Now of course there is no rule without exceptions. The signal shape or the similarity of the signals also plays a certain role. Let us look at the addition of two sinusoidal signals with different phases to each other. So we see that the addition in example 2 (middle column in picture below) does not lead to a doubling of the level as in example 1 (left column in picture below), but to a complete cancellation of the signals. This case of destructive addition is encountered from time to time in acoustics or audio technology, but should initially be left out of our level calculation.
However, we can already see that, although the effective values of all signals in examples 1 to 3 are the same, the result of an addition (third row) is different depending on the phase relationship of the signals to one another.
Sine and
Sine is referred to as coherent signals. They are maximally similar or the same. The addition again produces a sine signal with a peak value of 2. The signals
Sine and
Sine 180 are very similar in appearance, but due to their phase position (shifted by 180°), they add up to zero (
Sine+(-Sine)). The signals
Sine and
Cosine have a certain similarity, but are shifted 90° from each other. They add up to a sinusoidal signal with a peak value of approximately 1.414 (2 * sin(45°)).
In another example, two noise signals (Noise 1 and Noise 2) are maximally dissimilar or maximally non-coherent. Non-coherent signals are treated like power signals in the level calculation or their effective values are calculated using the level formulas for power. So if you want to add the two noise signals, you should use the formula with the prefactor 10 or divisor 10 in the exponent.
Noise 1 and Noise 2 from the figure above each have a level of -2.3 dBV. According to the formula for power signal, the resulting level is +0.7 dBV.
Or more simply, since it involves two signals with the same RMS value, with:
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