The discussion centers on the properties of logarithms in relation to the convolution of functions. Specifically, it addresses whether the equation ln(x*y) = ln(x) + ln(y) holds true when x and y are functions undergoing convolution. The consensus is that this equation does not apply, as convolution operates on functions rather than simple variables, resulting in another function rather than a product of two variables. The realization that convolution is an integral operation clarifies the misunderstanding.
PREREQUISITESMathematicians, students of calculus, and professionals in signal processing or functional analysis who seek to deepen their understanding of convolution and logarithmic properties.
tramar said:If I have a convolution of two variables, say x * y, and I take the natural logarithm of this operation, ln(x*y), do the same properties of logarithms apply?
So, does ln(x*y) = ln(x)+ln(y) ?