# FFT spectrum analyzer

FFT Spectrum Analyzer

Students should become familiar with the settings to perform measurements in the frequency domain.

The FFT spectrum analyzer

• acquires a N-point discrete-time signal - N is a power of two, e.g. 8, 128, 1024,
• computes the spectrum using the FFT algorithm,
• displays these frequency components.

Sampling time determines the spectrum's highest available frequency. Capture time determines the resolution bandwidth. The figure below illustrates these relationships for FFT measurements.  FFT measurements: Maximum detectable frequency is half the sampling rate. Frequency resolution is the reciprocal of the record length.

Sampling time and the number of samples taken determine the spectrum's highest frequency and resolution bandwidth.

$\Delta T=N\cdot {t}_{S}$ and ${f}_{\mathrm{max}}=\frac{1}{2{t}_{S}}$ and $\Delta f=\frac{1}{\Delta T}$

where

 ${t}_{S}$ Sampling time $N$ Number of samples (FFT length) $\Delta T$ Sample record length ${f}_{\mathrm{max}}$ Maximum detectable frequency $\Delta f$ Resolution bandwidth

This experiment illustrates the basic settings to control the FFT spectrum analyzer. The FFT spectrum analyzer acquires a discrete-time signal, computes the spectrum using the FFT algorithm and displays these frequency components. In this example, the number of samples (FFT length) $N$ is $128$.

 Sampling time ${t}_{S}=0.5\text{\hspace{0.17em}}\mu s$ Sample record length $\Delta T=N\cdot {t}_{S}=64\mu s$
 Highest frequency ${f}_{\mathrm{max}}=\frac{1}{2{t}_{S}}=\frac{1}{2\cdot 0.5\mu s}=1MHz$ Resolution bandwidth $\Delta f=\frac{1}{\Delta T}=\frac{1}{64\text{\hspace{0.17em}}\mu s}=15.625\text{\hspace{0.17em}}kHz$  Time record of signal (left) and corresponding spectrum (right).  Time record zoom shows sampling time (left) and spectrum zoom shows resolution bandwidth (right).  As the QPSK transmit symbols are random the spectrum varies for each time record (left). This shows the need to average the spectrum (right).

Start the simulation and open the spectrum analyzer settings and reduce the resolution bandwidth. Also switch Averaging off and on.  Spectrum analyzer settings (left). Spectrum with reduced resolution bandwidth $\Delta f=3.90625\text{\hspace{0.17em}}kHz$ (right).

Note that:

• The resolution bandwidth values are shown as 1, 2, 5, 10, 20, 50 kHz etc., i.e. 15.625 kHz is shown as 20 kHz.
• The labAlive simulation framework provides the Spectrum Analyzer with a sampled input signal. Therefore, the spectrum analyzer needs no anti-aliasing filter.
• Samples are represented as floating-point numbers (Java double-precision values) - no further quantization is applied.

This simulation app provides an online spectrum analyzer. It allows frequency domain analysis with similar control settings to RF spectrum analyzers. Students should become familiar with the settings to perform measurements in the frequency domain.   Spectrum analyzer display and control panel. It allows frequency domain analysis with similar control settings to RF spectrum analyzers.

Open the spectrum analyzer settings:

• Click on .
• Click on to view more details. Adjust Resolution Bandwidth.
• Click on to view more details. Switch Averaging off and on.