In Figure P6.52 (a), we show the magnitude of the frequency response for an ideal contin...

In Figure P6.52 (a), we show the magnitude of the frequency response for an ideal continuous-time differentiator. A nonideal differentiator would have a frequency response that is some approximation to the frequency response in the figure.

(a) Consider a nonideal differentiator with frequency response G(jω) for which is constrained to be within -±10% of the magnitude of the frequency response of the ideal differentiator at all frequencies; that is,

must be confined to meet this specification.

(b) The system in Figure P6.52(b), incorporating an ideal delay of T seconds, is sometimes used to approximate a continuous-time differentiator. For T = 10^-2 second, determine the frequency range over which the magnitude of the frequency response of the system in the figure is within ±10% of that for an ideal differentiator.