Gaussian Blur For Entire Image

Question

I am trying to simulate the blurring process (defocus) of a sinusoidal. For this I have build my own Gaussian filter and performed the convolution in Fourier domain.

The result of the blurred signal is shown below.

The effect in the left and right most part of the blurred image is I assume due to the filter size. If I take sufficiently narrow sized filter the effect becomes less visible.

However, is there a way to get rid of this effect? For example if I take a real picture of a sinusoidal which is out of focus, then one wouldn't observe this effect in the real captured image. What is the correct way to get rid of this effect?

Answer 1

The issue is probably because of the start-up transients. You can possibly fix this using the zi parameter on the filter function:

The other option might be to use the filtfilt method which attempts to choose the initial conditions:

If I take that approach, then the resulting filterings are shown below. The original sinusoid is in blue, the filter version (without matching the initial conditions) is in red and the filtfilt version is in black +s.

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Matlab code

N = 1000;
ts = 0.001;
t = (0:N-1)*ts;
omega = 2*pi*23;
phi = 2*pi*0.829879;
Nsmooth = 10;
Nextra = 10*Nsmooth;

x = sin(omega*t+phi);
xx = [ fliplr(x(1:Nextra)) x fliplr(x((end-Nextra):end)) ];
y = filter(ones(1,Nsmooth)/Nsmooth, 1, x);
zz = filtfilt(ones(1,Nsmooth)/Nsmooth, 1,x);

clf;
plot(x);
hold on;
plot(y,'r');
plot(zz,'k+');