API Reference

The package is separated into three groups of procedures. The Fourier Transforms perform 1D and 2D discrete Fourier transforms (DFT’s) with mixed precision floating point operations. For DFT conventions in 1D and 2D, see mp_dft and mp_dft2, respectively. The Sampling partition DFT frequencies and sample signals at partial sets of frequencies. The Inversion procedures invert sampled integer signals. The inversion algorithms implement the efficient dynammic programming algorithms in [LV].

Fourier Transforms

mp_dft(signal)	Compute the 1D discrete Fourier transform of a signal.
mp_idft(signal)	Compute the 1D inverse discrete Fourier transform of a signal.
mp_dft2(signal)	Compute the 2D discrete Fourier transform of a signal.
mp_idft2(signal)	Compute the 2D inverse discrete Fourier transform of a signal.

Sampling

get_coeff_classes_1D(N[, include_conjugates])	Returns a dictionary of classes of DFT coefficient frequencies for a 1D integer signal.
get_coeff_classes_2D(M, N[, include_conjugates])	Returns a dictionary of classes of DFT coefficient frequencies for a 2D integer matrix.
select_coeffs_1D(N[, Ls])	Selects a set of DFT coefficient frequencies.
select_coeffs_2D(M, N[, Ls])	Selects a set of DFT coefficient frequencies.
sample_1D(signal[, known_coeffs])	Sample DFT coefficients of a 1D integer signal.
sample_2D(signal[, known_coeffs])	Sample DFT coefficients of a 2D integer signal.

Inversion

invert_1D(signal[, known_coeffs])	Invert an integer signal from limited DFT spectrum.
invert_2D(signal[, known_coeffs])	Invert an integer matrix from limited DFT spectrum.
InversionError(msg, beta2, precision, epsilon)	Python-exception-derived object raised by inversion functions.

Examples

For examples, see the various functions. For all examples, it is assumed that the modules binvert, numpy, and gmpy2 have been imported.