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
128⋮8 ch∿01N = 125 kHz? kbit/s

A data logger samples 8 channels, each at 5 kHz with 12-bit resolution. Find the raw data rate Rb in kbit/s.

n = 8fs = 5 kHzN = 12
Rb = kbit/s
2.Easy
f0fs​/2fs​ = ?0.5 kHz

A sensor signal contains frequencies up to 0.5 kHz. Find the minimum sampling rate fs,min that captures it without aliasing.

fmax = 0.5 kHz
fs,min = kHz
3.Medium
Vin​N = 102.5 V2ᴺ − 101 LSB0.961 V?

A 10-bit ADC with an input range of 0 to 2.5 V truncates: its output code is ⌊Vin/LSB⌋ with 1 LSB = VFSR/2ᴺ. Find the decimal output code D for an input of 0.961 V.

N = 10VFSR = 2.5 VVin = 0.961 V
D =
4.Medium
tTs​ = 1/fs​f = 3.2 kHzfs​ = 2 kHz

A 3.2 kHz sine wave is sampled at 2 kHz without an anti-aliasing filter. At which frequency fa does it appear in the samples? Give it in Hz.

f = 3.2 kHzfs = 2 kHz
fa = Hz
5.Hard
f0fs​/2fs​2.4 kHz7f₁?

A 2.4 kHz square wave is sampled at 20 kHz with no anti-aliasing filter. A square wave contains the odd harmonics 3f₁, 5f₁, 7f₁, … At which frequency fa does its harmonic 7f₁ appear in the sampled data? Give it in kHz.

f₁ = 2.4 kHzfs = 20 kHzharmonic: 7f₁
fa = kHz
6.Hard
Vin​N = ?VFSR​2ᴺ − 101 LSB

An audio measurement needs an ideal signal-to-quantisation-noise ratio of at least 40 dB for a full-scale sine wave. Find the smallest number of ADC bits N.

SQNR ≥ 40 dB
N =

Answer key

  1. 1. Rb = 480 kbit/s
  2. 2. fs,min = 1 kHz
  3. 3. D = 393
  4. 4. fa = 800 Hz
  5. 5. fa = 3.2 kHz
  6. 6. N = 7

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