Performs deconvolution of two series in the frequency domain.
FDECONV(b, a)
(q, r) = FDECONV(b, a)
b |
- |
A series. |
a |
- |
A series. |
A series such that b = conv(a, q) + r.
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}
a = gnorm(1000, .001)
x = gsin(1000, .001, 3)
b = conv(x, a)
q = fdeconv(b, a)
q recovers the 3 Hertz sine wave.
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.