Copyright: (c) Copyright Agilent Technologies, 2000, 2001


About VSA Concepts

VSA (vector signal analyzer) concepts includes information you may need when making measurements with Agilent 89600-Series Vector Signal Analyzers. This includes information such as:

•	Analyzer Basics—the different types of analyzers and how the 89600-series analyzers differ from conventional analyzers.

•	FFT Basics—a thorough discussion of the terminology and methods used in analyzers such as the 89600-series to derive frequency (spectral) data from time records.

•	Windowing and the FFT—how to correctly apply windows (such as a Hanning or Uniform window) when converting signals from the time domain into the frequency domain.


Different Types of Spectrum Analyzers

There are two broad categories of spectrum analyzers: swept-tuned analyzers and real-time analyzers. Both swept-tuned analyzers and real-time analyzers have been around for many years. However, within the past decade or so, spectrum analyzers have become much more sophisticated. These newer spectrum analyzers use digital signal processing to provide additional measurement capability—and let you interpret measurement results much more easily.

Both swept-tuned and real-time spectrum analyzers display amplitude versus frequency. How they process and display this information, however, varies with the specific type of analyzer. A real-time spectrum analyzer displays the energy at all frequency components simultaneously. A swept-tuned spectrum analyzer displays measurement results sequentially—in other words, not in ''real time.''  This is because a swept-tuned analyzer, in effect, uses a single narrow filter that is tuned across a range of frequencies to produce a spectrum display.

Swept-tuned analyzers have been the traditional choice for higher frequency applications—for example, 100 kHz and above. Real-time analyzers are generally used for lower frequencies—for example, audio-frequency and vibration measurements.

For an additional overview of spectrum/network measurements, see Spectrum and Network Measurements by Robert A. Witte (Prentice Hall, Englewood Cliffs, New Jersey, 1993).

Swept-tuned spectrum analyzers

Swept-tuned spectrum analyzers are descended from radio receivers. So it should come as no surprise that swept-tuned analyzers are either tuned-filter analyzers (analogous to a TRF radio) or superheterodyne analyzers. In fact, in their simplest form, you could think of a swept-tuned spectrum analyzer as nothing more than a frequency-selective voltmeter with a frequency range that's tuned (swept) automatically.

Modern swept-tuned analyzers (superheterodyne analyzers, in particular) are precision devices that can make a wide variety of measurements. However, they are primarily used to measure steady-state signals because they can't evaluate all frequencies in a given span simultaneously. The ability to evaluate all frequencies simultaneously belongs exclusively to the real-time analyzer.

Real-time spectrum analyzers

Despite the high performance of modern superheterodyne analyzers, they still can't evaluate frequencies simultaneously and display an entire frequency spectrum simultaneously. Thus, they are not real-time analyzers. And the sweep speed of a swept-tuned analyzer is always limited by the time required for its internal filters to settle.

Parallel-filter analyzers

Another way to build a spectrum analyzer is to combine several bandpass filters, each with a different passband frequency. Each filter remains connected to the input at all times. This type of analyzer is called a parallel-filter analyzer. After an initial settling time, the parallel-filter analyzer can instantaneously detect and display all signals within the analyzer's measurement range.

The particular strength of such an analyzer is its measurement speed—this allows it to measure transient and time-variant signals. However, the frequency resolution of a parallel-filter analyzer is much coarser than a typical swept-tuned analyzer. This is because the resolution is determined by the width of the bandpass filters. To get fine resolution over a large frequency range, you would need many, many individual filters—thus increasing the cost and complexity of such an analyzer. This is why all but the simplest parallel-filter analyzers are expensive.

Typically, parallel-filter analyzers have been used in audio-frequency applications.

FFT analyzers

FFT spectrum analyzers (also referred to as dynamic signal analyzers) use digital signal processing to sample the input signal and convert it to the frequency domain. This conversion is done using the Fast Fourier Transform (FFT). The FFT is an implementation of the Discrete Fourier Transform, the math algorithm used for transforming data from the time domain to the frequency domain. This analyzer is an example of an FFT analyzer that can make real-time measurements.

