I need help in solving the below question. Bandwidth of the signal is 1KHz. Use a 12-bit ADC with SNR of 78dB for sampling. the sampling frequency is 12KHz. Choose suitable filter order and cut-off frequency
Assume no crud above 1Khz to be filtered out. In that case, no filter needed.
Assume the crud above 1Khz must be filtered out. This cannot be done without infinite steepness before sampling. This cannot be done.
What can be done? Simple example is to remove all the crud above 6KHz, attenuating down to 1 quanta level or to -78dBc.
Thus need the stopband to be -78dB, above 6KHz. That ratio 6KHz/1khz, or 2.5 octaves, is key in computing the rolloff steepness.
78/2.5 ~~ 75/2.5 == 30. Thus need 30dB/octave or 5 poles of 6dB each.
In this case, the spectrum from DC to 6KHz will be properly represented, including any crud. You can use DSP methods on this properly-represented spectrum and achieve whatever rolloff you need, limited by your word-length and compute power.