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SAMPLING
60 Hz, the interference may be eliminated with a discretetime highpass filter that has a frequency response of the form What is the smallest cutoff frequency w, that may be used and still eliminate the 60Hz interference True or False: If x ( n ) has a discretetime Fourier transform that is equal to zero for n / 4 < Iwl I r, DiscreteTime Processing of Analog Signals The system shown in Fig. 39 may be used to process an analog signal with a discretetime system. Assume that x,(t) is bandlimited with X,( f ) = 0 for If 1 > 10 kHz as shown in the figure below. If the discretetime system is an ideal lowpass filter with a cutoff frequency of n/4, find the Fourier transform of y o ( [ )when ( a ) f i = 20 kHz and f 2 = 10 kHz and ( b )f l = 10 kHz and fi = 20 kHz. For bandlimited inpul signals, the system shown in Fig. 310 is a linear timeinvariant continuoustime system. If find the frequency response of the equivalent continuoustime system. For bandlimited input signals, the system shown in Fig. 3 1 is a linear timeinvariant continuoustime system. If 0 the overall system is to be a differentiator, how should the frequency response of the discretetime system be defined
Sample Rate Conversion
The upsampler and downsampler are components that are found in interpolators and decimators, respectively. Are these systems linear Are they shiftinvariant A sequence x ( n ) corresponds to samples of a bandlimited signal using a sampling frequency of 10 kHz. However, the sequence should have been sampled using a sampling frequency f , = 12 kHz. Design a system for digitally changing the sampling rate. A signal x,(r) that is bandlimited to 10 kHz is processed by the following system:

