Hi everyone,
I am not sure if the post should be here or in DSP. So, I try first here.
I want to understand using the K-path sampling according to the book of MSD of Jacob Baker, but I am struggling to get the concept.
Question 1:
the equation numbered 1 seems strange for me as I would write : vin(n.Ts) and not vin(n.Ts/k) because the right side of the equation is the summation of vin sampled at Ts/k which is equivalent as sampling vin at Ts only!!!

Question 2:
if Z=exp(j2pi*f*Ts) and from equation (3) H(z)=Vout_1(z)/Vin_1(z). Then the equation (5) is not consistent with this definition as he considered now H(z)=Vout_1(z^1/k)/Vin_1(z^1/k)!!what I got wrong here?
Question 3:
He states that when using the k path, we can just plug the single z transform of one path to z^k. For me, it would be plugging z with z^1/k as in equation 6!!!
I am totally lost on this as I seem understanding everything the opposite!!
Link :kpath
I am not sure if the post should be here or in DSP. So, I try first here.
I want to understand using the K-path sampling according to the book of MSD of Jacob Baker, but I am struggling to get the concept.
Question 1:
the equation numbered 1 seems strange for me as I would write : vin(n.Ts) and not vin(n.Ts/k) because the right side of the equation is the summation of vin sampled at Ts/k which is equivalent as sampling vin at Ts only!!!

Question 2:
if Z=exp(j2pi*f*Ts) and from equation (3) H(z)=Vout_1(z)/Vin_1(z). Then the equation (5) is not consistent with this definition as he considered now H(z)=Vout_1(z^1/k)/Vin_1(z^1/k)!!what I got wrong here?
Question 3:
He states that when using the k path, we can just plug the single z transform of one path to z^k. For me, it would be plugging z with z^1/k as in equation 6!!!
I am totally lost on this as I seem understanding everything the opposite!!
Link :kpath