Signals and transforms: API index

Find an operation by its purpose. Entries link to the complete signature and contract.

HMath.Fourier

API	Purpose
Direction	Transform exponent convention; Inverse additionally divides by sample count.
Forward	Declaration and type contract below.
Inverse	Declaration and type contract below.
FFTAlgorithm	Explicit reference factorization, or Automatic mixed-radix with Bluestein for larger prime factors.
Automatic	Declaration and type contract below.
Direct	Declaration and type contract below.
Radix2	Declaration and type contract below.
Radix4	Declaration and type contract below.
MixedRadix	Declaration and type contract below.
SplitRadix	Declaration and type contract below.
Bluestein	Declaration and type contract below.
Rader	Declaration and type contract below.
FFTPlan	Opaque immutable plan with cached unit-circle roots and a fixed input length.
planFFT	Create a reusable plan after checking length, prime or radix requirements.
executeFFT	Apply a plan to exactly its declared number of finite complex samples; reject nonfinite intermediate results.
fft	Automatic forward/inverse FFT and bounded direct forward DFT, respectively.
ifft	Automatic forward/inverse FFT and bounded direct forward DFT, respectively.
dft	Automatic forward/inverse FFT and bounded direct forward DFT, respectively.
fftND	Transform all axes.
fftBatch	Apply one immutable plan independently to each batch; any inconsistent row length fails.
realFFT	Full complex spectrum; the real-spectrum inverse checks Hermitian symmetry.
inverseRealFFT	Inverse of a full real spectrum; require conjugate symmetry within the supplied absolute tolerance.
fftInPlace	The caller exclusively owns a valid, aligned, writable buffer of exactly N Complex Double elements for the duration of this call.
frequencies	Signed DFT frequency bins in cycles per coordinate unit, given sample count and positive sample spacing.
fftShift	Rotate zero frequency to/from the center; these operations are exact inverses for odd and even lengths.
ifftShift	Rotate zero frequency to/from the center; these operations are exact inverses for odd and even lengths.
TransformType	Orthonormal cosine/sine basis type I, II, III or IV.
TypeI	Declaration and type contract below.
TypeII	Declaration and type contract below.
TypeIII	Declaration and type contract below.
TypeIV	Declaration and type contract below.
dct	Apply an orthonormal cosine/sine basis or its transpose; type-I cosine needs at least two samples.
idct	Apply an orthonormal cosine/sine basis or its transpose; type-I cosine needs at least two samples.
dst	Apply an orthonormal cosine/sine basis or its transpose; type-I cosine needs at least two samples.
idst	Apply an orthonormal cosine/sine basis or its transpose; type-I cosine needs at least two samples.
hartley	Unnormalized real Hartley transform, Re(DFT)-Im(DFT); applying twice multiplies by N.
STFT	Frames include zero padding on both sides by one full window, so windows with zero endpoints reconstruct boundary samples.
stft	Windowed analysis with an explicit hop in samples, padded endpoint frames, and a 1048576-coefficient storage budget.
stftFrames	Read the full complex spectra in increasing frame-start order.
istft	Overlap-add inverse with squared-window normalization; reject every uncovered original sample.
magnitudeSpectrum	Elementwise complex magnitude, principal phase in radians, and squared magnitude; no PSD normalization.
phaseSpectrum	Elementwise complex magnitude, principal phase in radians, and squared magnitude; no PSD normalization.
powerSpectrum	Elementwise complex magnitude, principal phase in radians, and squared magnitude; no PSD normalization.
periodogram	Two-sided PSD in amplitude-squared/Hz: squared FFT magnitude divided by sample rate and window squared energy.
welch	Average full-window two-sided periodograms at the supplied hop; discard the incomplete final frame.
crossSpectrum	Two-sided conjugate(X)*Y cross PSD using the same sample-rate/window-energy normalization as periodogram.
spectrogram	Squared-magnitude STFT frames, retaining the explicit padding/frame order of stft.
cepstrum	Real cepstrum from inverse FFT of log(max(floor,abs(FFT(x)))); floor must be positive.
analyticSignal	Real signal plus imaginary Hilbert transform, formed by doubling positive-frequency bins and retaining DC/Nyquist.
hilbert	Imaginary part of the analytic signal; periodic finite-record boundary convention.
chirpZ	Direct bounded Z-transform along z_k=a*w^(-k); nonzero a,w required.
goertzel	One arbitrary-frequency DFT value from a second-order real resonator; omega is radians/sample.
fftConvolve	Full zero-padded complex linear convolution; padded transform length is limited to 65536.
fftCorrelate	Correlation lags -(length b-1)..length a-1, conjugating b.

