The real and imaginary components of a complex Gabor filter are phase sensitive,

i.e., as a consequence their response to a sinusoid is another sinusoid (see Figure

1.2). By getting the magnitude of the output (square root of the sum of squared

real and imaginary outputs) we can get a response that phase insensitive and thus

unmodulated positive response to a target sinusoid input (see Figure 1.2). In some

cases it is useful to compute the overall output of the two out of phase filters.

One common way of doing so is to add the squared output (the energy) of each

filter, equivalently we can get the magnitude. This corresponds to the magnitude

(more precisely the squared magnitude) of the complex Gabor filter output. In the

frequency domain, the magnitude of the response to a particular frequency is simply

the magnitude of the complex Fourier transform, i.e.