Peon666 said:Here's a question solved:
rect (t/2) = 2 sinc (w)
T=3:
f(t+3)+f(t-3) <=> 4 sinc (w) cos 3w
I don't understand how "4 sinc (w) cos 3w" comes in the final answer. Is there any step missing?
Thanks.
The Fourier Transform is a mathematical operation that decomposes a signal into its individual frequency components. It is used to convert a signal from its original representation (often a function of time) to a representation in the frequency domain.
The Fourier Transform is used in a variety of scientific fields, such as signal processing, image analysis, and physics. It is particularly useful for analyzing periodic signals and detecting patterns in data.
The Fourier Transform converts a signal from the time domain to the frequency domain, while the inverse Fourier Transform converts it back from the frequency domain to the time domain. Essentially, the Fourier Transform breaks down a signal into its component frequencies, while the inverse Fourier Transform reconstructs the original signal using those frequencies.
Yes, there are limitations to using the Fourier Transform. It assumes that the signal is periodic and stationary, meaning that it repeats itself over time and does not change. Additionally, the signal must have finite energy for the Fourier Transform to be applicable.
The Fourier Transform is closely related to other mathematical operations, such as the Laplace Transform and the Z-Transform. These transforms are all used to analyze signals, but they differ in the types of signals they can handle and the types of information they provide. The Fourier Transform is specifically designed for periodic signals, while the Laplace Transform is used for analyzing transient signals, and the Z-Transform is used for discrete-time signals.