Step 1: Understanding Reducing Agents in Printing: Reducing agents are used in textile printing, particularly with vat dyes and discharge printing. Vat Dye Printing: Vat dyes are insoluble in water. They must be reduced to a soluble "leuco" form to be applied to the fiber. After dyeing, the leuco form is oxidized back to the insoluble form, trapping the dye within the fiber.
Discharge Printing: A reducing agent is used to destroy the color of a previously dyed fabric, creating a white or light-colored design on a darker background.
Step 2: Identifying the Reducing Agent: Sodium Hydrosulphite (Sodium Dithionite, \(Na_2S_2O_4\)): This is a powerful reducing agent commonly used in vat dyeing and discharge printing.
Sodium Chlorite (\(NaClO_2\)): This is an oxidizing agent, used for bleaching, not reducing.
Sodium Nitrate (\(NaNO_3\)): This is an oxidizing agent.
Sodium Phosphate (\(Na_3PO_4\)): This is a buffering agent, not a reducing agent.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.