# Sampling Rate Calculator (with Practical Examples)

The sampling rate is a measure of how often a waveform is sampled. If it is sampled once every 10 seconds then the sampling rate is 0.1 Hz.

To calculate the sampling rate enter:

• Number of samples (NS)
• Time period over which the samples were collected (TS)

## Formula

Sampling rate = NS/TS

## Example Calculation

If 1000 samples are collected over a time period of 5 seconds, the sampling rate is 200 samples per second.

An important specification for an Analog-to-digital converter is its sampling rate. The AD9670 for instance, has a maximum sampling rate of 125*106 samples per second.

## Background

### What is sampling?

Sampling is the process of converting an analog signal into a digital equivalent.

An analog signal is a continuous waveform, while a digital signal is discrete and composed of individual samples. To accurately represent the original analog signal, it is sampled at regular time intervals. The value of the waveform at each sample point is recorded.

The number of samples taken per second is called the sample rate, and it is typically measured in samples per second. Sometimes the sample rate is also measured in Hz where 1 Hz is equal to 1 sample per second.

The sample rate determines the frequency content that can be accurately captured in the analog signal. The higher the sample rate, the more accurately high-frequency components can be captured.

The process of sampling also affects the dynamic range of the digital audio. The dynamic range is the difference between the loudest and softest sounds that can be accurately represented. The more accurately the amplitude of a sample is represented, the higher the quality of the recorded and reproduced signal.

ðŸ’¡ Analog-to-digital converters are used to sample analog waveforms and convert to digital representation. The higher the number of bits in an ADC, the higher the signal-to-noise ratio and dynamic range.

### What is sample rate?

Sample or Sampling rate refers to the number of samples taken per second in a digitization process such as audio sampling. Units are Samples per second (SPS), kilosamples per second (kSPS), Megasamples per second (MSPS), Gigasamples per second (GSPS).

When capturing and sampling digital audio, the continuous analog sound waves are converted into discrete digital samples. The sample rate is the measurement of how many samples were taken in a given second.

The picture below (from Wikipedia) shows a continuous signal S(t) represented with a green colored line and discrete samples indicated by the blue vertical lines. A higher sampling rate would be indicated by blue lines that are more closely spaced.

To put it in perspective, audio CDs have a standard sample rate of 44,100 samples per second. In the world of Radio Frequency signals like 5G and Wi-Fi the sampling rates are in the range of hundreds of Megahertz.

The higher the sample rate, the more accurately the analog waveform can be reproduced. In audio systems, a higher sample rate allows for capturing more detailed sound, especially at higher frequencies. By increasing the sample rate, the recording can capture a greater range of frequencies and nuances, resulting in a higher fidelity audio reproduction. However, it is worth noting that higher sample rates also require more storage space and processing power.

### What are sampling rate, bandwidth and throughput?

Sampling rate, bandwidth, and throughput are important concepts in the field of signal processing.

While sampling rate refers to the number of samples per second, Bandwidth refers to the range of frequencies that contain relevant information. It is usually measured in Hz/kHz/MHz/GHz.

In the case of a 4G radio signal, the maximum bandwidth of 20 MHz contains all the transmitted video and audio that is to be sent over the air.

Audio bandwidth is around 20 kHz while the human ear can hear less than this. Also as individuals age, this detectable range is reduced.

The Nyquist theorem, a fundamental principle in signal processing, states that the sampling frequency must be at least twice the maximum frequency contained in the original signal in order to accurately reconstruct the waveform and preserve the frequency spectrum.

Use the Nyquist calculator to find the sampling rate for a given signal frequency. In the event the sampling frequency is lower than the maximum frequency of the analog signal, aliasing will occur. Use this calculator to find the aliased frequency components.

In the case of an analog-to-digital system the architecture of the receiver and the bandwidth determine the required sampling rate.

High sample rates are desirable for achieving accurate signal capture and reproduction.

Throughput, in the context of signal processing, refers to the amount of data that can be transmitted or processed within a given period of time. If the data is to be transferred over the internet for example, the capacity of the network pipe will determine throughput. For instance a 1 Gbps (or 1000 Mbps) connection will provide higher throughput than a 100 Mbps connection.

Use this calculator to understand how throughput or network speed influences the time it takes to transfer a certain amount of data.