function denoiseInput(f, noise_RMS)

%f = [-1*ones(1000,1);3*ones(100,1);1*ones(500,1);-2*ones(800,1);0*ones(900,1)];
%f = detrend(f);

plot(f);
axis([1 length(f) y_range_min y_range_max]);
title('Original');
%g = f + .25*randn(length(f),1);

% figure;
% plot(g,'r');
% title('Noisy');
% axis([1 length(f) y_range_min y_range_max]);
fc = denoisetv(f,noise_RMS);

figure;
plot(fc,'g');
title('De-noised');
axis([1 length(f) y_range_min y_range_max]);

error = (fc-f);
figure;
hold on
plot(f, 'r')
plot(fc,'b')
%plot(error,'b');
hold off
title('Compare');
axis([1 length(f) y_range_min y_range_max]);
legend('input', 'denoise', 'error', 'best');



    function f = denoisetv(g,mu)
    I = length(g);
    u = zeros(I,1);
    y = zeros(I,1);
    rho = 10;

    eigD = abs(fftn([-1;1],[I 1])).^2;
    
        for k=1:100
            f = real(ifft(fft(mu*g+rho*Dt(u)-Dt(y))./(mu+rho*eigD)));
            v = D(f)+(1/rho)*y;
            u = max(abs(v)-1/rho,0).*sign(v);
            y = y - rho*(u-D(f));
        end
    end


    function y = D(x)
    y = [diff(x);x(1)-x(end)];
    end

    function y = Dt(x)
    y = [x(end)-x(1);-diff(x)];
    end

end