Hadamard Transform: Need Help Deriving or Source

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The discussion centers on deriving the Hadamard transform from the Fourier transform. The original poster initially sought assistance but later confirmed they successfully figured it out independently. No specific sources or tools were provided in the discussion, indicating a lack of external references. The focus remains on the relationship between these two mathematical transforms.

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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?
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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