Smoothing means LPFKey is in FFT Cooley-Tookey and FFTW (decomposition, recursive devide-and-conqure) realization, did you mean O(N*log(N)) (it can be space-time tradeoff, which is memory storage(RAM) vs computing cycles (clocksteps) in embedded, likely the maximal gain on computation steps saving/minimization, while what is the storage complexity?) complexity? What is this? I work, but no one hired me. Let's amend, employ me.
The main question is what are the feasible high-value, high-utility industrial applications of datum science, control systems engineering and dynamical modes and other specific domain strategies generation to sell the algorithms (find sponsors, buyers, investors, entrepreneours) and their implementations in TCE Matlab, Octave, C, C++, Scheme, Python as the only driving motivation for more in-depth analysis and elaboration within the scope.
This version doesn't run faster, but accurate in TCE GNU Octave (why? because of memory storage enlargement or which mistake to correct / improvement found in it?), while it contains less loops and it smoothes the input:
function filteredSignal = bilFil_vec(signal, sigma_spatial, sigma_range,ver)
%Roll Ver.
% Calculate the size of the 1-D signal
N = length(signal);
% Initialize the output signal
filteredSignal = zeros(size(signal));
% Apply bilateral filtering:
%ver1 (further rapidized as per loop operations minimization):
if ver == 1
%1. Construct spatial_diff and range_diff matrices as concatenated parametrized growth vectors2d
%, if not by loop then by reshape or repmat like procedures, how?
%spatial_diff = [0:-1:-N,
%range_diff = abs(circshift(signal) - signal);
spatial_diff = abs(0:-1:1-N);
range_diff = abs(signal(1) - signal);
for i = 2:N
spatial_diff = [spatial_diff;i-1:-1:i-N];
range_diff = [range_diff;abs(signal(i) - signal)];
end
%spatial_diff = spatial_diff';
%range_diff = range_diff';
%replace 2 loops by matrix multiplications:
weight = exp(-(spatial_diff.^2)./(2*sigma_spatial.^2)-(range_diff.^2)./(2*sigma_range.^2));
%weighted_sum = sum(weight.*signal);
%normaliz = abs(weight); %optional
%normaliz = sum(weight);
% Calculate the filtered value for the current sample
%filteredSignal = weighted_sum./normaliz; %*inv(normaliz);
filteredSignal = signal*weight; %./sum(weight);
else
%ver 2
for i = 1:N
spatial_diff = i-1:-1:i-N;
range_diff = abs(signal(i)-signal);
weight = exp(-spatial_diff.^2./(2*sigma_spatial^2)-range_diff.^2./(2*sigma_range^2));
filteredSignal(i) = sum(weight.*signal)./sum(weight);
end
end
end
Input signal to it:
Invokation:
filteredSignal = bilFil_vec(inp,2,10,1)
Output produced (as you can see it has been indeed smoothed by my version, which contains internal LPF) (ver == 1):
Please let me know.
