Editing Spectrum analyzer (section)

== Theory of operation ==

[[Image:BPFAnimationV2.gif|right|This animation shows how the resolution bandwidth of a swept-tuned spectrum analyzer is affected by the IF bandpass filter. Notice that wider bandwidth filters are unable to resolve the two closely space frequencies and the LO feedthrough causes the appearance of a baseband signal.]]

=== Swept-tuned ===
As discussed above in '''types''', a swept-tuned spectrum analyzer [[Superheterodyne receiver#High-side and low-side injection|down-converts]] a portion of the input signal spectrum to the center frequency of a [[band-pass filter]] by sweeping the [[voltage-controlled oscillator]] through a range of frequencies, enabling the consideration of the full frequency range of the instrument.

The bandwidth of the band-pass filter dictates the resolution bandwidth, which is related to the minimum bandwidth detectable by the instrument.  As demonstrated by the animation to the right, the smaller the bandwidth, the more spectral resolution. However, there is a trade-off between how quickly the display can update the full frequency span under consideration and the frequency resolution, which is relevant for distinguishing frequency components that are close together.  For a swept-tuned architecture, this relation for sweep time is useful:

: <math>\ ST=\frac{k(\mathrm{Span})}{RBW^2}</math>

Where ST is sweep time in seconds, k is proportionality constant, Span is the frequency range under consideration in hertz, and RBW is the resolution bandwidth in Hertz.<ref>''[https://www.keysight.com/us/en/assets/7018-06714/application-notes/5952-0292.pdf Keysight Spectrum Analyzer Basics] {{webarchive|url=https://web.archive.org/web/20180323154714/http://literature.cdn.keysight.com/litweb/pdf/5952-0292.pdf|date=2018-03-23}}'', p. 23, August 2, 2006, accessed July 7, 2011.</ref>
Sweeping too fast, however, causes a drop in displayed amplitude and a shift in the displayed frequency.<ref>''[https://www.keysight.com/us/en/assets/7018-06714/application-notes/5952-0292.pdf Keysight Spectrum Analyzer Basics] {{webarchive|url=https://web.archive.org/web/20180323154714/http://literature.cdn.keysight.com/litweb/pdf/5952-0292.pdf|date=2018-03-23}}'', p. 22, Figure 2–14, August 2, 2006, accessed July 7, 2011.</ref>

Also, the animation contains both up- and down-converted spectra, which is due to a [[frequency mixer]] producing both sum and difference frequencies. The [[local oscillator]] feedthrough is due to the imperfect isolation from the [[intermediate frequency|IF]] signal path in the [[Frequency mixer|mixer]].

For very weak signals, a [[pre-amplifier]] is used, although [[total harmonic distortion|harmonic]] and [[intermodulation]] distortion may lead to the creation of new frequency components that were not present in the original signal.

[[File:3D battery charger RF spectrum over time.jpg|thumb|right|350px|3D plot: 600 seconds RF spectrum over time from a battery charger]]

=== FFT-based ===
With an FFT based spectrum analyzer, the frequency resolution is <math>\Delta\nu=1/T</math>, the inverse of the time ''T'' over which the waveform is measured and Fourier transformed.

With Fourier transform analysis in a digital spectrum analyzer, it is necessary to sample the input signal with a sampling frequency <math>\nu_s</math> that is at least twice the bandwidth of the signal, due to the [[Nyquist rate|Nyquist limit]].<ref>{{cite web|url=https://www.keysight.com/main/editorial.jspx?cc=US&lc=eng&ckey=1775376&nid=-536900125.0.00&id=1775376&pselect=SR.GENERAL|title=How do I know what is the best sampling rate to use for my measurement? - Keysight (formerly Agilent's Electronic Measurement)|website=www.keysight.com|access-date=7 May 2018|url-status=live|archive-url=https://web.archive.org/web/20180323154748/https://www.keysight.com/main/editorial.jspx?cc=US&lc=eng&ckey=1775376&nid=-536900125.0.00&id=1775376&pselect=SR.GENERAL|archive-date=23 March 2018}}</ref> A Fourier transform will then produce a spectrum containing all frequencies from zero to <math>\nu_s/2</math>. This can place considerable demands on the required [[analog-to-digital converter]] and processing power for the Fourier transform, making FFT based spectrum analyzers limited in frequency range.

