Convolve N dimensional signals using the FFT for computation.
This function is equivalent to convn but using the FFT. It
convolves the two N dimensional A and B. The size of
output is controlled by the option shape which removes the
borders where boundary effects may be seen:
"full" (default)Return the full convolution.
"same"Return central part of the convolution with the same size as A.
"valid"Return only the parts which do not include zero-padded edges.
Using the FFT may be faster but this is not always the case and can be a lot worse, specially for smalls A and B. This performance increase also comes at the cost of increased memory usage, as well as a loss of precision.
a = randi (255, 1024, 1024); b = randi (255, 10, 10); t = cputime (); convn (a, b); cputime () -t ⇒ 0.096000 t = cputime (); fftconvn (a, b); cputime () -t ⇒ 1.2560 b = randi (255, 50, 50); t = cputime (); convn (a, b); cputime () -t ⇒ 2.3400 t = cputime (); fftconvn (a, b); cputime () -t ⇒ 1.2560
Note how computation time for convn increased with the size of
B but remained constant when using fftconvn. When
performing the convolution, fftconvn zero pads both A and
B so their lengths are a power of two on all dimensions.
This may further increase memory usage but will also increase
performance. In this example, the computation time will remain constant
until size (A) + size (B) -1 is greater than 2048
after which it will remain constant again until it reaches 4096.
a = randi (255, 1024, 1024); b = randi (255, 50, 50); t = cputime (); fftconvn (a, b); cputime () -t ⇒ 1.2760 a = randi (255, 2048-50+1, 2048-50+1); t = cputime (); fftconvn (a, b); cputime () -t ⇒ 1.2120 a = randi (255, 2049-50+1, 2049-50+1); t = cputime (); fftconvn (a, b); cputime () -t ⇒ 6.1520 a = randi (255, 4096-50+1, 4096-50+1); t = cputime (); fftconvn (a, b); cputime () -t ⇒ 6.2360 a = randi (255, 4097-50+1, 4097-50+1); t = cputime (); fftconvn (a, b); cputime () -t ⇒ 38.120
See also: convn, fftconv2, fftconv, padarray.
Package: image