Shape Factor Benefits of Digital Filters

Blog Post created by benz on Sep 23, 2016

Originally posted Jan 30, 2013


Even more Gaussian than Gaussian

Sometimes it’s not just a matter of analog vs. digital tradeoffs and a technology reaches the stage where digital technologies are really better overall.  This tends to be the case when the digital technologies have progressed to the point where cost and processing performance are no longer limiting factors.  Such is the case with spectrum/signal analyzers and digital IF (resolution bandwidth) filters as illustrated below.

Comparing shape of analog and digital filters in a spectrum analyzer

Comparing shape of analog and digital filters in a spectrum analyzer

The black trace is taken from a traditional swept spectrum analyzer with analog Gaussian resolution bandwidth (RBW) filters.  They’re also sometimes referred to as synchronously-tuned filters.  The shape is called Gaussian, though it’s only the very middle/top of the passband that’s especially Gaussian in shape.  The skirts of the filter make it look rather more triangular overall.

These partly-Gaussian filters were a good choice for swept spectrum analyzers for several reasons.  The Gaussian shape at the top was narrow and provided good selectivity for closely-spaced signals of similar amplitude, allowing spectrum analyzers to do one of their main jobs (separating and measuring such signals) well.  In addition the filters could be swept at a reasonable rate of RBW2/2 Hz/second with only modest frequency and amplitude errors due to the effects of sweeping.

As implemented, however, these filters also had drawbacks.  To minimize frequency and amplitude errors when measuring to meet all specifications they were often swept at about RBW2/8 Hz/second, slowing many measurements considerably.  The shape factor of the filters (the ratio of their 60 dB to 3 dB bandwidths) was around 11:1.  This is a modest figure and means that their selectivity for separating closely-signals of very different amplitudes is limited.  Thus when measuring such signals it was often necessary to use a much narrower RBW and suffer dramatically longer sweep times that generally got slower as the square of the RBW.  Wide span sweeps with narrow RBWs such as those used for spur searches could be painfully long.

In addition analog RBW filters do not have precisely predictable or constant bandwidths.  This is not a particular problem for CW signals but introduces errors when the analyzers are used to measure noise or noise-like signals, where the measured values of signals are proportional to the actual (and varying) bandwidth of the RBW filters.  The bandwidth of some of these filters varied by about ±20% from unit to unit.

Digital technologies came to the rescue, first for narrower RBWs and lower frequency analyzers, in the late 1980s.  The digital filters had shape factors closer to 4:1, similar to the shape shown in red in the figure above.  This dramatically improved their ability to resolve closely-spaced signals and thus allowed wider (and therefore faster-sweeping) RBW filters to be used for equivalent measurements.

Sweep times could be further improved by a technique known as “oversweep” where the predictable dynamic effects of faster-than-normal sweeping could be corrected very well.  The combination of better selectivity, oversweep, and correction of dynamic effects without slowing sweep allows for measurements that can be dozens of times faster than with analog filters.  Techniques for sweep correction of digital filters continue to evolve, and engineers can expect even faster sweeps in the future.

The consistent and accurate bandwidth of digital filters also improves measurement of noise and noise-like signals, where accuracy depends on knowing equivalent noise bandwidth.

For RF/microwave applications the culmination of this trend was the introduction of the first microwave swept spectrum analyzer, with an all-digital IF: the Agilent E4440A PSA spectrum analyzer in late 2000.  Now Agilent’s entire X-Series signal analyzer line uses all-digital IF sections with digital filters.


Gaussian digital filters may be the best choice for general spectrum analysis but they’re not the only one.  Future posts will discuss filters for other types of signal analysis and the tradeoffs they involve.