Frequency Modulation - an overview (original) (raw)
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Biomimetic bidirectional hand neuroprostheses for restoring somatosensory and motor functions
Francesco Iberite, ... Silvestro Micera, in Somatosensory Feedback for Neuroprosthetics, 2021
10.6.3 Frequency modulation
Frequency modulation is a straightforward approach for simple biomimetic encoding, as it is strongly related to how information is represented in the spiking rate. Experimental results using pulse frequency modulation to encode applied force confirmed this strategy as valid (Graczyk et al., 2018; Ortiz-Catalan et al., 2014). However, frequency modulation displays shorter adaptation times, namely the time taken by the prosthetic user until he/she stops perceiving a sustained neural stimulation, compared to amplitude modulation (Valle, Petrini, et al., 2018). Minimizing adaptation is important when designing a prosthesis intended for continuous manipulation of objects, for which a slowly changing modulation of force is applied. On the other hand, faster and nonconstant modulation of the frequency is known to deliver reliable tactile information over a manipulation task (Valle, Mazzoni, et al., 2018), suggesting the need for a more biomimetic approach compared to a simple linear frequency modulation. The frequency was also shown to change the quality of the evoked sensation (Graczyk et al., 2020) in a consistent way across multiple stimulation sites, proving its effectiveness as another tool to shape the sensory perception of the prosthesis user, alongside the magnitude. As stated above, both the frequency of pulses and charge per pulse contribute to the sensation magnitude. A step toward disentangling these phenomena was taken by Graczyk and colleagues (Graczyk et al., 2016); they proposed a metric of the activation charge rate which can be related to the sensation magnitude independently from the modulated parameter. This metric is consistent with the models which state that the population spike count is the most likely code for sensation magnitude (Güçlü & Dinçer, 2013; Muniak et al., 2007).
URL:
https://www.sciencedirect.com/science/article/pii/B9780128228289000113
Digital Systems
Martin Plonus, in Electronics and Communications for Scientists and Engineers, 2001
Frequency Modulation (FM)
In frequency modulation, the frequency rather than the amplitude of the carrier wave is made to vary in proportion to the varying amplitude of the modulating signal, as shown in Fig. 9.18_d_. A simple method to achieve FM is to vary the capacitance of a resonant LC circuit in a transmitter. Because the frequency of a radio wave is less vulnerable to noise than the amplitude, FM was originally introduced to reduce noise and improve the quality of radio reception. In order to accomplish this FM radio signals have bandwidth several times that of AM signals. Bandwidths six times or larger are common. For example, commercial stereo FM broadcasting (88–108 MHz) is assigned a bandwidth of 200 kHz in which to broadcast 15 kHz of audio-music bandwidth. One speaks of FM trading bandwidth for noise. Also in AM if the amplitude of modulation is to be increased, the power must be increased proportionately. In FM the amplitude of the frequency modulation can be increased without increasing the power at all. In addition, since the amplitude of the FM signal remains constant, amplitude limiters can be set close to the FM signal amplitude and thus very effectively reduce impulse noise. AM was adopted for the transmission of the video part of a TV signal because AM is the least wasteful of the radio frequency spectrum, which is a precious commodity in a wireless environment. FM, though, because of its relative noise-free reception, is used to transmit the audio part of the television signal.
URL:
https://www.sciencedirect.com/science/article/pii/B9780125330848500203
Broadband Interface Concepts
Louis E. FrenzelJr, in Handbook of Serial Communications Interfaces, 2016
Frequency Modulation
In frequency modulation, the carrier amplitude remains constant but its frequency is changed in accordance with the modulating signal. Specifically, the higher the amplitude of the information signal, the greater the frequency change. The actual carrier frequency deviates above and below the center carrier frequency as the information signal amplitude varies. Figure 63.3 shows frequency modulation with a sine wave information signal. Notice that the carrier frequency gets higher on the positive peaks and lower on the negative peaks of the information signal.
Figure 63.3. Analog frequency modulation.
Like AM, FM also produces sidebands. But unlike AM which produces a single pair of sidebands for each frequency in the modulating signal, the frequency modulation process produces an infinite number of pairs of sidebands for each frequency in the information signal. As a result, the bandwidth occupied by an FM signal is enormous. Luckily, the number of sidebands produced can be controlled by properly selecting the amount of deviation permitted in the carrier. Small deviations result in fewer sidebands. Further, some of the higher order sidebands are extremely low in amplitude and, therefore, contribute little to the FM signal. But while the bandwidth of an FM signal can be controlled and established to fit a desired frequency range, it does nevertheless usually require a wider bandwidth channel than an AM signal.
