# How can I generate time shifted Dirac delta function(impulse response)?

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SUNGKWANG LEE on 4 Mar 2021
Answered: Arthi Sathyamurthi on 26 Mar 2021
I want to make a impulse response of channel with below configuration.
How can I generate delta function with these value?
Ts = 2ns, fs = 50GHz, fc = 1GHz
impulse reponse of channel : h(τ) = 0.7δ(τ) 0.6δ(τ 4 · 10^−10) + 0.5δ(τ 6 · 10^−10)

Arthi Sathyamurthi on 26 Mar 2021
You can generate a time shifted dirac delta function by using the dirac function. Assuming the time shift to be a value ‘a’, dirac(x-a) generates a impulse at the value ‘a’. You can look how to do it in the Mathworks documentation here. This is how your impulse response equation would be,
h(tau) = (0.7*dirac(tau))- (0.6*dirac(tau-(4e-10)) + 0.5*(dirac(tau-(6e-10))))
You can either define ‘tau’ to be syms if you want h(tau) to be an equation or you can declare ‘tau’ as an array of values for which you want to plot the impulse response equation for a range.