11

Modulation and Demodulation

of Biomedical Signals

11.1 Introduction

In general, modulation is a process by which a dc or low-frequency signal of interest is combined nonlinearly with a high-frequency carrier wave to form a modulated carrier suitable for transmission to a receiver/demodulator where the signal is recovered. Modulators and demodulators form essential components of most communication and data transmission systems. Some modulation schemes involve multiplication of the carrier with a function of the modulating signal.

In biomedical engineering, recorded physiological signals are modulated because modulation permits robust transmission by wire or coaxial cable, fiber optic cable, or radio (telemetry by electromagnetic waves) from the recording site to the site where the signal will be demodulated, processed, and stored. As an example, in biotelemetry, physiological signals such as the ECG and blood pressure modulate a carrier sent as an FM radio signal from an ambulance to a remote receiver (in a hospital ER) where the signals are demodulated, interpreted, filtered, digitized, and stored. Five major forms of modulation involve altering a high-frequency sinusoidal carrier wave:

(1) amplitude modulation (AM); (2) single-sideband AM (SSBAM); (3) frequency modulation (FM); (4) phase modulation (PhM); and (5) double-side- band, suppressed-carrier modulation (DSBSCM).

Modulation can also be done using a square wave (or TTL) carrier and can involve FM, NBFM, and PhM. Delta modulation, pulse-position modulation (PPM), and pulse-width modulation (PWM) at constant frequency are done with digital carrier. AM, FM, and DSBSCM are expressed mathematically below for a sinusoidal carrier. vm(t) is the actual physiological signal. The maximum frequency of vm(t) must be ωc, the carrier frequency. The normalized modulating signal, m(t), is defined by the following equation:

431

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	432						Analysis and Application of Analog Electronic Circuits
	m(t) =	vm (t)	, 0 ≤		m(t)		≤ 1	Normalized modulating signal	(11.1A)
		vmmax
	ym (t) = A[1+ m(t)]cos(ωct)							AM	(11.1B)
	ym (t) = A m(t)cos(ωct)							DSBSCM	(11.1C)
							t	˘
	ym (t) = A cos ωc t + Kf m(t)dt˙ FM								(11.1D)
								˚
	ym (t) = A cos[ωc t + Kpm(t)]							PhM	(11.1E)

11.2Modulation of a Sinusoidal Carrier Viewed in the Frequency Domain

It is interesting to examine the frequency spectrums of the modulated signals.

For illustrative purposes, let the modulating signal be a pure cosine wave, vm(t) = mo cos(ωm t), 0 < mo ≤ 1. Thus, by using Equation 11.1B and a trig.

identity, the amplitude modulated (AM) signal can be rewritten:

y

m

(t) = A cos(ω

t)+ (A m

2) cos((ω

c

+ ω

m

)t)+ cos((ω

c

− ω

m

)t)

(11.2)

c

o

[

]

Thus, the AM signal has a carrier component and two sidebands, each spaced by the amount of the modulating frequency above and below the carrier frequency. In SSBAM, a sharp cut-off filter is used to eliminate the upper or the lower sideband; the information in both sidebands is redundant, so removing one means less bandwidth is required to transmit the SSBAM signal. SSBAM signals are more noise resistant than conventional AM because they require less bandwidth to transmit the same m(t).

FM and PhM are subsets of angle modulation. FM can be further classified as broadband (BBFM) or narrowband FM (NBFM). In BBFM, Kf ∫ 2πfd, where

fd is called the frequency deviation constant. In NBFM, fd/fmmax 1 fmmax is the highest expected frequency in vm(t), which is bandwidth-limited. Unlike

AM, the frequency spectrum of an FM carrier is tedious to derive. Using m(t) = mo cos(ωm t), the FM carrier can be written as:

ym		α	β	˘	(11.3)
	(t) = A cos ωct+ (Kf		ωm )mo sin(ωmt)˙
				˚

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Modulation and Demodulation of Biomedical Signals

433

Using the trigonometric identity cos(α + β) = cos(α)cos(β) − sin(α)sin(β), Equation 11.3 can be written as:

ym (t) = A cos(ωct)cos[(Kf ωm )m0 sin(ωmt)]

(11.4)

− A sin(ωct)sin[(Kf ωm )m0 sin(ωmt)]

Now the cos[(Kf/ωm)mo sin(ωm t)] and sin[(Kf /ωm)mo sin(ωm t)] terms can be expressed as two Fourier series whose coefficients are ordinary Bessel

functions of the first kind and argument β (Clarke and Hess, 1971); note that

β ∫ mo 2πfd/ωm:

cos[βsin(ωmt)]= J0 (β)

•

+ 2 J2n (β)cos(2nωmt)

(11.5A)

n=1

[

(

m

)]

•

2n+1

( )

( (

)

m

)

ω

= 2

J

(11.5B)

sin βsin

t

β

sin 2 n + 1 ω

t

n= 0

The two Bessel sum relations for cos[β sin(ωmt)] and sin[β sin(ωm t)] can be recombined with Equation 11.4 using the trigonometric identities cos(x) cos(y) = ½[cos(x + y) + cos(x − y)] and sin(x) sin(y) = ½[cos(x − y) − cos(x + y)], and one can finally write for the FM carrier spectrum, letting mo = 1:

ym (t) = A{J0 (β)cos(ωct)+ J1(β)[cos((ωc + ωm )t)− cos((ωc − ωm )t)]

+ J2 (β)[cos((ωc	+ 2ωm )t)+ cos((ωc	− 2ωm )t)]
+ J3 (β)[cos((ωc	+ 3ωm )t)+ cos((ωc	− 3ωm )t)]	(11.6)

+J4 (β)[cos((ωc + 4ωm )t)+ cos((ωc − 4ωm )t)]

+J5 (β)[cos((ωc + 5ωm )t)+ cos((ωc − 5ωm )t)]+≡}

At first inspection, this result appears quite messy. However, it is evident that the numerical values of the Bessel terms tend to zero as n becomes large. For example, let β = 2πfd/ωm = 1; then J0(1) = 0.7852; J1(1) = 0.4401; J2(1) = 0.1149; J3(1) = 0.01956; J4(1) = 0.002477; J5(1) = 0.0002498; J6(1) = 0.00002094; etc. Bessel constants Jn(1) for n ≥ 4 contribute less than 1% each to the ym(t) spectrum, so they can be neglected. Thus, the practical bandwidth of the FM carrier, ym(t), for β = 1 is ±3ωm around the carrier frequency, ωc. In general, as β increases, so does the effective bandwidth of the FM ym(t). For example,

© 2004 by CRC Press LLC