Howtosignalprocessing
- How do you find the convolution of two random variables?
- What does convolution do?
- What is the condition of convolution?
- What is convolution in Fourier transform?
How do you find the convolution of two random variables?
In the case of discrete random variables, the convolution is obtained by summing a series of products of the probability mass functions (pmfs) of the two variables. In the case of continuous random variables, it is obtained by integrating the product of their probability density functions (pdfs).
What does convolution do?
Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response.
What is the condition of convolution?
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms.
What is convolution in Fourier transform?
The convolution theorem (together with related theorems) is one of the most important results of Fourier theory which is that the convolution of two functions in real space is the same as the product of their respective Fourier transforms in Fourier space, i.e. f ( r ) ⊗ ⊗ g ( r ) ⇔ F ( k ) G ( k ) .
