# FDECONV

## Purpose:

Performs deconvolution of two series in the frequency domain.

## Syntax:

FDECONV(b, a)

(q, r) = FDECONV(b, a)

b |
- |
A series. |

a |
- |
A series. |

## Returns:

A series such that b = conv(a, q) + r.

## Example:

a = {0, 3, 2, 3};

x = {1, 2, 1};

b = conv(a, x);

(q, r) = fdeconv(b, a);

b == {0, 3, 8, 10, 8, 3}

q == {1, 2, 1}

r == {0, 0, 0, 0, 0, 0}

## Example:

a = gnorm(1000, .001)

x = gsin(1000, .001, 3)

b = conv(x, a)

q = fdeconv(b, a)

q
recovers the 3 Hertz sine wave.

## Remarks:

FDECONV is appropriate for recovering a series from a convolution process.
FDECONV uses the FFT to compute the
deconvolution with:

real(ifft(fft(b) / fft(a)))

If the denominator series a contains a zero, the FFT quotient value
is replaced by DEFAULT_MATH_VALUE.

See DECONV for a time domain implementation.

## See Also:

CONV

DECONV

FCONV

FFT

POLYDER