SignalProcessing
Convolution
compute the finite linear convolution of two arrays of samples
Calling Sequence
Parameters
Options
Description
Thread Safety
Examples
Compatibility
Convolution(A, B)
A, B
-
Arrays of real or complex numeric sample values
container : Array, predefined Array for holding result
algorithm : symbol, algorithm to use for computation
The Convolution(A, B) command computes the convolution of the Arrays A and B of length M and N respectively, storing the result in a Array C of length M+N−1 and having datatype float[8] or complex[8], which is then returned.
The convolution is defined by the formula
Ck=∑i=1kAiBk−i+1
for each k from 1 to M+N−1, with Aj=0 for M<j and Bj=0 for N<j.
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 an Array of size M+N−1 having datatype float[8] or complex[8].
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.
withSignalProcessing:
Example 1
ConvolutionArray5,7,Array−2,6,10
−10.16.92.70.
Example 2
a≔Array1,2,3,datatype=float8
a≔1.2.3.
b≔Array1,−1,1,−1,datatype=float8
b≔1.−1.1.−1.
Convolutiona,b,algorithm=auto
1.1.2.−2.1.−3.
c≔Array1..numelemsa+numelemsb−1,datatype=float8:
Convolutiona,b,container=c,algorithm=direct
c
Example 3
A≔Vectorrow2−I,0,5+3I,0,4I
A≔2−I05+3I04I
B≔Vectorrow−7,3+10I,9−2I,1
B≔−73+10I9−2I1
C1≔ConvolutionA,B,algorithm=fft
C1≔−14.+7.I16.0000000000000+17.I−19.−34.I−13.+58.I51.−11.I−35.+15.0000000000000I8.+36.I0.+4.00000000000000I
C2≔`~`roundC1
C2≔−14.+7.I16.+17.I−19.−34.I−13.+58.I51.−11.I−35.+15.I8.+36.I0.+4.I
The SignalProcessing[Convolution] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The SignalProcessing[Convolution] command was updated in Maple 2020.
The A, B parameter was updated in Maple 2020.
The algorithm option was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
See Also
SignalProcessing[AutoCorrelation]
SignalProcessing[CrossCorrelation]
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