I know the importance of the behaviour of a circuit when a sinusoidal signal is applied: by using Fourier Transform, I can see a generic signal as a (continuous) sum of sinusoidal signals with different frequencies. The question is: By applying Laplace Transform to a circuit, I can find the transient (if circuit is stable) response to this sum of sinusoidal signals. If the generic signal is an audio signal, does the transient influence what I hear? I mean, when I listen to a song, I should also hear a "transient" audio (which should be annoying), but I don't listen to this transient. Then: How is transient response dealt in audio circuits?
Example: if vin is a generic audio signal and by using Fourier I get vin= Asin(wt) + A'sin(w't) + A''sin(w''t) + ... and if the circuit is a simple amplifier with a gain equal to k, then vout = kvin In this case I have the same original audio signal, just amplified by a factor k. But we know that every input sinusoidal signal gives raise to transient (that will extinguish if the circuit is stable), then the output is vout = kvin + transient and thus the output audio signal is no more equal to the input audio signal (and i should hear some "modification" to the song I'm listening to...)