If a third-octave bandpass filter has a starting frequency of 500 Hz: What is the center frequency of the band in a proportional and the stop frequency of the bandpass?

Explain the significance of anti-aliasing filter and anti-imaging filter. The spectrum of a discrete time signal is shown in the bellow figure. Draw the spectrum of the signal if it is up-sampled by I=3. -2π -π -ποι 2 X(ejw) W π π 2π 2

a. Suppose a first order high pass filter has a cut-off frequency of 10 kHz and a capacitor of 2.5 nF. What is the value of the resistor?   b. For the filter in (a), what is the gain of the filter at 100 Hz? Express you answer in decibels. (Hint: this requires hardly any calculation.)