FFT spectrum analyzers are powerful instruments, because their processing power can extract more information from an input signal than just the amplitude of individual frequency components. For example, FFT analyzers can measure both magnitude and phase, and can also switch easily between the time and frequency domains. This makes them ideal instruments for the analysis of communication, ultrasonic, and modulated signals.

If an FFT analyzer samples fast enough, all input data is evaluated and the analyzer makes a real-time measurement. When operating in real time, FFT analyzers can make the same measurements traditionally done with parallel-filter analyzers—and make these measurements, if desired, with far greater frequency resolution.

In the past FFT analyzers have had the disadvantage of their restricted frequency range—most FFT analyzers could not make measurements above 100 kHz. The limiting factor has been the speed of the analog-to-digital converter used to sample the analyzer's input signal. This is why swept-tuned superheterodyne analyzers are still used for RF and microwave measurements, though some newer-generation swept-tuned analyzers, such as the Agilent 8560 family of analyzers can also make FFT measurements. As you will see, this trend toward hybrid technology has gone one step further with the Agilent 89600 Series Vector Signal Analyzers.


89600 Series Analyzers

The ideal analyzer combines the advantages of both swept-tuned and FFT analyzers while minimizing the disadvantages. To provide these advantages, the Agilent 89600 series analyzers use FFT technology to provide wideband and high frequency measurements as well as narrowband and low frequency measurements. The analog IF section is replaced by a digital IF section which incorporates FFT technology and digital signal processing to make very fast measurements.

Agilent 89600-series analyzers consist of measurement hardware and vector-signal analysis (VSA) software that runs on a Windows PC. The VSA software configures the hardware to perform either scalar measurements (also called stepped FFT measurements) or vector measurements. You click Start > Programs > Agilent 89600 VSA > Spectrum Analyzer to run the Spectrum Analyzer application, which performs scalar measurements. You click Vector Signal Analyzer to run the Vector Signal Analyzer application, which performs vector measurements.

Tip

For an overview of 89600-series products, see 89600-Series Product Overview.

Vector Measurements

Running the Vector Analyzer application configures the 89600 hardware to perform vector measurements. Vector measurements provide both phase and amplitude information.

The Agilent 89600 series analyzers expand FFT technology to perform vector measurements on narrow as well as relatively wide spans from baseband to the analyzer's upper frequency limits. Earlier FFT analyzers have been limited to narrow spans and low frequencies. These limitations restricted the ability to measure phase and to analyze time-variant, transient, and modulated signals. These measurements often require real-time analysis with a non-zero start frequency and wide frequency spans.

Vector measurements provide a single FFT measurement as wide as 36 MHz for RF and baseband measurements. The zoom capability of Vector measurements allows you to analyze spans away from DC. You may place a selected narrower span at any frequency within the analyzer's frequency range.

Tip

For additional details about vector measurements, see About the Vector Signal Analyzer

Scalar Measurements (Stepped FFT Measurements)

Running the Spectrum Analyzer application configures the 89600 hardware to perform scalar measurements. Scalar measurements provide only amplitude information—they do not provide phase information.

Note that the Spectrum Analyzer application is not available with some non-VXI measurement hardware.

Scalar measurements are implemented using stepped FFT technology to provide enhanced wideband measurements. Technological advances in analog-to-digital converters and digital signal processors combined with FFT technology offer the same results as a swept-tuned analyzer but with additional capability.

If you are familiar with swept-tuned analyzers for making high-frequency measurements you will find that the technology used in the Agilent 89600 series products has expanded the capability to make FFT measurements with excellent resolution at higher frequency ranges. This has been accomplished by translating the highest frequencies to a lower band, then performing FFTs on separate segments of the spectrum. These segments are displayed contiguously so that the result appears as it would with a swept-tuned spectrum analyzer.

If you have previously used FFT Dynamic Signal Analyzers, you will discover that with the Agilent 89600 series analyzers you can select spans and resolution bandwidths that have previously been unavailable in FFT analyzers.

