Data acquisition & sampling worksheet with answers

An ADC samples at 4 kHz. Find the Nyquist frequency f_N, the highest signal frequency it can represent without aliasing.

A sensor signal contains frequencies up to 22 kHz. Find the minimum sampling rate f_s,min that captures it without aliasing.

An 85 kHz sine wave is sampled at 50 kHz without an anti-aliasing filter. At which frequency f_a does it appear in the samples? Give it in kHz.

A recorder samples 8 channels at 5 kHz each with a 12-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).

A 10-bit ADC streams every sample over a UART at 230400 baud, format 8N1 (start bit, 8 data bits, 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 f_max that can be sampled without aliasing, in Hz.

A 900 Hz 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 f_a does its harmonic 3f₁ appear in the sampled data? Give it in Hz.