How to convert signal z(n) to z(t) mathematically?

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To convert the discrete signal z(n) to a continuous signal z(t), one must determine whether to apply a Z transform or to interpolate the discrete data points. The discussion highlights the need for clarity on the method of conversion, as both approaches serve different purposes. Interpolation techniques, such as linear or spline interpolation, can be utilized to create a continuous representation from the sampled data. Alternatively, applying a Z transform can provide insights into the signal's frequency components. Understanding the specific requirements of the conversion process is essential for accurate results.
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i have a signal y(t).I have sampled my signal at T0,so i got y(nT0).I multiply this signal with a random number r uniformly distributed in the range 0.95-1.05.Now z(t)=r*y(nT0).How to get z(t) mathematically?
 
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Are you're asking how to take a Z transform, given that you have discrete points, or are you asking how to interpolate your signal and form a continuous signal from the discrete data points that you have?
 
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