# SAMPLING

Updated: Feb 28, 2020

During digital data acquisition, output analog signals which must be digitized for a computer. A computer cannot store continuous analog time waveforms. So instead it breaks the signal into discrete ‘pieces’ or ‘samples’ to store them.

Data is recorded in the time domain, but often it is desired to perform a Fourier transform to view the data in the frequency domain

**Time Domain Terms**

# Sampling Rate (Fs) – Number of data samples acquired per second

# Block Size (N)- Total number of time data points that are captured to perform a Fourier transform during one frame. A block size of 2000 means that two thousand data points are acquired, then a Fourier transform is performed

# Frame Size (T) – Total time to acquire one block of data to perform a Fourier transform

**Frequency Domain Terms**

# Bandwidth (Fmax) – Highest frequency that is captured in the Fourier transform, equal to half the sampling rate. The Nyquist sampling criterion requires setting the sampling rate at least twice the maximum frequency of interest. A bandwidth of 1000 Hertz means that the sampling frequency is set to 2000 samples/second.

In fact, even with a sampling rate of 2000 Hz, the actual usable bandwidth can be less than the theoretical limit of 1000 Hertz. This is because in many data acquisition systems, there is an anti-aliasing filter which starts reducing the amplitude of the signal starting at 80% of the bandwidth

# Spectral Lines (SL)– After Fourier transform, total number of frequency domain samples

# Frequency Resolution (Δf) – Spacing between samples in the frequency domain