Confused about how Echo filter diagram works The picture above is the block diagram of an echo filter. My question is, how does the delay, and gain block affect the output signal? I think that when the input signal is outputted with a delay from when the user and a smaller amplitude.
The output is the sum of the input and a scaled and delayed version of the input

$$y[n] = 2 \cdot (x[n] + 0.8 \cdot x[n-4000])$$

The multiplier of 2 seems a little suspicious. Divide by 2 (or multiply by 0.5) would make more sense.