Please the solution must be step by step I will rate it ASAP

Please the solution must be step by step. I will rate it ASAP

Multidimensional Signal Processing

Problem Two (40 Points FIR Design from Ideal Filter A Finite Impulse Response (FIR) filter is a linear shift invariant filter whose impulse response function is a finite-extent discrete signal. For an FIR filter, the output can be determined from its input by means of the convolution sum, expressed as, Ke-1 Ki-1 with support over the region, (mo,n): 0s no, na

Solution

The backfin of a power mosfet has dimensions 1.0 cm x 1.3cm and a thickness of 1.585mm. It is made out of copper. The purpose of the backfin here is to carry away the heat from the si-based chip attached to the backfin (and here burried in a black plastic case). Thus the backfin is (usually) electrically connected to the mosfet. To mount to a grounded case (Aluminum, quite thick, and at room temperature, 23 oC), an electrically insulating, plastic layer of thickness 0.2873mm and of thermal conductivity 90 W/oC/m is placed between the fin and the aluminum. Assume that the aluminum stays throughout at 23 oC degrees. The mosfet will fail catastrophically (thermal runaway) if its temperature gets above 180oC.
(a) If its RDS in the \"on\" state is 78.88 mOhms, what is the maximum current it can safely conduct in steady state in this mount?
(b) Supose the mosfet was operating just at the breaking point...what would then be the temperature at the shared surface between the copper and the plastic layer?