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
f0fs​/2fs​ = ?4 kHz

A sensor signal contains frequencies up to 4 kHz. Find the minimum sampling rate fs,min that captures it without aliasing.

fmax = 4 kHz
fs,min = kHz
2.Easy
Vin​N = 1210 V2ᴺ − 101 LSB

A 12-bit ADC that rounds to the nearest code has an input range of 0 to 10 V. With 1 LSB = VFSR/2ᴺ, find the largest quantisation error eq,max in mV.

N = 12VFSR = 10 V
eq,max = mV
3.Medium
∿01N = 125 kHz? MB

A recorder samples one channel at 5 kHz with a 12-bit ADC. Each sample is stored in whole bytes. Find the memory M needed for a 2 min recording, in MB (1 MB = 10⁶ bytes).

n = 1fs = 5 kHzN = 12t = 2 min
M = MB
4.Medium
Vin​N = ?2.5 V2ᴺ − 10≤ 0.2 mV

An ADC with an input range of 0 to 2.5 V must resolve steps of 0.2 mV or smaller. Find the smallest number of bits N.

VFSR = 2.5 Vresolution = 0.2 mV
N =
5.Hard
T20 mV/°C×1∿01N = 8, 2.5 V? °C/LSB

A temperature sensor gives 20 mV/°C (0 V at 0 °C). Its signal is amplified 1 times and fed to an 8-bit ADC with a range of 0 to 2.5 V (1 LSB = VFSR/2ᴺ). Find the temperature change ΔTLSB that corresponds to one LSB.

S = 20 mV/°CG = 1N = 8VFSR = 2.5 V
ΔTLSB = °C
6.Hard
f0fs​/2fs​1.2 kHz3f₁?

A 1.2 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 3f₁ appear in the sampled data? Give it in Hz.

f₁ = 1.2 kHzfs = 5 kHzharmonic: 3f₁
fa = Hz

Answer key

  1. 1. fs,min = 8 kHz
  2. 2. eq,max = 1.221 mV
  3. 3. M = 1.2 MB
  4. 4. N = 14
  5. 5. ΔTLSB = 0.4883 °C
  6. 6. fa = 1400 Hz

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