# Please explain Multiplication property in Z transform?

I am having problem visualizing contour any example will be great help. As far as as where I need it I was trying to find Z transform of a contracted signal by first multiplication by impulse train.

• Imagine that you have a plane, much like a graph paper kind of thing. At every nodal point where two vertical lines meet, you have some quantity (for instance $a+ib$). Now draw a curve on the graph paper that does not intersect itself in any way. Contour integration is an integral of the quantities on the plane over an arbitrary curve. What is a "...contracted signal..."? (Do you mean truncated?)
– A_A
Mar 6 '19 at 7:29
• I mean to say that signal is compressed in discrete time.Can you point out any instance or example where above formula have been more useful then using partial fraction or other methods for finding inverse Z transform. Mar 6 '19 at 13:53
• "Compressed" in what sense? In terms of dynamic range or "data compression" (?). How does the "...impulse train..." "compress" the signal?This is the general formula for the multiplication of two signals. The inverse $Z$ transform is obtained differently. What are you trying to do?
– A_A
Mar 6 '19 at 14:04
• I mean for e.g. x{3n} type of compression. What i have is a Z transform of unknown signal its region of convergence is given .What I am trying to do is first multiply the given signal with u{n/3} for doing this I want to use above formula so that I solely operate in Z transform domain and don't have to go in n domain and then use time scaling formula to get X{z^1/3} .But facing difficulty in second step that is multiplication part . Mar 6 '19 at 14:56