TimeseriesTools

UnitfulIndex

A type alias for a union of AbstractArray, AbstractRange, and Tuple types with Unitful.Time elements.

IntervalSets.Interval(x::AbstractTimeSeries)

Returns an interval representing the range of the AbstractTimeSeries x.

Examples

julia> using IntervalSets;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x);
julia> IntervalSets.Interval(ts) == (1..100)

AbstractSpectrum{T, N, B}

A type alias for an AbstractDimArray in which the first dimension is Frequency.

AbstractTimeSeries{T, N, B}

A type alias for an AbstractDimArray with a time index.

Freq

A DimensionalData.jl dimension representing the frequency domain.

FreqIndex

A type alias for a tuple of dimensions, where the first dimension is of type FreqDim.

IrregularTimeSeries

A type alias for a potentially irregularly sampled time series.

MultivariateSpectrum{T} = AbstractSpectrum{T, 2} where T

A type alias for a multivariate spectrum.

MultivariateTimeSeries{T}

A type alias for a multivariate time series (A matrix, with a first Ti dimension and an arbitrary second dimension).

RegularFreqIndex

A type alias for a tuple of dimensions, where the first dimension is a regularly sampled Frequency.

RegularIndex

A type alias for a regularly sampled dimension, wrapping an AbstractRange.

RegularSpectrum{T, N, B}

A type alias for a spectrum with a regularly sampled frequency index.

RegularTimeIndex

A type alias for a tuple of dimensions containing a TimeIndex and any number of other dimensions.

RegularTimeSeries{T, N, B}

A type alias for a regularly sampled time series.

TimeIndex

A type alias for a tuple containing a time dimension and any number of other dimensions.

UnitfulTimeIndex

A type alias for a tuple of dimensions, where the first dimension is of type DimensionalData.Dimension{<:UnitfulIndex}.

UnitfulTimeSeries{T, N, B}

A type alias for an AbstractDimArray with a UnitfulTimeIndex.

Examples

julia> using Unitful;
julia> t = (1:100)u"s";
julia> x = rand(100);
julia> uts = TimeSeries(t, x);
julia> uts isa UnitfulTimeSeries

UnivariateSpectrum{T} = AbstractSpectrum{T, 1} where T

A type alias for a univariate spectrum.

UnivariateTimeSeries{T}

A type alias for a time series with one variable (a vector with only a Ti dimension).

Var

A DimensionalData.jl dimension representing the variables of a multivariate time series.

Base.cat(D::DimensionalData.Dimension, args...; kwargs...)

Concatenate the arrays given in args..., and give the resulting extra axis dimensions D.

step(x::RegularTimeSeries)

Returns the step size (time increment) of a regularly sampled RegularTimeSeries.

Examples

julia> t = 1:100;
julia> x = rand(100);
julia> rts = TimeSeries(t, x);
julia> step(rts) == 1

decompose(x::Union{<:AbstractTimeSeries, <:AbstractSpectrum})

Convert a time series or spectrum to a tuple of the dimensions and the data (as Arrays).

TimeSeries(t, v, x)

Constructs a multivariate time series with time t, variable v, and data x.

Examples

julia> t = 1:100;
julia> v = [:a, :b, :c];
julia> x = rand(100, 3);
julia> mts = TimeSeries(t, v, x)
julia> mts isa Union{MultivariateTimeSeries, RegularTimeSeries}

TimeSeries(t, x, timeunit::Unitful.Units)

Constructs a univariate time series with time t, data x and time units specified by timeunit. Note that you can add units to the elements of a time series x with, for example, x*u"V".

Examples

julia> using Unitful;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x, u"ms")*u"V";
julia> ts isa Union{UnivariateTimeSeries, RegularTimeSeries, UnitfulTimeSeries}

TimeSeries(t, x)

Constructs a univariate time series with time t and data x. Alteratively, use TS(t, x)

Examples

julia> using TimeseriesTools, Unitful;
julia> t = 1:100
julia> x = rand(100)
julia> ts = TimeSeries(t, x)
julia> ts isa Union{UnivariateTimeSeries, RegularTimeSeries}

_energyspectrum(x::RegularTimeSeries, f_min=samplingrate(x)/min(length(x)÷4, 1000))

Computes the energy spectrum of a regularly sampled time series x with an optional minimum frequency f_min.

