Editing Hadamard transform (section)

==Advantages of the Walsh–Hadamard transform==
=== Real ===
According to the above definition of matrix ''H'', here we let ''H'' = ''H''[''m'',''n'']
<math display="block">H[m,n]=\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}</math>

In the Walsh transform, only 1 and −1 will appear in the matrix. The numbers 1 and −1 are real numbers so there is no need to perform a [[complex number]] calculation.

=== No multiplication is required ===
The DFT needs irrational multiplication, while the Hadamard transform does not. Even rational multiplication is not needed, since sign flips is all it takes.

=== Some properties are similar to those of the DFT ===
{{Copyedit|date=May 2025|section|for=fixing lines containing only full stop}}
In the Walsh transform matrix, all entries in the first row (and column) are equal to 1.

sign change calculated 1st row 0

second row=1.

third row =2.

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eighth row=7.<math display="block">H[m,n] = \left(\begin{array}{rrrrrrrr}
  1 &  1 &  1 &  1 &  1 &  1 &  1 &  1\\
  1 &  1 &  1 &  1 & -1 & -1 & -1 & -1\\
  1 &  1 & -1 & -1 & -1 & -1 &  1 &  1\\
  1 &  1 & -1 & -1 &  1 &  1 & -1 & -1\\ 
  1 & -1 & -1 &  1 &  1 & -1 & -1 &  1\\
  1 & -1 & -1 &  1 & -1 &  1 &  1 & -1\\
  1 & -1 &  1 & -1 & -1 &  1 & -1 &  1\\
  1 & -1 &  1 & -1 &  1 & -1 &  1 & -1
\end{array}\right)</math>

Discrete Fourier transform：
<math display="block">e^{-j 2\pi mn/N}</math>

In discrete Fourier transform, when m equal to zeros (mean first row), the result of DFT also is 1.
At the second row, although it is different from the first row we can observe a characteristic of the matrix that the signal in the first raw matrix is low frequency and it will increase the frequency at second row, increase more frequency until the last row.

If we calculate [[zero crossing]]:

 First row  = 0 zero crossing
 Second row = 1 zero crossing
 Third row  = 2 zero crossings
            ⋮
 Eight row  = 7 zero crossings