Tip

For additional details about scalar measurements, see Using the Spectrum Analyzer Application

A swept-tuned analyzer changes the local oscillator frequency linearly over time and measures one frequency point at a time.
A stepped analyzer like the Agilent 89600-series changes the local oscillator frequency in sequential steps over time and measures multiple frequency points at one time.


Zero Response and DC Measurements

What is zero response?

When viewing frequency spans that start at 0 Hz (or very close to 0 Hz), a spectral line is usually visible at the extreme left of a spectrum analyzer's display. This is called zero response or LO feedthrough. In an FFT spectrum analyzer, zero response is caused by residual dc that originates in the analyzer's own input amplifiers. Zero response gives the illusion of a dc offset, even if the input signal has no dc component—and this occurs even if the analyzer has an ac-coupled input.

In the Agilent 89600 Series Vector Signal Analyzers, some degree of zero response is always present in the 0 Hz bin (sometimes called the dc bin). The residual dc that causes this offset may leak into the first several bins as well. If you don't want to see any zero response on the analyzer's display, simply start the frequency span several bins above 0 Hz.

Can spectrum analyzers measure DC?

Most spectrum analyzers are not intended to measure dc. However, analyzers such as the Agilent 89600 series analyzers can measure very low frequencies. This analyzer can, in fact, measure dc, but not without including a dc offset of its own that can contribute to (or obscure) a dc offset in the input signal. As we mentioned, this internal offset is caused by residual dc that originates in the analyzer's input amplifiers. Thus, measurement performance at dc is not specified.


Decibels

This topic contains an overview of how decibels are used to measure power and voltage ratios. The following tables contain handy information about decibels, such as equivalent decibel values for different units, decibel values for power and voltage ratios, decibel equations, and dbM-to-dbV conversion formulas.

EQUIVALENT DECIBEL VALUES (approximate)

dBm    (50 ohm)	dBVrms	dBVpk	Vrms	Vpk
20.0	6.99	10	2.24	3.162
13.0	0	3	1.00	1.414
10.0	−3.01	0	0 .707	1.0
3.0	−10	− 7	0.316	0 .447
0.0	−13.01	−10	0.224	0.316
− 7.0	−20	−17	0.01	0.1414
−10.0	−23.01	−20	0.0707	0.1
−20.0	−33.01	−30	0.0224	0.0316

DECIBEL VALUES FOR POWER AND VOLTAGE RATIOS

Voltage Ratio	Power Ratio (V2/V1)	Decibels (P2/P1)
1	1	0 dB
1.414	2	3 dB
2	4	6 dB
3.16	10	10 dB
10	100	20 dB

DECIBEL EQUATIONS

dB (power)	10 log (P2/P1)
dB (voltage)	20 log (V2/V1)
dBV	10 log (Vrms^2) = 20 log (Vrms)
dBV	10 log (real^2 + imag^2) *
dBm (power)	10 log (P/.001)
dBm (voltage)	10 log (Vrms^2/(.001 × Z)) **
dBm(50 ohm)	20 log (Vrms/.2236)
dBm(75 ohm)	20 log (Vrms/.2739)
dBm(600 ohm)	20 log (Vrms/.7746)
* The output of the FFT is an array of complex points. In polar form, dBV = 10 log Vrms^2. In rectangular form, dBV = 10 log (real^2 + imag^2). The imaginary component depends on the relative position of the waveform in the FFT time record.

** Z is the analyzer's input impedance.

dBm/dBV Conversions

dBm	dBV + 13.01 for 50 ohms
dBm	dBV + 11.25 for 75 ohms
Vrms	0.2236 log^-1 (dBm/20) for 50 ohms
Vrms	0.2739 log^-1 (dBm/20) for 75 ohms
where: log^-1 is the inverse logarithm.

Overview

The decibel is a logarithmic ratio of power or voltage. Because of this, the following is true:

•	0 dB is a ratio of 1 (voltage and power).

•	3 dB is a power ratio of 2.