[[Image:Aaronia Spectrum Analyzer Software.jpg|thumb|right|350px|Frequency spectrum of the heating up period of a switching power supply (spread spectrum) incl. [[spectrogram]] over a few minutes]]

=== Hybrid superheterodyne-FFT ===
Since FFT based analyzers are only capable of considering narrow bands, one technique is to combine swept and FFT analysis for consideration of wide and narrow spans. This technique allows for faster sweep time.

This method is made possible by first down converting the signal, then digitizing the [[intermediate frequency]] and using superheterodyne or FFT techniques to acquire the spectrum.

One benefit of digitizing the intermediate frequency is the ability to use [[digital filter]]s, which have a range of [[Digital filter#Comparison of analog and digital filters|advantages]] over analog filters such as near perfect shape factors and improved filter settling time. Also, for consideration of narrow spans, the FFT can be used to increase sweep time without distorting the displayed spectrum.

[[Image:Spectrum Analyser Time Domain Sampling and Blind Time.png|thumb|left|400px|Illustration showing Spectrum Analyzer Blind Time]]

=== Realtime FFT ===
A realtime spectrum analyser does not have any blind time—up to some maximum span, often called the "realtime bandwidth". The analyser is able to sample the incoming RF spectrum in the time domain and convert the information to the frequency domain using the FFT process. FFT's are processed in parallel, gapless and overlapped so there are no gaps in the calculated RF spectrum and no information is missed.

==== Online realtime and offline realtime ====
In a sense, any spectrum analyzer that has [[vector signal analyzer]] capability is a realtime analyzer. It samples data fast enough to satisfy Nyquist Sampling theorem and stores the data in memory for later processing. This kind of analyser is only realtime for the amount of data / capture time it can store in memory and still produces gaps in the spectrum and results during processing time.

==== FFT overlapping ====
Minimizing distortion of information is important in all spectrum analyzers. The FFT process applies windowing techniques to improve the output spectrum due to producing less side lobes. The effect of windowing may also reduce the level of a signal where it is captured on the boundary between one FFT and the next. For this reason FFT's in a Realtime spectrum analyzer are overlapped. Overlapping rate is approximately 80%. An analyzer that utilises a 1024-point FFT process will re-use approximately 819 samples from the previous FFT process.<ref>''[https://www.rohde-schwarz.com/us/applications/implementation-of-real-time-spectrum-analysis-white-paper_230854-15815.html Dr. Florian Ramian – Implementation of Real-Time Spectrum Analysis] {{webarchive|url=https://web.archive.org/web/20180209182434/https://www.rohde-schwarz.com/us/applications/implementation-of-real-time-spectrum-analysis-white-paper_230854-15815.html |date=2018-02-09 }}'', p. 6, March, 2015, accessed February 9, 2018.</ref>

==== Minimum signal detection time ====
This is related to the sampling rate of the analyser and the [[Fast Fourier transform|FFT]] rate.  It is also important for the realtime spectrum analyzer to give good level accuracy.

Example: for an analyser with {{nowrap|40 MHz}} of realtime [[Bandwidth (signal processing)|bandwidth]] (the maximum RF span that can be processed in realtime) approximately {{nowrap|50 Msample/second}} (complex) are needed.  If the spectrum analyzer produces {{nowrap|250 000 FFT/s}} an FFT calculation is produced every {{nowrap|4 μs.}}  For a {{nowrap|1024 point}} FFT a full spectrum is produced {{nowrap|1024 x (1/50 x 10<sup>6</sup>),}} approximately every {{nowrap|20 μs.}}  This also gives us our overlap rate of 80% (20 μs − 4 μs) / 20 μs = 80%.

[[Image:Comparison of Max Hold Spectrum Analyzer trace and Persistence Trace.png|thumb|left|400px|Comparison between Swept Max Hold and Realtime Persistence displays]]

===== Persistence =====
Realtime spectrum analyzers are able to produce much more information for users to examine the frequency spectrum in more detail. A normal swept spectrum analyzer would produce max peak, min peak displays for example but a realtime spectrum analyzer is able to plot all calculated FFT's over a given period of time with the added colour-coding which represents how often a signal appears. For example, this image shows the difference between how a spectrum is displayed in a normal swept spectrum view and using a "Persistence" view on a realtime spectrum analyzer.

[[Image:Bluetooth signal behind wireless lan signal.png|thumb|right|350px|Bluetooth signal hidden behind wireless LAN signal]]

===== Hidden signals =====
Realtime spectrum analyzers are able to see signals hidden behind other signals. This is possible because no information is missed and the display to the user is the output of FFT calculations. An example of this can be seen on the right.