Seamless looping of a signal without pops I'm trying to seamlessly loop an audio signal. When I loop the current audio signal I have, I hear audible clicks or pops right as it loops back to the beginning. I want to be able to loop the audio signal without having any pops.
I have tried changing the signal near the end by writing an interpolation which follows this formula
$$
B_n=\frac{(A_n d_1) + (Cd_2)}{d_1+d_2}
$$
Where $B$ is the output, $A$ is the audio signal itself, and $C$ is the first signal value within the audio signal. $d_1$ equals to how many signal values until the first sample. $d_2$ equals how many signal values since the specified start. And I choose when the specified start is based on how many milliseconds I wish for the interpolation to be. In this case I gave 15ms a try. So, the specified start will be 15ms before the end of the signal.
And in simple terms; it's a crossfader that is linearly transitioning from the signal source $A$ onto the single value $C$.
The end result is this.

The transition points are highlighted via the cursor. Also, do not mind that both signals are not exactly the same. For the upper signal, I cut a portion of the start so that it would start at a non-0 value.
Since the crossfade is fairly quick for human ears (15ms), I did not manage to hear any disintegration of audio. But is this good practice? I am new to signal processing and cannot tell whether or not this will work for all types of signals I might have. Is there any other way this could be done in a more &quot;proper&quot; manner?
But is this good practice?

Yes, that's a perfectly reasonable approach.

Will this will work for all types of signals I might have ?

There are a LOT of signals out there and there is always an outlier. In your case, I think the most &quot;vulnerable&quot; would be low frequency sine waves. A 40 Hz sine wave has a period of 25 ms and looping one at an inconvenient point without audible artifact is tricky. So this all boils down to: how likely are these signal for your application, what level audibility is acceptable and what are the constraints around resources,  looping points &amp; length, etc.

Is there any other way this could be done in a more &quot;proper&quot; manner?


If you have some leeway with the exact loop length and loop points, try to put the loop points at the nearest zero crossing. Ideally both zero crossing go in the same direction.
You can do an energy cross fade instead of a linear cross fade. This will minimize the volume dip in the middle of the cross fade, but at 15ms it's not going to make much of an audible difference.