How Does Aliasing Affect Signal Processing in a 500Hz Sampling System?

[zak8000]

Homework Statement

An ADC system samples at frequency of 500Hz. it is preceded by 4-pole low_pass Butterworth filter having a 3db frequency of 1KHZ. Three intefering signals are present at frequencies of 2kHz,2.6kHz and 4.4kHz

a) what is the Nyquist frequency of the process?
b) what will be the attenuation in db of each of the three interfering signals?
c) what's frequencies will the three interfering signals be aliased to?

Homework Equations

The Attempt at a Solution

a) F_Nyquist=F_s/2=250Hz
b) attenuation is A(db)=10log(1+(w/wo)^2n) n=4 f=2kHz fo=1kHz for first intefering signal si

A1(db)=10*2.5=25db

others are a similar process

c)? help!

 

[KataKoniK]

Hello,

Let me try to help you with this problem.

a) The Nyquist frequency is defined as half of the sampling frequency, so in this case, it would be 250Hz.

b) To calculate the attenuation in dB, we can use the formula A(db)=10log(1+(w/wo)^2n), where w is the frequency of the interfering signal, wo is the 3dB frequency of the filter (1kHz in this case), and n is the number of poles in the filter (4 in this case).

For the first interfering signal at 2kHz, the attenuation would be A(db)=10log(1+(2/1)^8)=10*2^8=25db.

Similarly, for the second interfering signal at 2.6kHz, the attenuation would be A(db)=10log(1+(2.6/1)^8)=10*2.6^8=32.5db.

For the third interfering signal at 4.4kHz, the attenuation would be A(db)=10log(1+(4.4/1)^8)=10*4.4^8=52.5db.

c) To determine the frequencies that the interfering signals will be aliased to, we can use the formula faliased=|fsampling-fsignal|, where fsampling is the sampling frequency (500Hz in this case) and fsignal is the frequency of the interfering signal.

For the first interfering signal at 2kHz, the aliased frequency would be faliased=|500-2000|=1500Hz.

Similarly, for the second interfering signal at 2.6kHz, the aliased frequency would be faliased=|500-2600|=2100Hz.

For the third interfering signal at 4.4kHz, the aliased frequency would be faliased=|500-4400|=3900Hz.

I hope this helps! Let me know if you have any further questions.