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
Vin​N = 102.5 V2ᴺ − 101 LSB

A 10-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 = 10VFSR = 2.5 V
eq,max = mV
2.Easy
123⋮3 ch∿01N = 2448 kHz? kbit/s

A data logger samples 3 channels, each at 48 kHz with 24-bit resolution. Find the raw data rate Rb in kbit/s.

n = 3fs = 48 kHzN = 24
Rb = kbit/s
3.Medium
tTs​ = 1/fs​f = 1.35 kHzfs​ = 1 kHz

A 1.35 kHz sine wave is sampled at 1 kHz without an anti-aliasing filter. At which frequency fa does it appear in the samples? Give it in Hz.

f = 1.35 kHzfs = 1 kHz
fa = Hz
4.Medium
122 ch∿01N = 245 kHz? MB

A recorder samples 2 channels at 5 kHz each with a 24-bit ADC. Each sample is stored in whole bytes. Find the memory M needed for a 1 min recording, in MB (1 MB = 10⁶ bytes).

n = 2fs = 5 kHzN = 24t = 1 min
M = MB
5.Hard
SD0​D1​D2​D3​D4​D5​D6​D7​PTb​11·Tb​115200 Bd, 8E1

A 12-bit ADC streams every sample over a UART at 115200 baud, format 8E1 (start bit, 8 data bits, even parity, 1 stop bit). Each sample is sent as 2 whole byte(s) and the link is busy all the time. Find the highest signal frequency fmax that can be sampled without aliasing, in Hz.

baud = 115200 BdN = 128E1
fmax = Hz
6.Hard
f0fs​/2fs​8 kHz3f₁?

An 8 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 3f₁ appear in the sampled data? Give it in kHz.

f₁ = 8 kHzfs = 20 kHzharmonic: 3f₁
fa = kHz

Answer key

  1. 1. eq,max = 1.221 mV
  2. 2. Rb = 3456 kbit/s
  3. 3. fa = 350 Hz
  4. 4. M = 1.8 MB
  5. 5. fmax = 2618 Hz
  6. 6. fa = 4 kHz

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