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angle modulation is called non linear modulation because the information is stored in phase of the carrier signal

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Q: Why is Angle Modulation called nonlinear modulation?
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Difference between narrow band angle modulation and wide band frequency modulation?

Preface:In communications, modulation is the process of "mixing" one signal (the one you intend to transmit, called the "message" and often simplified as being a simple sinusoid) with another (called the "carrier" and also often simplified as being a sinusoid) in some form. In Amplitude Modulation (AM), the two are simply linearly multiplied, ie:u(t) = Ac(1 + k*m(t))*cos(2*pi*fc*t)where Ac represents the amplitude of the carrier signal, k is a modulation index, fc is the carrier frequency, and u(t) represents the modulated signal. Through the trigonometric properties of sinusoids, it is possible (and in the case of AM fairly straightforward) to recover the original message signal m(t) in the absence of noise.Both Frequency Modulation (FM) and Phase Modulation (PM) are forms of Angle Modulation, in which your signal of interest m(t) modulates the angle of the carrier wave, which is a type of nonlinear modulation. This can be generalized as:u(t) = Ac*cos(2*pi*fc*t + p(t))where p(t) is linearly related to m(t), your message, and itself represents an angle shift. (For now it doesn't matter whether p(t) is modulating frequency or phase.)Assume p(t) described above is a sinusoid out of phase with the carrier by 90 degrees, specifically that the carrier is a cosine wave and the angle modulating message p(t) is a sine wave. Using the simple trigonometric identitycos(a + b) = cos(a)cos(b) - sin(a)sin(b)we can rewrite u(t) in its in-phase quadrature formu(t) = Ac[ cos(p(t))*cos(2*pi*fc*t) - sin(p(t))*sin(2*pi*fc*t) ]Trigonometrically speaking (see first-order Taylor Series approximation for further reading), for very small (close to zero) values of t in cos(t), cos(t) is almost 1, and sin(t) is almost t. If we assume that p(t), the angle modulating signal message, always has a very small value (nearly zero), we can reasonably simplify the modulated signal to the form:u(t) Ac[ cos(2*pi*fc*t) - p(t)*sin(2*pi*fc*t) ]which, if you compare with the form of the AM signal, is very similar. In fact, this "narrowband" angle modulation, which assumes a narrow range of angles possible, is nearly identical to the functionality of AM and therefore consumes almost the same amount of signal bandwidth and is analyzed in a very similar manner. This is because a first-order approximation (which narrowband is an example of) is linear and therefore is fundamentally the same as AM.Physically speaking, however, using a narrowband angle modulation technique is not reliable and provides little benefit over an AM technique. It consumes the same amount of signal bandwidth as AM and is just as susceptible to noise. (Consider some additive spectral noise variable, taken with our assumption that p(t) was extremely small, will indicate that the received signal will be unrecognizably different than the transmitted signal.)Wide band angle modulation, on the other hand, does not make this simplifying assumption that angles are small (first-order approximation). Without these assumptions, signal analysis is much more complex, and involves solving Bessel functions for multiple values of the message signal across the intended spectrum. However, because of its true nonlinearity, wide band angle modulation is much more resilient to noise than is narrowband/AM and consumes much more bandwidth.


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Related questions

Why frequency modulation and phase modulation are called angle modulation?

i dont know ans. of this.


Why angle modulation is called exponential modulation?

The reason it is called exponential (non-linear) modulation is that the information is encoded within the phase of carrier.


What are the two types of angle modulation?

Frequency Modulation and Phase Modulation


What is the difference between frequency modulation and phase modulation?

The difference between frequency modulation and phase modulation is that with frequency modulation the angular frequency of the signal is modified while with the phase modulation, the phase angle of the signal is modified.


Why is angular modulation called exponential?

It is called angle modulation because it changes the angle of the carrier which is exponential, e.g. sin theta = {(e*j theta + e (-j theta)} / 2


What is analog modulation?