_energyspectrum(x::RegularTimeSeries, f_min=0)

Computes the energy spectrum of a time series using the fast Fourier transform.

If f_min > 0, the energy spectrum is calculated for windows of the time series determined by f_min, the minimum frequency that will be resolved in the spectrum. If f_min > 0, the second dimension of the output will correspond to the windows. For an averaged periodogram, see energyspectrum.

If the input time series is a UnitfulTimeSeries, the frequency will also have units. Moreover if the elements of x are unitful, so are the elements of the spectrum.

Examples

julia> using TimeseriesTools
julia> t = range(0.0, stop=1.0, length=1000);
julia> x = sin.(2 * π * 5 * t);
julia> ts = RegularTimeSeries(t, x);
julia> S = _energyspectrum(ts);
julia> S isa MultivariateSpectrum

_powerspectrum(x::AbstractTimeSeries, f_min=samplingrate(x)/min(length(x)÷4, 1000); kwargs...)

Computes the power spectrum of a time series x in Welch periodogram windows. Note that the _powerspectrum is simply the _energyspectrum divided by the duration of each window. See _energyspectrum.

colorednoise(ts::AbstractRange; α=2.0)

Generate a colored-noise time series with a specified power-law exponent α on the given times ts.

Arguments

• ts: An AbstractRange representing the time range of the generated noise.
• α: The power-law exponent of the colored noise, which will have a spectrum given by 1/f^α. Defaults to 2.0.

Returns

• A TimeSeries containing the generated colored noise.

Example

julia> using TimeseriesTools
julia> pink_noise = colorednoise(1:0.01:10; α=1.0)
julia> pink_noise isa RegularTimeSeries

TimeseriesTools.convertconst(c::Number, u::Unitful.Quantity)

Converts a constant c to have the same units as u.

Examples

julia> using Unitful;
julia> c = 5;
julia> u = 3u"s";
julia> converted_c = TimeseriesTools.convertconst(c, u);
julia> typeof(converted_c) == typeof(u)

dimunit(x::UnitfulTimeSeries, dim)

Returns the unit associated with the specified dimension dim of a UnitfulTimeSeries.

Examples

julia> using Unitful;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x, u"ms");
julia> TimeseriesTools.dimunit(ts, Ti) == u"ms"

duration(x::AbstractTimeSeries)

Returns the duration of the @ref x.

Examples

julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x);
julia> TimeseriesTools.duration(ts) == 99

energyspectrum(x::RegularTimeSeries, f_min=0; kwargs...)

Computes the average energy spectrum of a regularly sampled time series x. f_min determines the minimum frequency that will be resolved in the spectrum. See _energyspectrum.

frequnit(x::UnitfulSpectrum)

Returns the frequency units associated with a UnitfulSpectrum.

Examples

julia> using Unitful;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x, u"ms");
julia> sp = fft(ts);  # assuming fft returns a UnitfulSpectrum
julia> frequnits(sp) == u"Hz"

powerspectrum(x::AbstractTimeSeries, f_minsamplingrate(x)/min(length(x)÷4, 1000); kwargs...)

Computes the average power spectrum of a time series x using the Welch periodogram method.

samplingperiod(x::RegularTimeSeries)

Returns the sampling period (step size) of a regularly sampled RegularTimeSeries.

Examples

julia> t = 1:100;
julia> x = rand(100);
julia> rts = TimeSeries(t, x);
julia> samplingperiod(rts) == 1

samplingrate(x::RegularTimeSeries)

Returns the sampling rate (inverse of the step size) of a regularly sampled RegularTimeSeries.

Examples

julia> t = 1:100;
julia> x = rand(100);
julia> rts = TimeSeries(t, x);
julia> samplingrate(rts) == 1

times(x::AbstractTimeSeries)

Returns the time indices of the AbstractTimeSeries x.

Examples

julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x);
julia> times(ts) == t

timeunit(x::UnitfulTimeSeries)

Returns the time units associated with a [UnitfulTimeSeries].

Examples

julia> using Unitful;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x, u"ms");
julia> timeunit(ts) == u"ms"

unit(x::AbstractArray)

Returns the units associated with the elements of an UnitfulTimeSeries` or UnitfulSpectrum.

Examples

julia> using Unitful;
julia> t = 1:100;
julia> x = rand(100);
julia> ts = TimeSeries(t, x, u"ms")*u"V";
julia> unit(ts) == u"V"