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What is the Fourier transform of the function f(x) 1/r?
The Fourier transform of the function f(x) 1/r is 1/k, where k is the wave number.
What are the key differences between the Fourier transform and the Laplace transform?
The key difference between the Fourier transform and the Laplace transform is the domain in which they operate. The Fourier transform is used for signals that are periodic and have a frequency domain representation, while the Laplace transform is used for signals that are non-periodic and have a complex frequency domain representation. Additionally, the Fourier transform is limited to signals that are absolutely integrable, while the Laplace transform can handle signals that grow exponentially.
What are the key differences between the Laplace transform and the Fourier transform?
The key differences between the Laplace transform and the Fourier transform are that the Laplace transform is used for analyzing signals with exponential growth or decay, while the Fourier transform is used for analyzing signals with periodic behavior. Additionally, the Laplace transform includes a complex variable, s, which allows for analysis of both transient and steady-state behavior, whereas the Fourier transform only deals with frequencies in the frequency domain.
What is the Fourier transform of the Coulomb potential?
The Fourier transform of the Coulomb potential is a function that describes how the electric field generated by a point charge varies with distance in reciprocal space.
Why you are considering sine wave as ac but not cosine wave?
Sine wave is considered as the AC signal because it starts at 0 amplitude and it captures the alternating nature of the signal. Cosine wave is just a phase shift of the sine wave and represents the same signal. So, either sine or cosine wave can be used to represent AC signals. However, sine wave is more conventionally used.
Fourier series of sine wave?
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
What is Fourier transformation?
Fourier transform. It is a calculation by which a periodic function is split up into sine waves.
Fourier analysis shows that the saw tooth wave consists of which type of wave?
Fourier analysis shows that the saw wave is constructed through manipulation of a sine wave, I can't remember the maths behind it but it's definitely a sine wave.
The process of breaking down sounds into the simple sine waves that constitute them is called?
Fast Fourier Transform
What is the Fourier transform of the function f(x) 1/r?
The Fourier transform of the function f(x) 1/r is 1/k, where k is the wave number.
What is the difference between Fourier transform and Wavelet transform?
Fourier transform analyzes signals in the frequency domain, representing the signal as a sum of sinusoidal functions. Wavelet transform decomposes signals into different frequency components using wavelet functions that are localized in time and frequency, allowing for analysis of both high and low frequencies simultaneously. Wavelet transform is more suitable than Fourier transform for analyzing non-stationary signals with localized features.
Why you use fast fourier transform?
The fast fourier transform, which was invented by Tukey, significantly improves the speed of computation of discrete fourier transform.
Application of fourier transform?
the main application of fourier transform is the changing a function from frequency domain to time domain, laplaxe transform is the general form of fourier transform .
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What is the difference between discrete fourier transform and fast fourier transform?
discrete fourier transformer uses digital signals whereas the fast fourier transform uses both analog and digital.
What is relation between laplace transform and fourier transform?
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.
What is the difference between the fourier laplace transform?
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