HMath.Signal

API	Purpose
convolution	Direct full real linear convolution, with explicit quadratic work budget; an empty operand yields an empty result.
circularConvolution	Length-N periodic convolution of two equally sized nonempty real signals (N<=4096).
correlation	Full real cross-correlation, equivalent to convolution with the reversed second signal.
autocorrelation	Unnormalized full autocorrelation with zero lag in the middle.
overlapAdd	Block FFT linear convolution; block is the number of new input samples, not the padded transform length.
overlapSave	Streaming FFT convolution with explicit transform length >= kernel length; retained block size is N-M+1.
Filter	Opaque normalized numerator/denominator and caller-visible persistent delay state.
iir	Normalize finite ascending z^-1 coefficients by nonzero a0 and initialize a zero transposed-direct-form-II state.
fir	Construct a causal zero-state finite-impulse-response filter; maximum 257 taps.
filterCoefficients	Read normalized padded (numerator,denominator) coefficients in increasing delay order.
filterState	Read explicit delay state after a block; the list is immutable and independently reusable.
resetFilter	Preserve coefficients while replacing every delay with zero.
filterSignal	Process a finite input block, returning both its output and the filter state for the next block.
FilterFamily	Classical analog prototypes with ripple/attenuation parameters in decibels.
Butterworth	Declaration and type contract below.
ChebyshevI	Declaration and type contract below.
ChebyshevII	Declaration and type contract below.
Elliptic	Declaration and type contract below.
Bessel	Declaration and type contract below.
FilterBand	Prewarped low/high edge or ordered band edges, all in Hz.
Lowpass	Declaration and type contract below.
Highpass	Declaration and type contract below.
Bandpass	Declaration and type contract below.
Bandstop	Declaration and type contract below.
designIIR	Orders 1..8; rippleattenuation in dB; all edges strictly inside (0, fs2).
frequencyResponse	Complex unit-circle response at omega radians/sample; reject poles and nonfinite arithmetic.
notch	Second-order notch or unity-magnitude all-pass with center omega in (0,pi) and positive quality factor Q.
allPass	Second-order notch or unity-magnitude all-pass with center omega in (0,pi) and positive quality factor Q.
movingAverage	Causal zero-state box FIR with supplied width; initial outputs include implicit leading zeros.
medianFilter	Centered odd-width running median using replicate endpoint padding.
gaussianFilter	Centered normalized Gaussian convolution with supplied sigma in samples and odd support width.
savitzkyGolay	Centered local QR polynomial fit; choose width, degree, derivative order and positive sample spacing.
wiener	Local mean/variance Wiener shrinkage; optional noise variance, otherwise average local variance is estimated.
Window	Symmetric endpoint-inclusive windows, with shape parameters betasigmaalpha/attenuation as appropriate.
Hann	Declaration and type contract below.
Hamming	Declaration and type contract below.
Blackman	Declaration and type contract below.
Bartlett	Declaration and type contract below.
Kaiser	Declaration and type contract below.
Gaussian	Declaration and type contract below.
Tukey	Declaration and type contract below.
FlatTop	Declaration and type contract below.
DolphChebyshev	Declaration and type contract below.
window	Generate a finite symmetric window.
windowedSinc	Given window kind, odd tap count in [1,257], cutoff frequency and positive sample rate, return normalized low-pass FIR coefficients.
downsample	Select indices congruent to offset modulo factor; this primitive performs no implicit anti-alias filtering.
