# Samples Per Second to Hertz (Hz) Calculator

This calculator converts from Samples per second to Frequency (Hz)

Enter the value and use the drop down menu to select the units of SPS, kSPS, MSPS or GSPS. The tool will provide the frequency in Hz, kHz, MHz or GHz.

F = S

## Example Calculation

For a sampling rate of 10,000 samples per second, the frequency is 10,000 Hz or 10 kHz.

## Background

Samples per second (SPS) and Hertz (Hz) are related concepts used in the context of digital signal processing (DSP) and Analog-to-Digital conversion, but they represent slightly different aspects of the same phenomenon as explained below:

1. Hertz (Hz): Hertz is a unit of frequency and represents the number of cycles or oscillations per second. In the context of analog signals, it typically describes the frequency of a waveform or how fast a signal is changing over time. For example, if you have an analog sine wave with a frequency of 1000 Hz, it means that the waveform completes 1000 cycles in one second.
2. Samples per Second (SPS): Samples per second is a measure of the rate at which an analog signal is converted into a digital format. In digital signal processing, particularly when working with analog-to-digital converters (ADCs), SPS represents the number of discrete samples taken from an analog signal in one second. These samples are essentially “snapshots” of the analog signal at specific time intervals. SPS is used to describe the digital representation of an analog signal.

## Sampling in ADCs

The relationship between Hz and SPS in an Analog-to-Digital conversion process is as follows:

• If an analog signal is sampled at the same rate as the frequency, it will result in aliasing
• If you want to accurately represent it in digital form, you need to sample it at a rate that is at least twice the frequency according to the Nyquist-Shannon sampling theorem. This minimum sampling rate is known as the Nyquist rate.

For example, if you have an analog signal with a frequency of 100 Hz, you should sample it at a rate of at least 200 SPS (samples per second) to avoid aliasing and accurately capture the original analog signal.

In summary, Hertz (Hz) refers to the frequency of an analog signal, while Samples per Second (SPS) refers to the rate at which an analog signal is sampled and converted into a digital format. The choice of SPS is crucial in digital signal processing to ensure that the digitized signal accurately represents the original analog signal.