Data acquisition & sampling worksheet with answers

Free printable Data acquisition & sampling worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
f0fN​ = ?20 kHz

An ADC samples at 20 kHz. Find the Nyquist frequency fN, the highest signal frequency it can represent without aliasing.

fs = 20 kHz
fN = kHz
2.Easy
Vin​N = 162.5 V2ᴺ − 101 LSB

A 16-bit ADC that rounds to the nearest code has an input range of 0 to 2.5 V. With 1 LSB = VFSR/2ᴺ, find the largest quantisation error eq,max in mV.

N = 16VFSR = 2.5 V
eq,max = mV
3.Medium
128⋮8 ch∿01N = 2450 kHz? MB

A recorder samples 8 channels at 50 kHz each with a 24-bit ADC. Each sample is stored in whole bytes. Find the memory M needed for a 10 min recording, in MB (1 MB = 10⁶ bytes).

n = 8fs = 50 kHzN = 24t = 10 min
M = MB
4.Medium
tTs​ = 1/fs​f = 3 kHzfs​ = 4 kHz

A 3 kHz sine wave is sampled at 4 kHz without an anti-aliasing filter. At which frequency fa does it appear in the samples? Give it in Hz.

f = 3 kHzfs = 4 kHz
fa = Hz
5.Hard
f0fs​/2fs​1.75 kHz5f₁?

A 1.75 kHz square wave is sampled at 5 kHz with no anti-aliasing filter. A square wave contains the odd harmonics 3f₁, 5f₁, 7f₁, … At which frequency fa does its harmonic 5f₁ appear in the sampled data? Give it in Hz.

f₁ = 1.75 kHzfs = 5 kHzharmonic: 5f₁
fa = Hz
6.Hard
128⋮8 ch∿01tc​ = 2 µstset​ = 2 µsfs​ = ?

An 8-channel multiplexer feeds one ADC. Each conversion takes 2 µs, and after every channel switch the input needs 2 µs to settle. The channels are scanned in turn without pause. Find the sampling rate fs of each channel, in kHz.

n = 8tc = 2 µstset = 2 µs
fs = kHz

Answer key

  1. 1. fN = 10 kHz
  2. 2. eq,max = 0.01907 mV
  3. 3. M = 720 MB
  4. 4. fa = 1000 Hz
  5. 5. fa = 1250 Hz
  6. 6. fs = 31.25 kHz

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