upsample	Insert factor-1 zeros after each sample, with a checked 1048576-element output budget.
resamplePolyphase	Zero-extended centered polyphase FIR resampling.
resample	Construct a Kaiser-windowed anti-alias/interpolation FIR, then evaluate only the necessary rational polyphase taps.
antiAlias	Centered replicate-padded low-pass before decimation by factor; cutoff is 0.45factor cyclessample.
Peak	Interior peak index, height, topographic prominence and half-prominence width in samples.
Peak	Declaration and type contract below.
peakIndex	Zero-based sample index of the detected peak.
peakHeight	Sample amplitude at peakIndex.
peakProminence	Peak height above its reference surrounding contour level.
peakWidth	Estimated width at the selected prominence height, measured in samples.
peaks	Interior local maxima; flat plateaus select the lower middle index.
zeroCrossings	Interpolated opposite-sign transitions; zero plateaus count once, leading/trailing zeros are ignored.
envelope	Magnitude of the periodic analytic-signal representation.
unwrapPhase	Remove nearest multiples of 2*pi from adjacent phase jumps; reject overflowing finite differences before integer conversion.
detrend	Subtract a constant mean or a fitted linear trend in sample index.
normalize	Divide by maximum absolute amplitude; reject an empty or identically zero signal.
smooth	Centered odd-width arithmetic mean with replicate endpoint padding.
noiseEstimate	Robust Gaussian noise sigma from median absolute adjacent differences divided by sqrt(2)*Phi^-1(0.75).
signalToNoise	20*(log10(signal RMS)-log10(noise RMS)) in dB; both energies must be positive.
rms	Scaled root-mean-square calculation that avoids overflow when the RMS itself is representable.
GaussianState	Mean and symmetric positive semidefinite covariance, dimension 1..64.
gaussianState	Validate a mean and symmetric positive semidefinite covariance; Cholesky roundoff tolerance is 1e-12*max(1,diagonal).
stateMean	Read the posterior mean vector.
stateCovariance	Read the symmetric posterior covariance matrix.
kalman	One linear Gaussian prediction+measurement update.
extendedKalman	EKF with checked central-difference Jacobians (step 1e-5*max(1,abs x)).
unscentedKalman	Scaled UKF. alpha>0, beta>=0, n+kappa>0, lambda+n>0.
Wavelet	Orthogonal Haar, 4-tap db2, 8-tap db4, and reversible CDF 5/3 lifting.
Haar	Declaration and type contract below.
Daubechies2	Declaration and type contract below.
Daubechies4	Declaration and type contract below.
Biorthogonal53	Declaration and type contract below.
WaveletTree	Opaque multilevel approximation and detail coefficients, retaining family and original length.
dwt	Periodic multilevel analysis; length must be divisible by 2^levels, with levels 0..20 and length <=1048576.
idwt	Invert multilevel analysis using orthogonal synthesis or inverse CDF 5/3 lifting.
waveletApproximation	Coarsest approximation coefficients after all requested levels.
waveletDetails	Detail bands ordered from finest first to coarsest last.
MotherWavelet	Admissible corrected complex Morlet, real Mexican hat, or real first Gaussian derivative.
Morlet	Declaration and type contract below.
MexicanHat	Declaration and type contract below.
GaussianDerivative	Declaration and type contract below.
cwt	Direct zero-extended CWT.
WaveletPacket	Opaque complete binary low/high analysis tree in natural binary order, rather than frequency-sorted Gray order.
waveletPackets	Recursively analyze both approximation and detail branches to the supplied depth.
inverseWaveletPackets	Reconstruct a complete packet tree exactly up to floating roundoff.
packetBands	Leaf coefficient bands in natural binary low/high tree order.
waveletDenoise	Soft-threshold detail coefficients; optional explicit threshold, otherwise finest-band MAD universal threshold.