The primary benefit of FM is that it is less sensitive to noise which is undesired amplitude variations which get involuntarily added to a signal. Noise is easily eliminated in an FM system where a constant carrier amplitude is used. Some of the most common applications of FM include FM radio broadcasting, and two-way mobile radio and marine radios.
URL:
https://www.sciencedirect.com/science/article/pii/B9780128006290000632
Analog Communications
Carl Nassar, in Telecommunications Demystified, 2001
12.3 Frequency Modulation (FM)
To some, FM is a dial on the radio where you can hear love songs, classic rock, or greatest hits. To engineers, FM is shorthand for frequency modulation.
9.2 The Modulator in FM
The idea in frequency modulation is to map the information x(t) into the frequency of the transmitted signal s(t). Mathematically, what is done is this: Given an information bearing signal x(t), you send out over the channel
(12.24)s(t)=Accos(ωct+θ(t))
where
(12.25)θ(t)=Kf∫−∞tx(τ)dτ.
Looking at this equation, you really can't tell that the information x(t) is placed in the frequency of s(t). So let's do a little math that will show that x(t) has indeed been placed in the frequency of s(t). The frequency of s(t), at any moment in time t, is given by
(12.26)ω(t)=ddt(ωct+θ(t))
(12.27)ω(t)=ddt(ωct+Kf∫−∞tx(τ)d τ)
(12.28)ω(t)=ωcKfx(t)
This tells us that at time t, the frequency of the sent signal s(t) is ωc + Kf x(t), which indicates that x(t) is determining the frequency of s(t).
Let's use pictures to see what is going on in FM. Let's say we have the information-bearing signal x(t) as shown in Figure 12.11(a). Using this, we can determine some important information about s(t):
Figure 12.11. (a) Information signal x(t) (b) Transmitted FM signal s(t)
At times when x(t) = −1, the frequency of s(t) is ω(t) = ωc + Kf x(t) = ωc - Kf.
At times when x(t) = +1, the frequency of s(t) is ω(t) = ωc + Kf x(t) = ωc +Kf.
Using this information, we can get the plot of s(t) shown in Figure 12.11(b). Here, we see the variation in the frequency of s(t) as a direct result of changes to x(t).
For another example, take a look at Figures 12.12(a) and (b). There, we see the input x(t) = cos(Wt) (where W is a ver y small number). We also see the output in Figure 12.12(b)—as x(t) gets bigger, the frequency of s(t) gets bigger, and as x(t) gets smaller the frequency of s(t) gets smaller.
Figure 12.12. (a) Information signal x(t) (b) Sent signal s(t) in FM
Let's see if we can characterize the sent signal s(t) in the frequency domain—that is, let's see if we can evaluate the Fourier transform of s(t), called S(f). To help us out, let's start by rewriting s(t) :
(12.29)s(t)=Accos(ωct+θ(t))
(12.30)s(t)Re{Acejωct+θ(t)}
(12.31)s(t)Re{[Acejθ(t)]ejωct}
(12.32)s(t)Re{g(t)ejωct}
where g(t) =Acejθ(t). Taking the Fourier transform of s(t) and applying properties of the Fourier transform, we end up with
(12.33)S(f)=12G(f−fc)+12G(−f−fc)
where G(f) is the Fourier transform ofAcejθ(t) andθ(t)=∫−∞tx(τ)d τ. The relationshipbetween G(f) and x(t) is so complex that there is no simple mathematical equation to relate the value G(f) to the value X(f)—that means there is no simple equation to relate S(f) to X(f).
In the simple case when x(t) = cos(Wt) and W is small, we can derive an equation relating X(f). to S(f), but this equation is messy, involving Bessel functions, and I just want to offer an introduction to analog communications here. Look in the reference list to see a book that covers the joys of Bessel functions.
Example
Draw the output of an FM modulator when the input corresponds to Figure E12.7.
Figure E12.7. Input to FM modulator
Solution:
The output corresponds to equation (12.24), which shows that the output corresponds to a sinusoid with constant amplitude. Equation (12.28) tells us that the frequency of the FM output changes linearly with x(t). Putting this information together leads to the output plot of Figure E12.8.
Figure E12.8. Output of FM modulator
12.3.2 The Demodulator in FM
We now know about how the FM modulators work and what they do. At the receiver side, you want to build an FM demodulator that gets the received signal r(t) = s(t) and turns that back into your information x(t).
You know that there is no information x(t) in the amplitude of r(t) = _s(t)_—all the information is in the instantaneous frequency ω(t) = ωc + Kf x(t). The demodulator works to get ω(t), the instantaneous frequency, out of r(t) = s(t), the received signal.
