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Are there any algorithms for efficient computation of convolution?
Data can be split in time domain according to overlap-save and overlap-add scheme [22, 23], respectively. Combining these two schemes with fast convolution one can receive a quasi-optimal solution that can be efciently computed on any computer. Again, the solution naturally leads to a possible parallelization.
How can we understand the meaning of convolution?
In order to understand the meaning of convolution, we are going to start from the concept of signal decomposition. The input signal is decomposed into simple additive components, and the system response of the input signal results in by adding the output of these components passed through the system.
How is convolution used in signal processing and analysis?
Convolution is the most important and fundamental concept in signal processing and analysis. By using convolution, we can construct the output of system for any arbitrary input signal, if we know the impulse response of system.
How is impulse function decomposition used in convolution?
Impulse Function Decomposition In order to understand the meaning of convolution, we are going to start from the concept of signal decomposition. The input signal is decomposed into simple additive components, and the system response of the input signal results in by adding the output of these components passed through the system.
How is a convolution computed in the time domain?
While the convolution in time domain performs an inner product in each sample, in the Fourier domain [20], it can be computed as a simple point-wise multiplication. Due to this convolution property and the fast Fourier transform the convolution can be performed in time O (N log N ). This approach is known as a fast convolution [1].
How is the repetitive application of convolution reduced?
In this concept, the repetitive application of convolution kernel is reduced due to the fact that neighbouring positions overlap. Hence, the convolution in each individual sample is obtained as a weighted sum of both input samples and previously computed output samples.
Is the recursive version of convolution nontrivial?
The conversion of general convolution kernel into its recursive version is a nontrivial task. Moreover, the recursive ltering often suffers from inaccuracy and instability [2]. While the convolution in time domain performs an inner product in each sample, in the Fourier domain [20], it can be computed as a simple point-wise multiplication.