Search results
Results from the WOW.Com Content Network
Wavelet OFDM is the basic modulation scheme used in HD-PLC (a power line communications technology developed by Panasonic), and in one of the optional modes included in the IEEE 1901 standard. Wavelet OFDM can achieve deeper notches than traditional FFT OFDM, and wavelet OFDM does not require a guard interval (which usually represents ...
Wavelets have some slight benefits over Fourier transforms in reducing computations when examining specific frequencies. However, they are rarely more sensitive, and indeed, the common Morlet wavelet is mathematically identical to a short-time Fourier transform using a Gaussian window function. [ 13 ]
Lifting sequence consisting of two steps. The lifting scheme is a technique for both designing wavelets and performing the discrete wavelet transform (DWT). In an implementation, it is often worthwhile to merge these steps and design the wavelet filters while performing the wavelet transform.
A necessary condition for the orthogonality of the wavelets is that the scaling sequence is orthogonal to any shifts of it by an even number of coefficients: ∑ n ∈ Z a n a n + 2 m = 2 δ m , 0 {\displaystyle \sum _{n\in \mathbb {Z} }a_{n}a_{n+2m}=2\delta _{m,0}} ,
Even though these wavelets are not orthogonal they have some special properties that have made them quite popular. [3] The terminology spline wavelet is sometimes used to refer to the wavelets in this class of spline wavelets. These special wavelets are also called B-spline wavelets and cardinal B-spline wavelets. [4]
The study of wavelets, and even the term "wavelet", did not come until much later. As a special case of the Daubechies wavelet, the Haar wavelet is also known as Db1. The Haar wavelet is also the simplest possible wavelet. The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable.
Early work in time–frequency analysis can be seen in the Haar wavelets (1909) of Alfréd Haar, though these were not significantly applied to signal processing. More substantial work was undertaken by Dennis Gabor, such as Gabor atoms (1947), an early form of wavelets, and the Gabor transform, a modified short-time Fourier transform.
In magnetic resonance spectroscopy imaging, the Morlet wavelet transform method offers an intuitive bridge between frequency and time information which can clarify the interpretation of complex head trauma spectra obtained with Fourier transform.