A demodulator for an FM signal is shown in Figure 12.13. First, a limiter is applied. The limiter takes r(t) = s(t) and gets rid of all amplitude fluctuations, by simply forcing all positive values to +1 and all negative values to −1. The output is called r´(t). The limiter's operation does not affect the ability to extract the information signal x(t), since the information is stored in the frequency (not in the amplitude). Then, the signal r´(t) is passed through a discriminator. The discriminator outputs a value r˝t), which is proportional to the instantaneous frequency ω(t). That is, it outputs
Figure 12.13. FM demodulator
(12.34)r″(t)=Kω(t)
(12.34)r″(t)=K(ωc+Kfx(t))
Once we have this output, a processor doing a simple subtraction and a scalar multiplication creates the outputx^(t).
And that, my friends, is FM, its modulation and its demodulation.
URL:
https://www.sciencedirect.com/science/article/pii/B9780080518671500184
Complex Electronic System Design Example
Peter Wilson, H. Alan Mantooth, in Model-Based Engineering for Complex Electronic Systems, 2013
13.3.3.2.2 Frequency Modulation
Frequency modulation (FM) takes a similar approach in that a carrier signal is modulated by the input signal except, in this case, the amplitude of the modulated signal is constant, but its frequency changes. A simple example of a kind of frequency modulator could be a voltage-controlled oscillator (VCO), where the frequency of the output is controlled by the input voltage.
Mathematically, we can consider the carrier signal to be the same as for AM; however, rather than the amplitude changing, the frequency of the modulated signal changes by a factor called the frequency variation, or frequency deviation. The amount of deviation is usually specified as part of a commercial radio standard. The carrier frequency for a zero input is the nominal frequency, and the frequency deviation can be positive or negative, so the total carrier swing is twice the frequency deviation. For example, if the FM signal is assigned a 200 kHz bandwidth, this is equivalent to the carrier swing and so the frequency deviation would be 100 kHz. FM radio stations are usually assigned a frequency in the range of 88 to 108 MHz in contrast to AM radio which is in the range of 0.55 to 1.6 MHz, and this is one reason why AM radio has a longer range; however, FM radio operates better in reception areas that are closed in, such as tunnels and buildings, owing to the higher frequency and corresponding shorter bandwidth.
We can see an example of a signal that is FM modulated with a frequency of 1 kHz on a carrier of 50 kHz, with a full range sensitivity in Figure 13.11.
Figure 13.11. FM modulated signals
The massive improvement in quality inherent in FM signals over AM signals is the result of almost all of the power being contained in the modulated signal, whereas in AM, as we discussed previously, most is wasted in transmitting the carrier.
FM demodulation takes place using a “superheterodyne” demodulator as shown in Figure 13.12. This is actually quite similar to an AM demodulator often used in integrated circuits.
Figure 13.12. Superheterodyne FM demodulator
The major drawbacks with FM systems are the relatively wide bandwidths required per channel and, although similar, the transceiver topology complexity is greater than that of a basic AM demodulator.
URL:
https://www.sciencedirect.com/science/article/pii/B9780123850850000130
The Phase-locked Loop (PLL)
Brahim Haraoubia, in Non-Linear Electronics 2, 2019
3.9.3 Frequency modulation and demodulation
3.9.3.1 Frequency modulation principle
In general, in signal transmission, the useful signal s(t) to be transmitted is a low-frequency signal (modulating signal). To transmit this signal, we resort to a carrier signal, which has a high frequency. When the useful information is carried by variations in the carrier frequency, this is referred to as frequency modulation. The carrier is a sinusoidal signal. It is expressed using the relation:
vpt=V0.cosθ
with V0: carrier amplitude.
θ=∫0tωpdtandωp=2πfp
For frequency modulation, the frequency f (or angular frequency ω) of the modulated signal linearly varies with the amplitude of the modulating signal s(t).
ω=ωp+2kπ.st
The expression of the frequency-modulated (FM) signal is given by:
vFMt=V0.cosθ1
with:
θ1=∫0tωt.dt=∫0tωp+2kπstdt
Finally, the FM signal will have the general expression:
vFM=V0cos∫0tωp+2kπstdt
The carrier frequency fp (ωp = 2πfp) is constant:
vFM=V0cosωpt+∫0t2kπstdt
3.9.3.2 Frequency modulation circuit based on a PLL
The circuit that is to be designed from a PLL must produce a frequency-modulated output signal (see the synoptic diagram in Figure 3.81).
Figure 3.81. Frequency modulation using a PLL circuit. For a color version of this figure, see www.iste.co.uk/haraoubia/nonlinear2.zip
The use of a PLL and adding a summator circuit enables a frequency-modulated signal to be obtained. When the carrier frequency falls within the capture range of the PLL, the latter is locked and the output frequency in the absence of a modulating signal will be equal to the carrier frequency.
When the signal modulator is added to the signal related to the phase error, the output of the voltage-controlled oscillator will vary at the rate of this modulating signal around the carrier frequency.
