Signal Processing - July 2017 - 187

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Table 1. Envelope detector performances.
Highest output SNR

Asynchronous complex square-law [Figure 3(a)]

.

Asynchronous Hilbert complex [Figure 2(d)]

.

Asynchronous full-wave [Figure 2(b)]

.

Asynchronous real square-law [Figure 2(c)]

.

Asynchronous complex [Figure 3(c)]

.

Synchronous real [Figure 3(b)]

Lowest output SNR

Asynchronous half-wave [Figure 2(a)]

software modeling of the various envelope
detectors, with
■ Sample rate: fs = 8, 000 Hz
■ RF carrier frequency: 600 Hz
■ Modulation: 60 Hz sine +30 Hz cosine
wave
■ Modulated RF signal SNR: +23 dB
■ LP filter: third-order Butterworth infinite impulse response (≈240 Hz cutoff
frequency)
I rank the detectors' performances (from
best to worst) as shown in Table 1.

Summary
Various popular methods of envelope
detection were listed and briefly described. Although computationally simple
to implement, the Figure 2(a) detector
should be avoided due to its high output
noise behavior.
For moderate-performance applications, such as AGC or analyzing medical signals, the detectors in Figures 2(b)

and (c) and 3(b) and (c) are appropriate
choices. Note that, despite its computationally simple implementation, the
Figure 2(b) detector performs quite well
compared to the other detectors in this
moderate-performance category.
For high-performance applications,
such as in digital communications systems, the detectors in Figures 2(d) and
3(a) are the preferred choices. While their
SNR performances are very similar, note
that the Figure 2(d) detector requires far
fewer arithmetic operations per output
sample than the Figure 3(a) detector.
As a general rule, if you need an
envelope detector in your signal processing application, I suggest you implement several of the aforementioned
detectors to see which method is optimum for your input signals, your fs data
sample rate, and your data throughput
requirements. To quote Forrest Gump,
"And that's all I have to say about that."

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Richard Lyons (R.Lyons@ieee.org) is
a consulting signal processing engineer.
Winner of the IEEE 2012 Education
Award, he is the author of Understanding
Digital Signal Processing 3/E (Prentice
Hall, 2010). He is the editor of, and
contributor to, Streamlining Digital
Signal Processing, A Tricks of the Trade
Guidebook (IEEE Press/Wiley, 2007)
and the coauthor of The Essential
Guide to Digital Signal Processing
book (Prentice Hall, 2014).

References

[1] C. Johnson, Jr., W. Sethares, and A. Klein,
Software Receiver Design. Cambridge, U.K.:
Cambridge Univ. Press, 2011, pp. 82-84.
[2] S. A. Tretter. Amplitude modulation. [Online].
Ava ilable: ht t p://www.ece.umd.edu /~t ret ter/
commlab/c6713slides/ch5.pdf
[3] R. Lyons, Understanding Digital Signal
Processing, 3rd ed. Englewood Cliffs, NJ: Prentice
Hall, 2011, pp. 786-784.
[4] D. Cia rdullo. A fast envelope detector,
Brookhaven Nat. Lab., AGS/AD/Tech. Note No. 386.
[Online]. Available: http://www.agsrhichome
.bn l.gov/AGS/Accel / Repor ts/ Tech%20Notes/
TN386.pdf
[5] M. E. Frerking, Digital Signal Processing in
Communications Systems. London: Chapman &
Hall, 1994, pp. 235-238.
[6] MathWorks, Inc. Envelope detection. [Online].
Available: https://www.mathworks.com/help/dsp/
examples/envelope-detection.html?s_tid=gn_loc_
drop
[7] C. Turner. Fast magnitude calculation. [Online].
Ava i lable: ht t p://w w w.clayst u r ner.com /dsp/
FastMagnitude.pdf

SP

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