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algorithm : keyword auto, direct, or fft for the algorithm to use for computation; default is direct

container : Array or Vector, predefined container for holding result

shape : keyword full, same, or valid for the shape of the convolution; default is full

subtype : keyword Array, Vector, Vector[column], or Vector[row] for the subtype of the output; default is Array

The Convolution(A, B) command computes the full convolution of the signals A and B of length $M$ and $N$ respectively, storing the result in a container C of length $M+N-1$ and having datatype float[8] or complex[8], which is then returned.

The full convolution is defined by the formula

for each $k$ from $1$ to $M+N-1$, with $A_j=0$ for $M<j$ and $B_j=0$ for $N<j$.

For all choices of shape, the full convolution of size $P=M+N-1$ is computed. When shape=same, the full convolution is trimmed on both sides so that the result is of length $Q=M$. Note that when the number of elements to be trimmed is odd, one more element will be trimmed from the left side than the right. When shape=valid, the final convolution will be found in a similar manner to the shape=same case, but the value of the size $Q$ will be $M$ when $N=0$, and $\max \left(M-N+1\&comma;0\right)$ otherwise. The valid convolution effectively discards the elements which involve padded zeros for the signals.

Before the code performing the computation runs, A and B are converted to datatype float[8] (if the values are all real-valued) or complex[8] (if all the values are complex-valued, but not all real-valued) if they do not have that datatype already. For this reason, it is most efficient if A and B have one of these datatypes beforehand.

If either A or B is an rtable that is not a 1-D Array, it is accepted by the command and converted to an Array. Should this not be possible, an error will be thrown.

If the container=C option is provided, then the results are put into C and C is returned. With this option, no additional memory is allocated to store the result. The container must be a 1-D rtable of appropriate size having datatype float[8] (for two real signals) or complex[8] (for one or two complex signals).

The algorithm=name option can be used to specify the algorithm used for computing the convolution. Supported algorithms:

auto - automatically choose the fastest algorithm based on input.

direct - use direct convolution formula for computation. This is the default.

fft - use an algorithm based on the Fast Fourier Transform (FFT). This is a much faster algorithm than the direct formula for large samples, but numerical roundoff can cause significant numerical artifacts, especially when the result has a large dynamic range.

The SignalProcessing[Convolution] command is thread-safe as of Maple 17.

For more information on thread safety, see index/threadsafe .

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\&colon;$

The SignalProcessing[Convolution] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17 .

The A and B parameters were updated in Maple 2020.

The algorithm option was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020 .

The SignalProcessing[Convolution] command was updated in Maple 2023.

The shape and subtype options were introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023 .