Is subtraction a common method for efficient filtering? I've recently been doing some DSP programming with regard to filter banks. One topic that I've come across was that of the dyadic filter bank. This filter bank essentially breaks a signal into sub-band signals corresponding to some octave. 

Looking at some diagrams, I notice that many of them illustrate implementing both a highpass filter and low pass filter. This will essentially generate two sub-band signals. Conceptually, this makes sense.

However, it seems rather inefficient to implement two separate filters. Would it not be more efficient to implement a single filter, and then subtract the output from the original signal to determine the other signal?

In other words, implement just the low pass filter to obtain the lower subband signal. Then simply subtract that lower subband signal from the inputted signal. This should yield the higher band signal.

So my question: 


Is this technique common? 
Furthermore, would it be vulnerable to phase distortion in the sense that your low pass filter may have phase distorted or lagged the lower band signal?
You are right about the importance of the phase.

Subtraction in the time domain is equivalent to subtraction in the frequency domain. If the frequency domain phase at some frequency is not equal between the complex number being subtracted and the complex number subtracting, even if their magnitudes are the same, the result will be non-zero:


Figure 1. Subtraction of complex numbers of equal magnitude does not always result in a zero. The calculation is black = red - blue.

If the black dot represents the combined frequency response for a system output = input - filtered input at a frequency that you intend to be part of a stop band, you must ensure that the filter is zero-phase. Or if the filter is linear-phase and has in its impulse response a center of symmetry at some time, you must delay the copy of the input by the same amount of time before subtraction. This will not work with efficient infinite impulse response (IIR) filters because of their non-linear phase.