float64`: Stop band high corner frequency.
- `fs::Float64`: Sampling rate in Hz.
- `fs::Int`: Filter corners / order.
- `zerophase::Bool`: If True, apply filter once forwards and once backwards.
This results in twice the filter order but zero phase shift in
the resulting filtered trace.
"""
function bandstop!(A::AbstractArray{<:Union{Float32,Float64},1},
freqmin::Float64,freqmax::Float64,fs::Float64;
corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
low = freqmin / fe
high = freqmax / fe
# warn if above Nyquist frequency
if high > 1
@warn "Selected high corner frequency ($freqmax) is"
"above Nyquist ($fe). Setting Nyquist as high corner."
freqmax = fe
end
# throw error if low above Nyquist frequency
if low > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Bandstop(freqmin, freqmax; fs=fs)
designmethod = Butterworth(corners)
if zerophase
A[:] = filtfilt(digitalfilter(responsetype, designmethod), A)
else
A[:] = filt(digitalfilter(responsetype, designmethod), A)
end
return nothing
end
bandstop(A::AbstractArray{<:Union{Float32,Float64},1},freqmin::Float64,
freqmax::Float64, fs::Float64; corners::Int=4,zerophase::Bool=false) =
(U = deepcopy(A);bandstop!(U,freqmin,freqmax,corners=corners,
zerophase=zerophase);return U)
function bandstop!(A::AbstractArray{<:Union{Float32,Float64},2},
freqmin::Float64,freqmax::Float64,fs::Float64;
corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
low = freqmin / fe
high = freqmax / fe
M,N = size(A)
# warn if above Nyquist frequency
if high > 1
@warn "Selected high corner frequency ($freqmax) is"
"above Nyquist ($fe). Setting Nyquist as high corner."
freqmax = fe
end
# throw error if low above Nyquist frequency
if low > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Bandstop(freqmin, freqmax; fs=fs)
designmethod = Butterworth(corners)
if zerophase
for ii = 1:N
A[:,ii] = filtfilt(digitalfilter(responsetype, designmethod), A[:,ii])
end
else
for ii = 1:N
A[:,ii] = filt(digitalfilter(responsetype, designmethod), A[:,ii])
end
end
return nothing
end
bandstop(A::AbstractArray{<:Union{Float32,Float64},2},freqmin::Float64,
freqmax::Float64, fs::Float64; corners::Int=4,zerophase::Bool=false) =
(U = deepcopy(A);bandstop!(U,freqmin,freqmax,corners=corners,
zerophase=zerophase);return U)
"""
lowpass(A,freq,fs,corners=4,zerophase=false)
Butterworth-Lowpass Filter.
Filter data `A` over certain frequency `freq` using `corners` corners.
# Arguments
- `A::AbstractArray`: Data to filter
- `freq::Float64`: Filter corner frequency.
- `fs::Float64`: Sampling rate in Hz.
- `fs::Int`: Filter corners / order.
- `zerophase::Bool`: If True, apply filter once forwards and once backwards.
This results in twice the filter order but zero phase shift in
the resulting filtered trace.
"""
function lowpass!(A::AbstractArray{<:Union{Float32,Float64},1},freq::Float64,
fs::Float64; corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
f = freq / fe
# warn if above Nyquist frequency
if f >= 1
@warn """Selected corner frequency ($freq) is
above Nyquist ($fe). Setting Nyquist as high corner."""
freq = fe - 1. / fs
end
# create filter
responsetype = Lowpass(freq; fs=fs)
designmethod = Butterworth(corners)
if zerophase
A[:] = filtfilt(digitalfilter(responsetype, designmethod), A)
else
A[:] = filt(digitalfilter(responsetype, designmethod), A)
end
return nothing
end
lowpass(A::AbstractArray{<:Union{Float32,Float64},1},freq::Float64, fs::Float64;
corners::Int=4,zerophase::Bool=false) = (U = deepcopy(A);
lowpass!(U,freq,fs,corners=corners,zerophase=zerophase);return U)
function lowpass!(A::AbstractArray{<:Union{Float32,Float64},2},freq::Float64,
fs::Float64; corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
f = freq / fe
M,N = size(A)
# warn if above Nyquist frequency
if f >= 1
@warn """Selected corner frequency ($freq) is
above Nyquist ($fe). Setting Nyquist as high corner."""
freq = fe - 1. / fs
end
# create filter
responsetype = Lowpass(freq; fs=fs)
designmethod = Butterworth(corners)
if zerophase
for ii = 1:N
A[:,ii] = filtfilt(digitalfilter(responsetype, designmethod), A[:,ii])
end
else
for ii = 1:N
A[:,ii] = filt(digitalfilter(responsetype, designmethod), A[:,ii])
end
end
return nothing
end
lowpass(A::AbstractArray{<:Union{Float32,Float64},2},freq::Float64, fs::Float64;
corners::Int=4,zerophase::Bool=false) = (U = deepcopy(A);
lowpass!(U,freq,fs,corners=corners,zerophase=zerophase);return U)
"""
highpass(A,freq,fs,corners=4,zerophase=false)
Butterworth-Highpass Filter.
Filter data `A` removing data below certain frequency `freq` using `corners` corners.
# Arguments
- `A::AbstractArray`: Data to filter
- `freq::Float64`: Filter corner frequency.
- `fs::Float64`: Sampling rate in Hz.
- `fs::Int`: Filter corners / order.
- `zerophase::Bool`: If True, apply filter once forwards and once backwards.
This results in twice the filter order but zero phase shift in
the resulting filtered trace.
"""
function highpass!(A::AbstractArray{<:Union{Float32,Float64},1},freq::Float64,
fs::Float64; corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
f = freq / fe
# warn if above Nyquist frequency
if f > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Highpass(freq; fs=fs)
designmethod = Butterworth(corners)
if zerophase
A[:] = filtfilt(digitalfilter(responsetype, designmethod), A)
else
A[:] = filt(digitalfilter(responsetype, designmethod), A)
end
return nothing
end
highpass(A::AbstractArray{<:Union{Float32,Float64},1},freq::Float64,fs::Float64;
corners::Int=4,zerophase::Bool=false) = (U = deepcopy(A);
highpass!(U,freq,fs,corners=corners,zerophase=zerophase);return U)
function highpass!(A::AbstractArray{<:Union{Float32,Float64},2},freq::Float64,
fs::Float64; corners::Int=4, zerophase::Bool=false)
fe = 0.5 * fs
f = freq / fe
M,N = size(A)
# warn if above Nyquist frequency
if f > 1
ArgumentError("Selected low corner frequency is above Nyquist.")
end
# create filter
responsetype = Highpass(freq; fs=fs)
designmethod = Butterworth(corners)
if zerophase
for ii = 1:N
A[:,ii] = filtfilt(digitalfilter(responsetype, designmethod), A[:,ii])
end
else
for ii = 1:N
A[:,ii] = filt(digitalfilter(responsetype, designmethod), A[:,ii])
end
end
return nothing
end
highpass(A::AbstractArray{<:Union{Float32,Float64},2},freq::Float64,fs::Float64;
corners::Int=4,zerophase::Bool=false) = (U = deepcopy(A);
highpass!(U,freq,fs,corners=corners,zerophase=zerophase);return U)