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​ = ?20 kHz

A sensor signal contains frequencies up to 20 kHz. Find the minimum sampling rate fs,min that captures it without aliasing.

fmax = 20 kHz
fs,min = kHz
2.Easy
f0fN​ = ?40 kHz

An ADC samples at 40 kHz. Find the Nyquist frequency fN, the highest signal frequency it can represent without aliasing.

fs = 40 kHz
fN = kHz
3.Medium
Vin​N = 1010 V2ᴺ − 11 LSB1.04 V?

A 10-bit ADC with an input range of 0 to 10 V truncates: its output code is ⌊Vin/LSB⌋ with 1 LSB = VFSR/2ᴺ. Find the decimal output code D for an input of 1.04 V.

N = 10VFSR = 10 VVin = 1.04 V
D =
4.Medium
SD0​D1​D2​D3​D4​D5​D6​D7​PTb​11·Tb​1200 Bd, 8E1

A UART sends bytes at 1200 baud in the format 8E1: 8 data bits, an even parity bit and 1 stop bit(s), plus the start bit. Find the largest number of data bytes per second it can transfer.

baud = 1200 Bd8E1
RB = B/s
5.Hard
f0fs​/2fs​2.4 kHz5f₁?

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 5f₁ appear in the sampled data? Give it in kHz.

f₁ = 2.4 kHzfs = 20 kHzharmonic: 5f₁
fa = kHz
6.Hard
SD0​D1​D2​D3​D4​D5​D6​D7​1/fbaud​20 MHz / (16·D)

A microcontroller with a 20 MHz clock sets its UART baud rate as fclk/(16·D), with D a whole number rounded to the nearest value. The target is 115200 baud. Find the percentage error of the real baud rate (positive when it is too fast).

fclk = 20 MHztarget = 115200 Bd
e = %

Answer key

  1. 1. fs,min = 40 kHz
  2. 2. fN = 20 kHz
  3. 3. D = 106
  4. 4. RB = 109.1 B/s
  5. 5. fa = 8 kHz
  6. 6. e = −1.357 %

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