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jimmycricket
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Could anybody help me either derive the Hadamard transform from the Fourier transform or point me towards a good source please?
The Hadamard Transform is a mathematical operation used in linear algebra and signal processing to convert a set of data points into a different representation. It is also known as the Hadamard-Walsh Transform, after mathematicians Jacques Hadamard and Joseph Walsh.
The Hadamard Transform is derived from the Hadamard matrix, which is a square matrix with entries of either 1 or -1. The transform is obtained by multiplying the input data vector with the Hadamard matrix, and then dividing the result by the square root of the matrix size.
The Hadamard Transform is significant because it allows for efficient computation of the Fourier Transform, which is used to analyze signals and data in various fields such as engineering, physics, and computer science. It also has applications in data compression and error correction.
The Hadamard Transform is a special case of the Fourier Transform, where the Fourier basis functions are limited to just 1 and -1. This makes the Hadamard Transform simpler to compute and more efficient for certain applications. Additionally, the Hadamard Transform is reversible, meaning the original data can be recovered from the transformed data.
One excellent source for further reading on the Hadamard Transform is the book "Fast Hadamard Transform and Applications" by K.R. Rao, E.D. Miller, and D.N. Kim. It covers the mathematical principles behind the transform, as well as its applications in various fields.