Creating Frequency Selective time invariant channel

Started by chess 6 years ago2 replieslatest reply 6 years ago188 views

Hi everyone

I am wondering if anyone can explain how to generate frequency selective time invariant channel. This means that no Doppler shift and I only need to implement multipath Rayleigh fading channel. I know it is a FIR filter and can be implemented as Tapped delay line. However I do not understand since the equation can be written as 


and how can I implement this.like how to shift delta function.Is this equation implemented like with for loop and each time instant channel gain is multiplied by a shifted delta function?


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Reply by Tim WescottJune 29, 2017

"The equation" that you refer to is an impulse response.  You might want to study up on what that means.  If you did know what it means, you'd know that it defines the system 

\[ h \left(x\left(t\right)\right) = \sum_{n=0}^{N-1} \tilde a_n x \left( t - \tau_n \right) \]

where \(x\left(t\right)\) is the input signal and the output signal is implied.

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Reply by chessJune 29, 2017

Well I was asking about impulse response of a Rayleigh fading channel. By the way the expression I wrote is correct and I insert it from gaudsianwaves website.