# determining walsh function components of signal after passing through non linear process

When a sum of sine waves is passed through a non linear process, harmonics and intermodulation distortion products are created, which are visible when applying an FFT to the signal. This causes potential problems when figuring out which sine waves were present in the signal originally.

Does something similar happen when a sum of walsh functions is passed through a non linear process and the walsh transform is applied?

Thanks, B

• Yes. ${}{}{}{}{}{}$ Commented Dec 25, 2013 at 16:30
• @DilipSarwate thanks - can you elaborate what exactly happens? if you have any links to where I can read more that would be great. Commented Dec 25, 2013 at 16:59
• Since the Walsh transform basis function $h_i(t)$ has the properties that $(h_i(t))^{2k} = 1 = h_0(t)$ fand $(h_i(t))^{2k+1} = h_i(t)$ or all integers $k$, then any nonlinear distortion, say $y(t) = x(t)+0.001x^2(t)+0.0001x^3(t)$, where $x(t) = \sum_i a_ih_i(t)$ will give $y(t) = \sum_i a_{2i+1}^{2i+1}h_i(t) + \sum_i a_{2i}^{2i}h_0(t)$ and separating out what part of the coefficient of $h_0(t)$ is from the signal and what part from the distortion is a mess. Commented Dec 26, 2013 at 2:26