# Concepts: Ideal and Non Ideal Channel Resulting in Inter Symbol Interference

I am following the book: Blind equalization and Identification by Zhi Ding and Ye Li. In Chapter 2, the concept of T spaced equalizers is presented. It is mentioned that the output of the channel is $x[k] = \sum_{i=-\infty}^\infty h[i]s[k-i] + w[k]$ where $h$ is the impulse response, $s$ are the symbols / source input and $w[k]$ is iid noise. Then it is defined that *

"When the channel is non-deal, its impulse response $h[k]$ has more than one nonzero component. Consequently, undesirable signal distrotion as the channel output $x[k]$ depends on multiple symbols in $\{s[k]\}$. This phenomenon is known as inter-symbol interference (ISI)."

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I do not understand why the impulse response has to be zero when it is ideal channel - no ISI. If $h$ is zero then $h[i].s[k-i] = 0$ where $dot$ is the multiplication operator. Or am I mistaken and in the equation $h$ is convolved with $s$ and not multiplied and essentially impulse response will be zero for ideal channel. What is the concept and reason? I do know that convolution in time domain is equivalent to multiplication in frequency domain. But the above representation is in time domain. A brief explanation will work and then I can follow on from the key points mentioned in the answer. Thank you.