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I am currently reading about adding echo effects on signals. I was wondering if my understanding is correct.

In the attached figure, the blue line represents the original signal and the red line is the delayed original signal. Is it correct to add these two signals to represent the echo effect, resulting in the green line, assuming no attenuation?

I understand that an echo effect also attenuates the signal. However I just assumed that there is no attenuation for simplicity.

Echo effect on sinusoids

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Is it correct to add these two signals to represent the echo effect, resulting in the green line, assuming no attenuation?

Yes

I understand that an echo effect also attenuates the signal. However I just assumed that there is no attenuation for simplicity.

To continue along your example, if you delay the signal half the period of your sinusoid, the "memorised" positive front from the delay will be added with the negative front of the second half of its period and the result will be zero.

This exact mechanism is responsible for the frequency response of the comb filter.

You can create more complex environments by using an impulse response and convolution.

Hope this helps.

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