•	6 dB is a voltage ratio of 2.

•	Inverting a ratio changes sign of decibel value (ratio of 2 is 3 dB; 1/2 is −3 dB).

•	10 dB is a power ratio of 10 (the only point where the decibel value and the ratio value are the same for power).

•	As a number increases by a factor of 10, the decibel value increases by 10 for power ratios and 20 for voltage ratios.

The decibel is sometimes used to express electrical quantities in a convenient form. The definition of the decibel is based on the ratio of two power levels (log indicates the base ten logarithm):

  dB = 10 log (P2/P1)

The decibel equation can be modified to express the decibel as a ratio of two voltage levels:

  P2 = (V^2/R2)

  P1 = (V^2/R1)

  dB = 10 log ((V2^2/R2)/(V1^2/R1))

And, if R1 = R2 (the resistances are the same):

  dB = 10 log (V2/V1)^2

  dB = 20 log (V2/V1)

Strictly speaking, the voltage equation is valid only if the two resistances are the same. For instance, if the input voltage and the output voltage of an amplifier were being compared and the input resistance and output resistance are different, they must be accounted for when calculating decibels. In practice, however, this is often ignored. For example, in operational amplifier circuits, the input impedance is very large while the output impedance is quite small. Usually, the important parameter in this type of circuit is voltage gain (not power gain). In this type of system, the decibel equation for voltage is used almost exclusively.

Decibels compress widely varying electrical values onto a more manageable logarithmic scale. For example, the range of powers from 100 watts to 1 microwatt is a ratio of 10,000,000 but is expressed in decibels as only 80 dB.


Time Domain and Frequency Domain Measurements

Measurements made in the time domain are the basis of all measurements in this analyzer. The time domain display shows a parameter (usually amplitude) versus time. You are probably familiar with time domain measurements as they appear in an oscilloscope. Similar measurements may be viewed with the time measurement data capability.

Frequency-domain displays show a parameter (again, usually amplitude) versus frequency. A spectrum analyzer takes an analog input signal—a time-domain signal—and uses the Fast Fourier Transform (FFT) to convert it to the frequency domain. The resulting spectrum measurement shows the energy of each frequency component at each point along the frequency spectrum.

Many signals not visible in the time domain (such as noise and distortion products) are clearly visible in the frequency domain. Because spectrum displays show frequency components distributed along the frequency axis, it's possible to view many different signals at the same time. This is why the spectrum analyzer is such a useful tool for looking at complex signals—it lets you easily measure (and compare) the frequency and amplitude of individual components.

The Y axis (amplitude)

Time-domain measurements are usually viewed with a linear X axis and a linear Y axis (think of an oscilloscope). Frequency-domain measurements are sometimes viewed with a linear Y axis and a linear X axis, but usually must be viewed with a logarithmic Y axis, because this is the only way to view very small signals and much larger signals simultaneously.

Let's look at the spectrum of a sine wave. Because the amplitude of any harmonic is small relative to the fundamental frequency, it's nearly impossible to view a harmonic on the same display as the fundamental unless the Y-axis scale is logarithmic. That's why most measurements made with spectrum analyzers use a logarithmic amplitude scale—a scale based on decibels. And because the dB scale is by definition logarithmic, there's no need to use logarithmically-spaced graticule lines.

The X axis (frequency)

Sometimes it's convenient to use a logarithmic X axis. Perhaps most familiar to you is the frequency response measurement. This is traditionally displayed with a log X axis (frequency) versus a log Y axis (relative magnitude).

But most measurements do not require a logarithmic frequency scale. In fact, when making spectrum measurements it's easier to characterize harmonics with a linear X-axis scale because harmonics that are multiples of the same fundamental will appear at evenly spaced intervals.


How the FFT Creates Frequency Data

The Fourier transform integral converts data from the time domain into the frequency domain. However, this integral assumes the possibility of deriving a mathematical description of the waveform to be transformed—but real-world signals are complex and defy description by a simple equation. The Fast Fourier Transform (FFT) algorithm operates on sampled data, and provides time-to-frequency domain transformations without the need to derive the waveform equation.

