Description

If a can be expressed as the convolution of an unknown vector c with b, S3L_deconv deconvolves the vector b out of a. The result, which is returned in c, is such that conv(c,b)=a.

In the general case, c will only represent the quotient of the polynomial division of a by b.

The remainder of that division can be obtained by explicitly convolving with b and subtracting the result from a.

If ma, mb, and mc are the lengths of a, b, and c respectively, ma must be at least equal to mb. The length of mc will be such that mc+mb-1=ma or, equivalently, mc=ma-mb+1.

S3L_deconv is most efficient when all arrays have the same length and when this length is such that it can be computed efficiently by S3L_fft or S3L_rc_fft. See "S3L_fft " and "S3L_rc_fft and S3L_cr_fft " for additional information.

Restriction

The dimensions of the array c must be such that the 1D or 2D complex-to-complex FFT or real-to-complex FFT can be computed.

Scaling

The results of the deconvolution are scaled according to the underlying FFT that is used. In particular, for multiple processes, if a and b are real 1D, the result is scaled by n/2, where n is the length of c. For single processes, it is scaled and by n. In all other cases, the result is scaled by the product of the extents of c.

Side Effects

Because a and b are used internally for auxiliary storage, they may be destroyed after the deconvolution calculation is complete. If a and b must be used after the deconvolution, they should first be copied to temporary arrays.