Hi,
I am learning about digital decimation. The problem is like this:
Z-transform of input sequence and filter aree X(z), H(z) respectively.
After the filter H(z), there is a 2 decimation. From one book talking
about decimation, it says the Z-transform of output sequence after
decimation is:
V(z)=(1/2)*[H(z^(1/2)*X(z^(1/2))+H(-z^(1/2)*X(-z^(1/2))]
I have learned Z transform, but no Z transform with exponential of
(1/2). Can you tell me how to get the above result? Or, give me some
link relate to that. I have checked DSPGuru website without success.
Thanks in advance.

Posted by Rune Allnor●September 7, 20042004-09-07

freelait2000@yahoo.com (Jeff) wrote in message news:<6cdef69d.0409061348.159386ca@posting.google.com>...

> Hi,
> I am learning about digital decimation. The problem is like this:
> Z-transform of input sequence and filter aree X(z), H(z) respectively.
> After the filter H(z), there is a 2 decimation. From one book talking
> about decimation, it says the Z-transform of output sequence after
> decimation is:
>
> V(z)=(1/2)*[H(z^(1/2)*X(z^(1/2))+H(-z^(1/2)*X(-z^(1/2))]
>
> I have learned Z transform, but no Z transform with exponential of
> (1/2). Can you tell me how to get the above result? Or, give me some
> link relate to that. I have checked DSPGuru website without success.
>
>
> Thanks in advance.

We are examining the system [use fixed-width font]
+-----+
| | |
x(n) ------>| | 2 |------> x'(m)
| V |
+-----+
A very crude argument would go something like
X(k)=ZT{x(n)} <-> x(n)
is a Z transform pair. Define the decimated sequence x'(m) such that
x'(m)= x(2n), n=...,-2,-1,0,1,2,...
which means
x(n) <-> x'(m/2), m=...,-4,-2,0,2,4,...
Set up the formal exptression for X'(k)=ZT{x'(m)} and then substitute
n/2 for m.
CAVEAT - The book by Proakis & Manolakis does not mention scaling of
the running index under the "Properties of the Z transform" section,
so there may be one or two pitfalls in the derivation that I am not
aware of. In fact, when I re-read what I just wrote, the line of
"arguments" sound so shaky that I am tempted to hit the "cancel" button
instead of "send"...
Rune

100% of our work is cutting-edge DSP
We are a small, high tech, sonar-processing company that develops state-of-the-art sonar, signal processing software systems used in naval aircraft.
Tasks:
* 60-75% signal processing algorithm development
* 25% real time code development in C++ Full relocation will be provided for the right candidate (e.g. relocation package up to $20,000).