David83
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Hello,
I always have this question in my mind, but have never actually asked it: usually the channel impulse response is expressed as:
\[c(\tau,t)=\sum_pc_p\delta(\tau-\tau_p)\]
So, assuming that the transmitted signal is denoted by s(t), the received signal is expressed as:
\[r(t)=\sum_pc_ps(t-\tau_p)+n(t)\]
where n(t) is AWGN noise. The question is: how did we get this expression of the received signal? In other words: what is the result of the convolution:
\[s(t)*\delta(\tau-\tau_p)\]
since one is a function of t and the other is a function of tau?
Thanks in advance
I always have this question in my mind, but have never actually asked it: usually the channel impulse response is expressed as:
\[c(\tau,t)=\sum_pc_p\delta(\tau-\tau_p)\]
So, assuming that the transmitted signal is denoted by s(t), the received signal is expressed as:
\[r(t)=\sum_pc_ps(t-\tau_p)+n(t)\]
where n(t) is AWGN noise. The question is: how did we get this expression of the received signal? In other words: what is the result of the convolution:
\[s(t)*\delta(\tau-\tau_p)\]
since one is a function of t and the other is a function of tau?
Thanks in advance