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What does z transform gives?

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I'm pretty familiar with solving z transform, Region of convergence, all I've read throughout my semester while working with digital signal. But intuitively i somehow lack what does z-transform gives geometrically. I know that it's a power series expansion. If x[n] is the sequence, then it's z transform is given as:

$$ X(Z) = sum_n=-infty^infty x[n] z^-n $$

It's just the power series expansion,where:

$$z = r*e^itheta$$

To clarify my question consider the unit step signal.

$$x[n] = 0 for n<0, 1 for n>0 $$

for the above signal Z transform is:

$$X(z) = fraczz-1, ROC: |Z|>1$$

What is the geometrical interpretation for that? Likewise, determinant of 3 by 3 matrix gives the volume.

power-series analytic-geometry z-transform

share|cite|improve this question

edited Mar 20 at 18:38

Surya Bhusal

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

$endgroup$

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  $begingroup$
  There isn't a particularly strong geometric motivation. This is essentially a Fourier transform, though, so if you have intuition there then you might find that it applies here as well.
  $endgroup$
  – davidlowryduda♦
  Mar 28 at 9:43
  

  
  
  
  

add a comment | 

0

$begingroup$

I'm pretty familiar with solving z transform, Region of convergence, all I've read throughout my semester while working with digital signal. But intuitively i somehow lack what does z-transform gives geometrically. I know that it's a power series expansion. If x[n] is the sequence, then it's z transform is given as:

$$ X(Z) = sum_n=-infty^infty x[n] z^-n $$

It's just the power series expansion,where:

$$z = r*e^itheta$$

To clarify my question consider the unit step signal.

$$x[n] = 0 for n<0, 1 for n>0 $$

for the above signal Z transform is:

$$X(z) = fraczz-1, ROC: |Z|>1$$

What is the geometrical interpretation for that? Likewise, determinant of 3 by 3 matrix gives the volume.

power-series analytic-geometry z-transform

share|cite|improve this question

edited Mar 20 at 18:38

Surya Bhusal

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There isn't a particularly strong geometric motivation. This is essentially a Fourier transform, though, so if you have intuition there then you might find that it applies here as well.
  $endgroup$
  – davidlowryduda♦
  Mar 28 at 9:43
  

  
  
  
  

add a comment | 

$begingroup$

I'm pretty familiar with solving z transform, Region of convergence, all I've read throughout my semester while working with digital signal. But intuitively i somehow lack what does z-transform gives geometrically. I know that it's a power series expansion. If x[n] is the sequence, then it's z transform is given as:

$$ X(Z) = sum_n=-infty^infty x[n] z^-n $$

It's just the power series expansion,where:

$$z = r*e^itheta$$

To clarify my question consider the unit step signal.

$$x[n] = 0 for n<0, 1 for n>0 $$

for the above signal Z transform is:

$$X(z) = fraczz-1, ROC: |Z|>1$$

What is the geometrical interpretation for that? Likewise, determinant of 3 by 3 matrix gives the volume.

power-series analytic-geometry z-transform

share|cite|improve this question

edited Mar 20 at 18:38

Surya Bhusal

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

$endgroup$

share|cite|improve this question

edited Mar 20 at 18:38

Surya Bhusal

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

share|cite|improve this question

edited Mar 20 at 18:38

Surya Bhusal

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136

asked Mar 20 at 18:23

Surya BhusalSurya Bhusal

136