Consider a continuous-time ideal high-pass filter that removes all frequencies below a given cut-off frequency, and allows all frequencies at or above that cut-off frequency to pass through the system unchanged. That is, the filter will keep frequency w if w] 2we and remove frequency w if ww Let the cutoff frequency we have value 2π.a) Sketch this filter's frequency response H(ju). (b) Let x(t) 4-3 cos(3m) + 6eMt. Find ak, the Fourier series coefficients of x(t) (c) Now, let r(t) (defined as in part b) be the input to this high-pass filter. Let y(t) represent the filter's output, and let bk represent the Fourier series coefficients of y(t) Write an expression for bk (d) Write an expression for y(t)

Determine the time of the day and month of the year at which the peak sensible cooling load occurs for a top floor, north-eastern corner room of an office building in durban for the following conditions: floor area: 8 x 8 x 3 m east and north walls: 115 mm face brick (outside), 20 mm air space, 115 mm ordinary brick (inside) with 15 mm plaster roof construction: suspended plasterboard ceiling, 450 mm air space, 150 mm concrete, 75mm screed, waterproofing no heat transfer across other surfaces window area 3x 1,5 m high in north wall only. ordinary glass with venetian blinds. lights and occupants : from 07: 00 to 18: 00 average light density: 25 w/m2 number of occupants : 5 seated, light office work room temperature 24°c