As we have pointed out, the modulating signal is a low-frequency signal. The PLL is very effective to ensure frequency modulation provided that the modulating signal is not too fast. Conversely, the PLL may not follow.
3.9.3.3 Frequency demodulation
Frequency demodulation consists of recovering the signal that carries the information or modulating signal that is carried by the variations of the carrier frequency. To this end, we make use of the synoptic diagram, based on a PLL, in Figure 3.82.
Figure 3.82. Frequency demodulation principle. For a color version of this figure, see www.iste.co.uk/haraoubia/nonlinear2.zip
In a transmission, the FM signal picked by the receiver is applied to the PLL input. It then locks up and follows changes in frequency due to modulation.
The low-pass filter is calculated to let through the frequencies of the modulating signal. As such, the signal s(t) is collected (low-pass filter output), which is the image of the initial modulating signal.
It should be noted here that there are other methods to ensure frequency demodulation that naturally do not rely on PLL circuits. Their effectiveness is nevertheless reduced.
URL:
https://www.sciencedirect.com/science/article/pii/B9781785483011500039
Analog and Time Division Multiple Access Wireless Communications
Michael Parker, in Digital Signal Processing 101 (Second Edition), 2017
15.2 Frequency Modulation
Information can be carried by a sinusoidal wave using varying the amplitude, frequency, and phase. In quadrature amplitude modulation (QAM), the amplitude and phase are changed. In FM, only the frequency is modified. FM is a modulation method inherently suitable for an analog input or baseband signal. Basically, the instantaneous frequency of the carrier is made to increase or decrease from the carrier frequency by an amount proportional to the modulating or baseband signal. This change in the carrier frequency is known as the frequency deviation. The frequency deviation is proportional to the amplitude of the baseband input. The rate of change (derivative) of the carrier frequency is proportional to the frequency of the baseband input. The AMPS used FM with peak derivative of 12 kHz.
Since there is no amplitude modulation (AM), the FM signal is of constant amplitude. This is the inherent FM superior characteristic over AM, and why FM radio, from its beginnings in the 1930s, was designed for high fidelity compared with AM radio. Any additive noise with an AM signal will cause distortion of the amplitude, which is the baseband signal. In contrast with FM, the frequency carries the baseband signal and is much less affected by additive noise. This additive noise causes phase distortion, which can affect the frequency demodulation, but most of this can be filtered out of the resulting baseband signal. Another important characteristic of FM is that, due to constant amplitude characteristic, it can be very efficiently amplified. This will be further discussed in a subsequent chapter.
URL:
https://www.sciencedirect.com/science/article/pii/B9780128114537000159
Data Transmission Media
John S. Sobolewski, in Encyclopedia of Physical Science and Technology (Third Edition), 2003
VI.F Comparison of Modulation Techniques
The various modulation techniques that have been described have distinct advantages and disadvantages in terms of cost, immunity to noise, and other impairments commonly encountered in communication channels. Amplitude modulation (AM) is widely used for radio programs. It is easy to maintain and relatively low in cost, but it is susceptible to noise. Frequency modulation is more effective in terms of noise tolerance and more suited for data transmission than AM. Phase modulation is more complex and costly but is relatively immune to noise and theoretically makes the best use of bandwidth for a given transmission rate. Various forms of phase and hybrids of phase and amplitude modulation (QAM and TCM) are increasingly used for data communication over analog channels at rates up to 56,000 bits/sec. Although it requires higher bandwidth, PCM has the advantage that the signal is regenerative and has greatest immunity to noise. Optical fibers, with their very high bandwidth, are well suited for PCM. Consequently, fibers and PCM are rapidly becoming the two leading technologies for transmission of data and digitized analog signals.
URL:
https://www.sciencedirect.com/science/article/pii/B0122274105001654
URL:
https://www.sciencedirect.com/science/article/pii/S0888327008002690
Headend Signal Processing
Walter Ciciora, ... Michael Adams, in Modern Cable Television Technology (Second Edition), 2004
Modulation Process
Audio is frequency modulated onto an aural carrier. Frequency modulation is usually accomplished by applying the audio directly to an oscillator, such that the frequency of oscillation depends in part on the instantaneous modulating voltage. As shown in Figure 8.5, the modulation is applied to LO2, a 4.5-MHz oscillator (other frequencies may be used with conversion).
Some method must be employed to stabilize the center frequency of the oscillator. Though not the only means to accomplish this, a commonly used stabilization method is a phase locked loop (PLL). It generates a frequency correction to the oscillator if the center frequency wanders. The bandwidth of the PLL is very low to avoid having the loop “Fight” the modulation, which is intentionally forcing the frequency of LO2 to deviate instantaneously.
URL:
https://www.sciencedirect.com/science/article/pii/B9781558608283500102