# FFT Spectrum Analyzer

### - the Fast Fourier Transform spectrum analyser uses digital signal processing techniques to provide in depth waveform analysis with greater flexibility than other methods.

### Spectrum Analyzer Tutorial Includes

The FFT or Fast Fourier Transform spectrum analyser uses digital signal processing techniques to analyser a waveform with Fourier transforms to provide in depth analysis of signal waveform spectra.

With the FFT analyzer able to provide facilities that cannot be provided by swept frequency analyzers, enabling fast capture and forms of analysis that are not possible with sweep / superheterodyne techniques alone.

## Advantages and disadvantages of FFT analyzer technology

As with any form of technology, FFT analysers have their advantages and disadvantages:

**Advantages of FFT spectrum analyzer technology**

In view of the fact that the waveform is analysed digitally, the waveform can be captured in a relatively short time, and then the subsequently analysed. This short capture time can have many advantages - it can allow for the capture of transients or short lived waveforms.*Fast capture of waveform:*The short capture time means that the FFT analyzer can capture non-repetitive waveforms, giving them a capability not possible with other spectrum analyzers.*Able to capture non-repetitive events:*As part of the signal capture process, data is gained which can be processed to reveal the phase of signals.*Able to analyse signal phase:*Using FFT technology, it is possible to capture the waveform and analyse it later should this be required.*Waveforms can be stored*

**Disadvantages of the FFT spectrum analyzer technology**

The main limit of the frequency and bandwidth of FFT spectrum analyzers is the analogue to digital converter, ADC that is used to convert the analogue signal into a digital format. While technology is improving this component still places a major limitation on the upper frequency limits or the bandwidth if a down-conversion stage is used.*Frequency limitations:*The high level of performance required by the ADC means that this item is a very high cost item. In addition to all the other processing and display circuitry required, this results in the costs rising for these items.*Cost:*

## Fast Fourier Transform

At the very heart of the concept of the FFT analyzer is the fast Fourier Transform itself. The fast Fourier Transform, FFT uses the same basic principles as the Fourier transform, developed by Joseph Fourier (1768 - 1830) in which one value in, say, the continuous time domain is converted into the continuous frequency domain, including both magnitude and phase information.

However to capture a waveform digitally, this must be achieved using discrete values, both in terms of the values of samples taken, and the time intervals at which they are taken. As the time domain waveform is taken at time intervals, it is not possible for the data to be converted into the frequency domain using the standard Fourier transform. Instead a variant of the Fourier transform known as the Discrete Fourier Transform, DFT must be used.

As the DFT uses discrete samples for the time domain waveform, this reflects into the frequency domain and results in the frequency domain being split into discrete frequency components of "bins." The number of frequency bins over a frequency band is the frequency resolution. To achieve greater resolution, a greater number of bins is needed, and hence in the time domain a large number of samples is required. As can be imagined, this results in a much greater level of computation, and therefore methods of reducing the amount of computation required is needed to ensure that the results are displayed in a timely fashion, although with today's vastly increased level of processing power, this is less of a problem. To ease the processing required, a Fast Fourier Transform, FFT is used. This requires that the time domain waveform has a the number of samples equal to a number which is an integral power of two.

## FFT spectrum analyzer

The block diagram and topology of an FFT analyzer are different to that of the more usual superheterodyne or sweep spectrum analyzer. In particular circuitry is required to enable the digital to analogue conversion to be made, and then for processing the signal as a Fast Fourier Transform.

The FFT spectrum analyzer can be considered to comprise of a number of different blocks:

**FFT Spectrum Analyser Block Diagram**

The test instrument requires attenuators of gain stages to ensure that the signal is at the right level for the analogue to digital conversion. If the signal level is too high, then clipping and distortion will occur, too low and the resolution of the ADC and noise become a problems. Matching the signal level to the ADC range ensures the optimum performance and maximises the resolution of the ADC.*Analogue front end attenuators / gain:*The signal is passed through an anti-aliasing filter. This is required because the rate at which points are taken by the sampling system within the FFT analyzer is particularly important. The waveform must be sampled at a sufficiently high rate. According to the Nyquist theorem a signal must be sampled at a rate equal to twice that of the highest frequency, and also any component whose frequency is higher than the Nyquist rate will appear in the measurement as a lower frequency component - a factor known as "aliasing". This results from the where the actual values of the higher rate fall when the samples are taken. To avoid aliasing a low pass filter is placed ahead of the sampler to remove any unwanted high frequency elements. This filter must have a cut-off frequency which is less than half the sampling rate, although typically to provide some margin, the low pass filter cut-off frequency is at highest 2.5 times less than the sampling rate of the analyzer. In turn this determines the maximum frequency of operation of the overall FFT spectrum analyzer.*Analogue low pass anti-aliasing filter:*In order to perform the analogue to digital conversion, two elements are required. The first is a sampler which takes samples at discrete time intervals - the sampling rate. The importance of this rate has been discussed above. The samples are then passed to an analogue to digital converter which produces the digital format for the samples that is required for the FFT analysis.*Sampling and analogue to digital conversion:*With the data from the sampler, which is in the time domain, this is then converted into the frequency domain by the FFT analyzer. This is then able to further process the data using digital signal processing techniques to analyze the data in the format required.*FFT analyzer:*With the power of processing it is possible to present the information for display in a variety of ways. Today's displays are very flexible and enable the information to be presented in formats that are easy to comprehend and reveal a variety of facets of the signal. The display elements of the FFT spectrum analyzer are therefore very important so that the information captured and processed can be suitably presented for the user.*Display:*

* By Ian Poole*

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