Contents

**Introduction**

Converting data rate to frequency isn’t a direct conversion in the way one might convert miles to kilometers, because they represent different concepts.

In this post we explain the relationship between data rate (the amount of data transmitted per unit of time, usually measured in bits per second, **bps**) and frequency (the number of oscillations or cycles per unit of time, measured in hertz, **Hz**).

A tool is provided for easy computation.

**Calculator**

**Formula**

**B = C/(2*Log _{2}(M))**

where

**C**is the throughput in bits per second**M**is the number of distinct signal or modulation levels (usually a power of 2)**B**is the bandwidth in Hz

**Example Calculation**

A signal with 16 levels can be represented by 4 bits. In order to transfer 10 Megabit per second, 1.25 MHz of bandwidth is required.

If the signal has 32 levels, transfer of 10 Megabit per second requires a smaller bandwidth of 1 MHz.

The bandwidth reduction is due to the fact that more bits are packed into a signal level.

**Background**

**Data Rate**

The data rate in digital communications is a measure of how fast data is transmitted or received, expressed in bits per second (bps). It is determined by various factors, including the bandwidth of the channel, the modulation scheme used, and the efficiency of the coding.

**Frequency**

Frequency refers to the number of cycles of a periodic signal per second. In the context of communication systems, the term can refer to either the carrier frequency (the central frequency of the transmitted signal) or the bandwidth (the range of frequencies the signal occupies).

*For the purposes of this calculation, frequency refers to the bandwidth.*

**Nyquist Theorem**

According to the Nyquist theorem, the maximum data rate **C** that can be transmitted over a noiseless channel of bandwidth **B** is given by **C=2B*Log _{2}â€‹(M)** bits per second, where

**B**is the bandwidth in hertz, and

**M**is the number of discrete signal or modulation levels. For Binary Signaling, the formula simplifies to

**C = 2B**.

**Noiseless vs Noisy channel**

The Nyquist theorem applies to a noiseless channel. In order to perform the same computation for a noisy channel we use the Shannon-Hartley theorem. This calculator gives the bit rate as a function of bandwidth and SNR.

**References**

[1] Nyquist Theorem