You are given a signal with the samples $\backslash (\backslash \{1,0,-1,2,3,-1,0,1,-2\backslash \}\backslash )$ and a template with the samples $\backslash (\backslash \{1,-1\backslash \}\backslash ).$ Perform template matching to compute the cross$-$correlation and derive the sample values for the output. Additionally, address the following:

$($a$)$ What is the purpose of template matching in ECG QRS complex detection, and how does normalized cross$-$correlation aid in the process?

$($b$)$ Describe the steps involved in preparing a template for QRS detection using a sample ECG segment. Using the provided signal and template, explain how cross$-$correlation is computed and interpret the results.

$($c$)$ How is a threshold value determined for detecting potential QRS complexes in the crosscorrelation output? What happens if the threshold is set too high or too low?