The Fast Fourier Transform (FFT) is an implementation of the Discrete Fourier Transform, the math algorithm used for transforming data from the time domain to the frequency domain. Before an analyzer uses the FFT algorithm, it samples the input signal with an analog-to-digital converter (the Nyquist sampling theorem states that if samples are taken twice as fast as the highest frequency component in the signal, the signal can be reconstructed exactly). This transforms the continuous (analog) signal into a discrete (digital) signal.

Because the input signal is sampled, an exact representation of this signal is not available in either the time domain or the frequency domain. However, by spacing the samples closely, the analyzer provides an excellent approximation of the input signal.

Using the FFT in an analyzer

As with the swept-tuned analyzer, the input to the analyzer is a continuous analog voltage. The voltage might come directly from an electronic circuit (for example, a local oscillator) or through a transducer (for example, when measuring vibration). Whatever the source of the input signal, the FFT algorithm requires digital data. Therefore, the analyzer must convert the analog voltage in to a digital representation. So the first steps in building an FFT analyzer are to build a sampler and an analog-to-digital converter (ADC) in order to create the digitized stream of samples that feeds the FFT processor.

The FFT algorithm works on sampled data in a special way. Rather than acting on each data sample as the ADC converts it, the FFT waits until a number of samples (N) have been taken and transforms the complete block of data. The sampled data representing the time-domain waveform is typically called a time record of size-N samples.

But the FFT analyzer cannot compute a valid frequency-domain result until at least one time record is acquired—this is analogous to the initial settling time in a parallel-filter analyzer. After this initial time record is filled, the FFT analyzer is able to determine very rapid changes in the frequency domain. A typical size for N might be 1024 samples in one time record.

During the FFT process, the FFT algorithm transforms the N time domain samples into N/2 equally spaced lines in the frequency domain. Each line contains both amplitude and phase information—this is why half as many lines are available in the frequency domain (actually, slightly less than half the number of lines are used, because some data is corrupted by anti-aliasing filters).

See Also

FFT Terminology.

Real-Time Bandwidth


Terminology Used in FFT Analyzers

These terms used by FFT Analyzers that may be new to you:

•	Frequency points

•	Bins

•	Lines

•	Display points

•	Sample points

•	Time-domain points

•	Measurement points

The best way to understand these terms is with a block diagram.

This is a generic block diagram for an FFT (Fast Fourier Transform) analyzer. It is not a complete block diagram of this analyzer.

Time-Domain Samples

Basically, the input signal is first conditioned for optimum performance, and then converted by the ADC (Analog-to-Digital Converter) from analog to digital data (blocks 1 and 2). This digital data is frequently referred to as samples. It is also often called by any of these names:

•	Time-domain samples

•	Time samples

•	Sample points

•	Time-domain points

The samples are then mixed with the analyzers LO (local oscillator) if necessary. The LO is used to achieve start frequencies greater than 0 Hertz. In this analyzer, you can also enable the LO when the start frequency is 0 Hz by selecting time data zoom.

The Time Record

Next, the samples are filtered by a digital filter to achieve the selected span. The samples coming out of the digital filter are stored in RAM as one or more time records. A time record is simply a collection of samples and is a digital representation of the input signal.

Usually, the FFT (Fast Fourier Transform) operates on an entire time record; and an entire time record is needed before the FFT can compute the spectrum information. This analyzer can, with some configurations, operate on a partial time record− this happens for very narrow spans immediately after a start or continue while in real time (in this case, the analyzer displays "FILLING TIME RECORD" instead of "REAL-TIME MEASUREMENT").

The length of a time record is in seconds. In this analyzer, the time-record length is computed as follows:

                        Window Shapefactor
  Time-record length = ------------------
                              RBW

  where: RBW is the resolution bandwidth

Measurement Points

A time record consisting of many time-domain samples goes into the FFT; frequency-domain samples come out of the FFT. These frequency-domain samples are often referred to as measurement points.

