# CT and DT signal processing

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#### svensl

##### Full Member level 1
Hello all,

I was wonderig whether I can mix CT and DT processing blocks. For example. Consider a CT integrator Fs/s in series with discrete time differentiator 1-z^(-1). I would like to find the overall transfer function and am inclined to write the poduct of the two:
Fs/jw*(1-exp(-jwTs)) where Ts is the sampling time? Can I do this and mix CT and DT blocks?

sven

#### v_c

I don't think you can just multiply them direclty -- it would not make sense. It is like mixing apples and oranges. So you have to transform one of the transfer functions, then you can do the multiplication. For example, you can take the s-domain transfer function and use
the Tustin (Bilinear) Discretization. See page 3 of this document https://www.ccec.ece.ucsb.edu/people/smith/classnotes/147b/lecture4_small.pdf

In this transformation you basically use the replacement
$s=\frac{2}{T} \frac{z-1}{z+1}$
where $T$ is your sampling period.

This transformation is also available in Matlab. Take a look at the documentation for the
c2d function.
Code:
discap1 = c2d(contap,0.1,'tustin');
bode(contap,discap,discap1)

Best regards,
v_c

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### svensl

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#### svensl

##### Full Member level 1
Thanks v_c for this informaton. It was really helpful.

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