TimeseriesTools.closeneighbours Method

closeneighbours(x, y; Δt)

Constructs a sparse matrix of distances between neighbouring spikes in two sorted spike trains.

Arguments

• x: A sorted array representing the first spike train.

• y: A sorted array representing the second spike train.

• Δt: The maximum time difference allowed for two spikes to be considered neighbours.

Returns

A sparse matrix D where D[i, j] represents the distance between the i-th spike in x and the j-th spike in y, for pairs of spikes within Δt of each other.

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TimeseriesTools.gammarenewal! Method

gammarenewal!(spikes, α, θ; t0 = randn() * α / θ, kwargs...)

Generate a sequence of gamma-distributed renewal spikes.

Arguments:

• spikes::AbstractVector: The vector to store the generated spikes.

• α: The shape parameter of the gamma distribution.

• θ: The scale parameter of the gamma distribution.

• t0: The initial time of the spike train. Defaults to a random value drawn from a normal distribution with mean of 0 and standard deviation equal to the mean firing rate.

• kwargs...: Additional keyword arguments to be passed to pointprocess!.

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TimeseriesTools.gammarenewal Method

gammarenewal(N, α, θ; t0)

Generate a spike train with inter-spike intervals drawn from a Gamma process.

Arguments

• N: Number of spikes to generate.

• α: Shape parameter of the gamma distribution (equivalent to the mean ISI divided by the

Fano factor).

• θ: Scale parameter of the gamma distribution (equivalent to the Fano factor).

• t0: The initial time of the spike train, prior to the first sampled spike. Defaults to a

random value drawn from a normal distribution with mean of 0 and standard deviation equal to the mean firing rate.

Returns

• A SpikeTrain containing the generated spike times.

See also gammarenewal!.

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TimeseriesTools.pointprocess! Method

pointprocess!(spikes, D::Distribution; rng = Random.default_rng(), t0 = 0.0)

Simulate a point process by sampling inter-spike intervals from a given distribution.

Arguments

• spikes: An array to store the generated spike times.

• D::Distribution: The distribution from which to sample inter-spike intervals.

• rng: (optional) The random number generator to use. Defaults to Random.default_rng().

• t0: (optional) The initial time. Defaults to 0.0.

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TimeseriesTools.stoic Method

stoic(a, b; kpi = npi, σ = 0.025, Δt = σ * 10)

Compute the spike-train overlap-integral coefficient between two spike trains, after normalizing both convolutions to unit energy

See the unnamed metric from "Schreiber S, Fellous JM, Whitmer JH, Tiesinga PHE, Sejnowski TJ (2003). A new correlation based measure of spike timing reliability. Neurocomputing 52:925-931."

Arguments

• a: Spike train a.

• b: Spike train b.

• kpi: Kernel product integral, a function of the distance between two spikes. Default is npi, the integral of two gaussians with equal variance at a given distance from each other.

• σ: Width parameter of the kernel. For npi, this is the width of the unit-mass Gaussian kernels. Default is 0.025.

• Δt: Time window for considering spikes as close. Default is σ * 10.

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TimeseriesTools.sttc Method

sttc(a, b; Δt = 0.025)

The spike-time tiling coefficient, a measure of correlation between spike trains [1].

Arguments

• a::Vector{<:Real}: A sorted vector of spike times.

• b::Vector{<:Real}: A second sorted vector of spike times .

• Δt::Real=0.025: The time window for calculating the STTC.

Returns

• sttc::Real: The STTC value.

References

[1] [Cutts & Eglen 2014](https://doi.org/10.1523%2FJNEUROSCI.2767-14.2014)

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TimeseriesTools._energyspectrum Method

_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.

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TimeseriesTools._energyspectrum Method

_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(x, t);
julia> S = _energyspectrum(ts);
julia> S isa MultivariateSpectrum

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TimeseriesTools._powerspectrum Method

_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.

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TimeseriesTools.colorednoise Method

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

using TimeseriesTools
pink_noise = colorednoise(1:0.01:10; α=1.0)
pink_noise isa RegularTimeseries

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TimeseriesTools.energyspectrum Method

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.

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TimeseriesTools.powerspectrum Method

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

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

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