Periodograms - periodogram estimation

arraysplit(s, n, m)

Split an array into arrays of length n with overlapping regions of length m. Iterating or indexing the returned AbstractVector always yields the same Vector with different contents.

periodogram(s; onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, window=nothing)

Computes periodogram of a signal by FFT and returns a Periodogram object.

For real signals, the two-sided periodogram is symmetric and this function returns a one-sided (real only) periodogram by default. A two-sided periodogram can be obtained by setting onesided=false.

nfft specifies the number of points to use for the Fourier transform. If length(s) < nfft, then the input is padded with zeros. By default, nfft is the closest size for which the Fourier transform can be computed with maximal efficiency.

fs is the sample rate of the original signal, and window is an optional window function or vector to be applied to the original signal before computing the Fourier transform. The computed periodogram is normalized so that the area under the periodogram is equal to the uncentered variance (or average power) of the original signal.

welch_pgram(s, n=div(length(s), 8), noverlap=div(n, 2); onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, window=nothing)

Computes the Welch periodogram of a signal s based on segments with n samples with overlap of noverlap samples, and returns a Periodogram object. For a Bartlett periodogram, set noverlap=0. See periodogram for description of optional keyword arguments.

mt_pgram(s; onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, nw=4, ntapers=iceil(2nw)-1, window=dpss(length(s), nw, ntapers))

Computes the multitaper periodogram of a signal s.

If window is not specified, the signal is tapered with ntapers discrete prolate spheroidal sequences with time-bandwidth product nw. Each sequence is equally weighted; adaptive multitaper is not (yet) supported.

If window is specified, each column is applied as a taper. The sum of periodograms is normalized by the total sum of squares of window.

See also: dpss

spectrogram(s, n=div(length(s), 8), noverlap=div(n, 2); onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, window=nothing)

Computes the spectrogram of a signal s based on segments with n samples with overlap of noverlap samples, and returns a Spectrogram object. See periodogram for description of optional keyword arguments.

stft(s, n=div(length(s), 8), noverlap=div(n, 2); onesided=eltype(s)<:Real, nfft=nextfastfft(n), fs=1, window=nothing)

Computes the STFT of a signal s based on segments with n samples with overlap of noverlap samples, and returns a matrix containing the STFT coefficients. See periodogram for description of optional keyword arguments.

periodogram(s::AbstractMatrix; nfft=nextfastfft(size(s)), fs=1, radialsum=false, radialavg=false)

Computes periodogram of a 2-d signal by FFT and returns a Periodogram2 object.

Returns a 2-d periodogram by default. A radially summed or averaged periodogram is returned as a Periodogram object if radialsum or radialavg is true, respectively.

nfft specifies the number of points to use for the Fourier transform. If size(s) < nfft, then the input is padded with zeros. By default, nfft is the closest size for which the Fourier transform can be computed with maximal efficiency. fs is the sample rate of the original signal in both directions.

For radialsum=true the value of power[k] is proportional to $\frac{1}{N}\sum_{k\leq |k'|<k+1} |X[k']|^2$. For radialavg=true it is proportional to $\frac{1}{N \#\{k\leq |k'|<k+1\}} \sum_{k\leq |k'|<k+1} |X[k']|^2$. The computation of |k'| takes into account non-square signals by scaling the coordinates of the wavevector accordingly.

freq(p)

Returns the frequency bin centers for a given Periodogram or Spectrogram object.

Returns a tuple of frequency bin centers for a given Periodogram2 object.

See also: fftfreq, rfftfreq

power(p)

For a Periodogram, returns the computed power at each frequency as a Vector.

For a Spectrogram, returns the computed power at each frequency and time bin as a Matrix. Dimensions are frequency × time.

time(p)

Returns the time bin centers for a given Spectrogram object.