Fourier Transforms Flashcards
What is a Fourier transform
A Fourier transform is a mathematical operation that transforms a function or signal from its original domain (typically time or space) into a representation in the frequency domain. It decomposes the signal into its constituent frequencies, showing how much of each frequency is present in the original signal
What are the three parameters to desribe a wave
What another way to represent waves
In real space, we describe objects or structures in terms of their actual physical distances (e.g., the distance between atoms in a crystal). In contrast, reciprocal space describes the structure in terms of the wavelengths or periodicities of waves that can describe the repeating patterns in that material
What is an inverse Fourier transform
What is the Fourier transform of this wave
What is the DC component
In a Fourier transform, the DC component refers to the part of the signal that has zero frequency, meaning it represents the constant or average value of the entire signal over time. “DC” stands for Direct Current, which in electrical terms is a constant, non-varying signal
If you imagine a signal that oscillates up and down, like a wave, the DC component is the horizontal baseline around which the wave fluctuates.
If the signal is purely oscillating (like a sine wave centered at zero), the DC component is zero.
If the signal has some constant offset (for example, it oscillates but is always above zero), that constant part is the DC component
What are 2D waves
2D waves, or two-dimensional waves, are waves that propagate in two spatial dimensions, such as across a flat surface
What is the frequency and wavelength of this wave
Explain this 2D Fourier transform
What are 3D waves
3D waves, or three-dimensional waves, are waves that propagate in all three spatial dimensions—length, width, and height. These waves spread out in every direction from their source, not just along a line (1D) or a plane (2D).
Examples of 3D Waves:
Sound Waves in Air: When you speak or clap, sound waves spread out spherically in all directions through the air. These waves are compressions and rarefactions of air molecules that move in three dimensions.
Light Waves: Light, being an electromagnetic wave, also propagates in 3D. A light bulb, for instance, emits light waves
