A real-valued analog signal with a flat spectrum between f = 0 Hz, and fmax is sampled at a sampling frequency fs = 24 kHz. The sampled signal is then processed with an ideal lowpass filter with cutoff frequency = 0.25pi.

How can we specify the range for omega in which aliasing can be torelated and also determine the maximum signal frequency fmax of the analog signal such that no aliasing components are present in the filter output?

  • $\begingroup$ What is omega in this question? $\endgroup$ – Dan Szabo Mar 27 '19 at 2:45
  • $\begingroup$ Omega is the frequency in the discrete domain. i.e. omega_cutoff = 0.25pi. $\endgroup$ – Niousha Mar 27 '19 at 8:19
  • $\begingroup$ Determine the minimum sampling rate according to the bandwith contained at the output of the lowpass filter... $\endgroup$ – Fat32 Mar 27 '19 at 9:30
  • $\begingroup$ @Fat32 I didn't get that. Could you please explain? $\endgroup$ – Niousha Mar 27 '19 at 12:30

An ideal low pass filter has perfect attenuation above the cut off frequency. So any aliasing distortion in that band will be filtered out. In your example, this means any content above 3kHz.

For this application fmax can be made to extend up to the sample rate less the cutoff frequency of the low pass, or 21kHz.


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