# FFT Resolution Bandwidth Calculator

This tool calculates the Resolution Bandwidth (RBW) of a Fast Fourier Transform. It also includes the effect of decimation or further downsampling of the digitized signal.

Enter:

• NFFT = Length of the FFT
• Fs = Sampling rate (Samples-per-second or kSPS/MSPS/GSPS)
• D = Decimation (=1 when the signal is not down-sampled)

R = Fs/(D*NFFT)

## Example Calculation

For a sampling rate of 1 GSPS and FFT length 4096, the resolution bandwidth is 244 kHz. If the decimation factor is 16, the RBW drops to 15.2 kHz.

## Background

### What is resolution bandwidth?

Resolution Bandwidth (RBW) refers to the bandwidth over which signals can be resolved in spectrum analysis. It defines the frequency range over which the spectrum analyzer can reduce the input signal into its individual frequency components for analysis.

The RBW is often set by the user and is a key factor in determining the accuracy and detail of the analysis.

By selecting a smaller RBW value, the frequency resolution of the spectrum analyzer is increased, providing more precise measurements of the individual frequencies within the input signal.

Conversely, a larger RBW value will reduce the frequency resolution, resulting in less detail being displayed on the spectrum analyzer.

The RBW setting can be adjusted to match the specific requirements of the analysis, balancing frequency resolution and measurement time. In general, the lower the RBW the greater the measurement time. A 1 Hz RBW requires more computation time relative to a 10 kHz RBW.

Overall, RBW acts as a filter for the input signal. It controls the length of time the analyzer will spend analyzing each frequency and the amplitude of the individual frequency peaks displayed on the spectrum analyzer’s frequency-domain display.

Modern real-time spectrum analyzers use a Fast Fourier Transform (FFT) to compute the power spectrum

### What is Sampling Rate?

It is the number of samples collected divided by the time interval over which the samples were collected. Calculate the sampling rate.

What is Decimation?

Decimation represents a reduction in samples and therefore the effective sampling rate. For example a sampling rate of 10 Megasamples per second decimated by 10 gives an effective sampling rate of 1 Megasamples per second. Wikipedia link.

### What are FFT bins and bin width?

In FFT (Fast Fourier Transform) analysis, the FFT length determines the number of bins produced by the transformation. Each bin represents a certain frequency range of the signal being analyzed. The bin width is defined as the bandwidth covered by each bin. It is also called the resolution bandwidth.

The resolution bandwidth is inversely proportional to the FFT length and directly proportional to the sampling rate. It can be calculated by dividing the sample rate by the FFT length. A longer FFT length results in a higher frequency resolution but a smaller bin width.

The amplitude value of each bin represents the strength or power of the corresponding frequency range in the signal. Therefore, understanding the concept of FFT bins and bin width is crucial for accurate frequency analysis in various applications.

The resolution bandwidth is the spacing between consecutive bins in the FFT output spectrum. The smaller the RBW, the easier it is to discern two closely spaced signals.

For a high sampling rate, a larger number of samples (FFT size) are required to get the same RBW as for a lower sampling rate.