Howtosignalprocessing
- What does it mean for a signal to be absolutely integrable?
- Is Fourier transform integrable?
- What are the conditions for the Fourier transform to exist?
- What is the sufficient condition for existence of Fourier series?
What does it mean for a signal to be absolutely integrable?
In mathematics, an absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite. For a real-valued function, since. where. both and must be finite.
Is Fourier transform integrable?
The Fourier transform can be formally defined as an improper Riemann integral, making it an integral transform, although this definition is not suitable for many applications requiring a more sophisticated integration theory.
What are the conditions for the Fourier transform to exist?
Condition for Existence of Fourier Transform
The function x(t) has a finite number of maxima and minima in every finite interval of time. The function x(t) has a finite number of discontinuities in every finite interval of time. Also, each of these discontinuities must be finite.
What is the sufficient condition for existence of Fourier series?
For the Fourier Series to exist, the following two conditions must be satisfied (along with the Weak Dirichlet Condition): In one period, f(t) has only a finite number of minima and maxima. In one period, f(t) has only a finite number of discontinuities and each one is finite.