The measurement points are then processed as necessary before plotting them on the analyzer's display to create a trace.

The Trace

Each trace is divided along its x axis into a fixed number of evenly-spaced points. For frequency-domain data, these points are called frequency points and determine the frequency resolution of the analyzer's display. Frequency points are also sometimes referred to as lines, bins, or display points.

Hint

The frequency points parameter determines the number of "frequency points" that the analyzer displays.

Frequency points, display points, and lines refer to the actual point that is plotted on the display. Bins refers to the region between display points.

Note

The greater the number of frequency points, the greater the resolution. The lower the number of frequency points, the poorer the resolution.

The picture below is shows the relationship between frequency points and bins (bins 0 through 9 are shown).

Each frequency point has a nominal value. This is the value used for the marker's x-axis readout. The nominal value of the first frequency point is the start frequency. The nominal value of the last frequency point is the stop frequency.

	Analyzer's Display  +-------------------------------------------------+  |          .                                      |  |        .  .                                     |  |      .      .<--Frequency point (display point) |  |    .          .                                 |  |  .              .                               |  |.                  . . . . . . . . . . . . . . . |  |-------------------------------------------------|   0 1 2 3 4 5 6 7 8 9 ...                       Bins
Measurement Points Versus Frequency Points

For Vector and measurements, the output of the FFT yields as many measurement points as there are frequency points, and each bin contains one measurement point.

For Scalar measurements, the output of the FFT can yield more measurement points than there are frequency points, and each bin contains several measurement points.

The following picture shows a scenario where the FFT in a Scalar measurement yields more measurement points than there are frequency points. In other words, there are more measurement points than there are frequency points.

	Analyzer's Display  +-------------------------------------------------+  |          .                                      |  |        .  .                                     |  |      .      .<--Frequency point (display point) |  |    .          .                                 |  |  .              .                               |  |.                  . . . . . . . . . . . . . . . |  |-------------------------------------------------|   0 1 2 3 4 5 6 7 8 9                       Bins
	Bin 0  Bin 1  Bin 2  Bin 3  ----> Bin N   |      |      |      |  ..  |     |     |   |      |      |    ..|.. .. |     |     |   |      |    . | .... |      |---->|     |   |  . . |.... .|      |      |     |     |   |. .. .|      |      |      |     |.....|   |      |      |      |      |     |     |
As shown, each bin represents a band of frequencies. Scalar measurements use detection to determine how the analyzer interprets multiple measurement points into a single frequency point.

The width of a bin is related to the current frequency span:

For FFT measurements, a bin represents all frequencies between (NF − 1/2 PBW) and (NF + 1/2 PBW), where NF is the nominal frequency and PBW is the bin bandwidth.


Time Records

As mentioned in Terminology Used in FFT Analyzers, a time record is the amount of time-domain data the analyzer needs to perform one FFT operation. The time record and its FFT are the building blocks the analyzer needs for all subsequent measurements.

Why is a time record needed?

Essentially, the time record is a block of time-domain sample points. Because the actual Fourier Transform does not have explicit time or frequency references (it simply operates on a sequential collection of points), FFT analyzers must assign arbitrary start and finish times for data to be transformed. These blocks of input data are called time records.

For example, with the default display resolution of 401 frequency points, the analyzer takes up to 1024 samples of time data to produce 512 points of frequency domain data. The analyzer usually displays the first 401 points of this data and discards the rest (this accommodates the anti-aliasing filters, but that's beyond the scope of this discussion).

The time record can be described by both a length and a size. The time record length is the amount of time required to acquire a time record and is altered by changing resolution bandwidth, window, main length, or gate length. The time record size is the number of time points in the time record and is dictated by the time record length in combination with the sample rate (and sample rate, in turn, is directly related to span).

Time record size refers to the number of time points (samples) in a time record. Time record length refers to the amount of time needed to acquire a time record.

