Referred to as FCFT (Fast Continuous Fourier Transforms), new algorithme are proposed to evaluate the (integral)
Fourier transform of a continuons signal . These algorithms compute without truncation error the Fourier integral,
over the sampling duration, of a continuous pseudo signal deduced from samples by polynomial interpolations of
order 0 (step by step function) to 3 (cubic spline) . They are very fast because an FFT (Fast Fourier Transform)
algorithm is used for the calculation of quadrature formulas . They seem to be especially applicable to the Fourier
transform computation of non periodic and/or not band limited signais because the yielded spectrum is not periodic.
In particular, with transient signais, calculations made beyond the half of the sampling frequency can be significant.
The FCFT algorithme based upon polynomial interpolations of order 2 and 3 are particularly efficient .Ces algorithmes sont proposés pour évaluer la transformée de Fourier d'un signal continu. Ces algorithmes calculent sans erreur de troncature l'intégrale de Fourier sur la durée d'échantillonnage, d'un pseudo signal continu déduit des échantillons par interpolations polynomiales d'ordre 0 à 3. Pour les signaux transitoires, les calculs au-delà de la demi-fréquence d'échantillonnage peuvent être significatifs. Les algorithmes TFCR d'ordres 2 et 3 sont particulièrement efficace
