1www.pentek.comOne Park Way Upper Saddle River New Jersey 07458Tel: 201.818.5900 Fax: 201.818.5904 Email: info@pentek.com

Pentek, Inc.

Spectrum Analysis is a very broadtopic. In this article we intend toaddress real-time bandwidth andoverlap processing.

Since everyone knows what we meanwith the expression real-time, we are notgoing to spend too much time on this sub-ject. However, wed like to define whatreal-time means in connection with doingFFT spectrum analysis.

Real-Time BandwidthThe correct term is Real-Time Band-

width and it defines the highest frequencyat which we can calculate a spectrum with-out missing any data. This frequency isdetermined by the processing speed of ourDSP processor, i.e. the time it takes to calcu-late the FFT and whatever other functionsare requested.

As shown in Figure 1, if frequencieshigher than the real-time bandwidth arepresent and processed, there will be gapsin the data acquired while the DSP proces-sor is doing its calculations. This is hardly aproblem if the data is stationary, i.e. peri-odic: no vital information is lost, since thesignal repeats itself in the subsequent cycle.On the other hand, if the signal is a short-duration, one-time transient, the possibilityexists that it cannot be analyzed.

High processing speed is also importantin other cases, such as when input signalparameters are changing rapidly; its alsoimportant when we want to perform aver-aging, especially with a large number ofaverages. Conversely, when analyzing datawhose bandwidth is less than the real-timebandwidth, we might consider doingsomething while the DSP processor is wait-ing for the data block to be collected. Wecan perform what is called Overlap Processing.

Real-Time Bandwidth and Overlap Processing

Data Collection

Data Collection

Start

Start

Start

Data Collection belowReal-Time Bandwidth

Data Collection atReal-Time Bandwidth

Data Collection aboveReal-Time Bandwidth Data Collection

Data Collection

Data Collection

Data Collection

Data Collection

Data Collection Data Collection

Analysis

Analysis

Analysis Analysis Analysis

Analysis Analysis

Analysis Analysis

(A)

(B)

(C)

Figure 1. Data collection andReal-Time bandwidth. The FFTprocessor waits for thecompletion of data collection in(A). In (B), data gaps areproduced. Data acquisition atthe real-time bandwidth isshown in (C).

Overlap ProcessingAssume we are collecting and analyzing

10 kHz data with 25.6 kHz sampling fre-quency, and we wish to calculate a 1k FFT.The data collection time (also known asTime Window) for collecting 1024 timesamples is exactly 40 msec. If the FFTprocessor calculates and displays a spec-trum in 10 msec, then it will sit and waitfor 30 msec until the acquisition of the nextblock is completed.

Once the first block is collected, ratherthan waiting for the next block to be fullycollected, we can proceed to calculate anew spectrum by using part of the datafrom the new block and part of the datafrom the old block. If the data is stationary,there is no reason why we cannot mixdata from the two blocks.

With the values given above, we couldinitiate a new FFT calculation by using 75%of the previous block and 25% of the latestone. We would then be performing what iscalled 75% overlap processing and ourapparent processing time (after the firstblock) would be 10 msec per spectrum,rather than 40 msec.

Where this process becomes even moresignificant is when we are operating atvery low frequencies, i.e. below 1 kHz,when we want to calculate large transforms,i.e. greater than 1k, or when we want tocalculate many spectra in order to do aver-aging. For example, lets assume we areoperating in a 100 Hz frequency range andwish to calculate 16 averages. The data collec-tion time is 4 sec and, without overlapprocessing, we need 64 sec. With 75% over-lap, we need 4 sec for the first block and 1 secfor each successive one, or 4x1 + 1x15 = 19 secto perform the same task.