##G(\omega)## isn't equal to 1. That's the Fourier transform of a single delta function. You have a train of delta functions.nikki92 said:Homework Statement
x(t) = 5cos(2*pi*1000*t) and g(t) = ∑ from n=-infinity to infinity delta(t-n/10000)
find Fourier transform of x(t) and g(t) and the product of the two
The Attempt at a Solution
x(w) = 5*sqrt(pi/2) [delta(w-2000pi)+delta(w+2000pi)]
g(w) = 1
so would the product of the two just be the x(w) ?
Fourier transformation is a mathematical technique used to decompose a complex signal into its individual frequency components. It is used in signal processing, image processing, and various other fields of science and engineering.
Fourier transformation works by breaking down a signal into a sum of sine and cosine waves of different frequencies and amplitudes. This allows for the analysis and manipulation of the individual frequency components of a signal.
Fourier transformation is used for continuous signals, while Fourier series is used for periodic signals. Fourier transformation converts a signal from the time domain to the frequency domain, while Fourier series decomposes a signal into a series of sine and cosine waves with different frequencies and amplitudes.
Fourier transformation is important because it allows for the analysis and processing of signals in the frequency domain, which can provide insights and solutions that are not easily visible in the time domain. It is also a fundamental tool in many areas of science and engineering, including image processing, data compression, and digital signal processing.
Fourier transformation has a wide range of applications in various fields, including audio and video compression, image processing, speech recognition, and medical imaging. It is also used in solving differential equations, pattern recognition, and filtering in signal processing.