See Also

Time Record Length


Time Records and Frequency Data

The relationship between a time record and the frequency data is relatively straight forward if the minimum resolution bandwidth (and therefore the maximum time record length) is used. In this case the time record size is equal to the time record size required by the FFT (which is dictated by the number of frequency points and must be a power of 2n). Therefore, the FFT converts the samples in the time record directly to display points.

If a higher resolution bandwidth is selected, the time length necessary to acquire the time samples is shorter and fewer samples are required. However, the FFT must still operate on the same time record length for display purposes, so the extra time record length is set to zero (zero padded) before the FFT process. This enables the FFT to properly convert the time record to the required number of display points without adversely affecting the frequency data.

The time record calculations

The length of the time record determines how long a given measurement will take and the maximum frequency resolution you can measure. As described above the FFT time record size may differ from the size dictated by the resolution bandwidth. The FFT record size must be a power of 2 equal to or greater than the number of frequency points.


Real-Time Bandwidth

Real-time bandwidth is a specification used to characterize the performance of an FFT analyzer.

Real-time bandwidth (RTBW) applies to Vector and Demodulation measurements, and is the maximum frequency span that can be set without missing any event on the input signal.

RTBW specifications apply to:

•	Log magnitude displays.

•	Non-arbitrary frequency spans.

•	Markers off.

•	One trace.

The real-time bandwidth is the frequency span at which the FFT processing time equals the time record length−this means all input data is included in the average (in other words, there is no gap between the end of one time record and the beginning of the next).

However, if you increase the span past the real-time bandwidth, the record length becomes shorter than the FFT processing time. Time records are no longer contiguous, and some data is missed. Therefore, you can overlap records only when measuring below the real-time bandwidth, because the time record length must be longer than the FFT processing time to achieve any overlap.

The actual real-time bandwidth achieved varies with the amount of processing time the analyzer needs. As with overlap processing, this depends on the current frequency span, the type of average selected, and how busy the analyzer is servicing marker functions and events in the Windows environment.

Enhancing Real Time Bandwidth

To enhance real-time bandwidth as well as measurement speed, the following suggestions apply:

•	Follow the suggestions outlined in Enhancing Measurement Speed.

•	Run the 89600 VSA software on a fast workstation. The speed of your CPU significantly impacts measurement speed and real-time bandwidth.


Windowing

Windowing is useful when converting signals from the time domain into the frequency domain. This analyzer uses the FFT (Fast Fourier Transform) to perform time-to-frequency domain transformations.

The FFT assumes that the signal it's processing is periodic from time record to time record. If the signal is not periodic in the time record, the FFT won't estimate the frequency components accurately. The result is called leakage, and it has the effect of spreading the energy from a single frequency across a range of frequencies, as shown below:

	Signal Periodic        Signal Not Periodic    in Time Record         in Time Record
	|        .            |   |        .            |        .   |        .            |       . .   |        .            |     .    .   |        .            |   .        .   |........ .......     |...          ...   +----------------     +-----------------
Windowing is the solution to the leakage problem. Multiplying the time record by a weighting function, or a window, forces the signal to be periodic in the time record. Windowing weights the data in the time domain to improve accuracy in the frequency domain.

FFT analyzers usually have several window types available. Each window offers particular advantages. Because each window type produces different measurement results (just how different depends on the characteristics of the input signal and how you trigger on it), you should carefully select a window type appropriate for the measurement you're trying to make.

See Also

Window Types

Windowing Frequency Response


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Acknowledgements

The following products are mentioned in one or more places in the Agilent 89600-series documentation.

Product	Acknowledgement
Adobe® and Acrobat®	These products are trademarks of Adobe Systems Incorporated.
Microsoft®, Windows NT®, Windows®, and MS Windows®	These products are U.S. registered trademarks of Microsoft Corporation.
MS Excel, MS Word, MS Office, VBScript	These products are products of Microsoft Corporation.
MATLAB	MATLAB is a product of The MathWorks, Inc.


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This document was not available for inclusion in the online help. You can download the PDF from the 89600 [image] Web page .


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This document was not available for inclusion in the online help. You can download the PDF from the 89600 [image] Web page .