Analog modulationIn analog modulation, the modulation is applied continuously in response to the analog information signal.Common analog modulation techniques are:Amplitude modulation (AM) (here the amplitude of the modulated signal is varied) Double-sideband modulation (DSB) Double-sideband modulation with unsuppressed carrier (DSB-WC) (used on the AM radio broadcasting band)Double-sideband suppressed-carrier transmission (DSB-SC)Double-sideband reduced carrier transmission (DSB-RC)Single-sideband modulation (SSB, or SSB-AM), SSB with carrier (SSB-WC)SSB suppressed carrier modulation (SSB-SC)Vestigial sideband modulation (VSB, or VSB-AM)Quadrature amplitude modulation (QAM)Angle modulation Frequency modulation (FM) (here the frequency of the modulated signal is varied)Phase modulation (PM) (here the phase shift of the modulated signal is varied)


What are the advantages and disadvantages of phase modulation?

Advantage - 1. Phase modulation & demodulation is easy compared to Frequency modulation. 2. Phase modulator is used in determining velocity of moving target by extracting Doppler information. Doppler information needs stable carrier which is possible in phase modulation but not in frequency modulation. Disadvantage - 1. Phase ambiguity comes if we exceed its modulation index pi radian(180 degree). 2. we need frequency multiplier to increase phase modulation index. Visit my website http://harshit.org


What is amplitude modulation and frequency modulation and difference between them?

Both angle and amplitude modulation are involved in radio wavelength patterns. Angle modulation is where the modulating wave manipulates the angle of a sine-wave carrier. The two types of angle modulation include frequency and phase modulation. On the other hand, Amplitude modulation is the strength behind carrying the waveform in radio.


What is the difference between amplitude shift keying and AM modulation?

Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a http://wiki.answers.com/wiki/Radio http://wiki.answers.com/wiki/Carrier_wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. Angle modulation is a class of http://wiki.answers.com/wiki/Analog_signal http://wiki.answers.com/wiki/Modulation. These techniques are based on altering the http://wiki.answers.com/wiki/Angle or http://wiki.answers.com/wiki/Phase_%28waves%29 of a http://wiki.answers.com/wiki/Sinusoidal http://wiki.answers.com/wiki/Carrier_wave to http://wiki.answers.com/wiki/Transmission_%28telecommunications%29 data. The two main types of angle modulation are: http://wiki.answers.com/wiki/Frequency_modulation (FM) in which the http://wiki.answers.com/wiki/Frequency is varied, http://wiki.answers.com/wiki/Phase_modulation (PM) in which the http://wiki.answers.com/wiki/Phase_%28waves%29 is varied.


How do amplitude modulation and frequency modulation differ?

Amplitude modulation is where a constant carrier is modulated by the signal, so that the envelope of the carrier represents the signal. Frequency modulation is where a constant carrier is modulated by the signal, so that the frequency of the carrier represents the signal. Phase modulation is where a constant carrier is modulated by the signal, so that the phase angle of the carrier represents the carrier.


Difference between narrow band angle modulation and wide band frequency modulation?

Preface:In communications, modulation is the process of "mixing" one signal (the one you intend to transmit, called the "message" and often simplified as being a simple sinusoid) with another (called the "carrier" and also often simplified as being a sinusoid) in some form. In Amplitude Modulation (AM), the two are simply linearly multiplied, ie:u(t) = Ac(1 + k*m(t))*cos(2*pi*fc*t)where Ac represents the amplitude of the carrier signal, k is a modulation index, fc is the carrier frequency, and u(t) represents the modulated signal. Through the trigonometric properties of sinusoids, it is possible (and in the case of AM fairly straightforward) to recover the original message signal m(t) in the absence of noise.Both Frequency Modulation (FM) and Phase Modulation (PM) are forms of Angle Modulation, in which your signal of interest m(t) modulates the angle of the carrier wave, which is a type of nonlinear modulation. This can be generalized as:u(t) = Ac*cos(2*pi*fc*t + p(t))where p(t) is linearly related to m(t), your message, and itself represents an angle shift. (For now it doesn't matter whether p(t) is modulating frequency or phase.)Assume p(t) described above is a sinusoid out of phase with the carrier by 90 degrees, specifically that the carrier is a cosine wave and the angle modulating message p(t) is a sine wave. Using the simple trigonometric identitycos(a + b) = cos(a)cos(b) - sin(a)sin(b)we can rewrite u(t) in its in-phase quadrature formu(t) = Ac[ cos(p(t))*cos(2*pi*fc*t) - sin(p(t))*sin(2*pi*fc*t) ]Trigonometrically speaking (see first-order Taylor Series approximation for further reading), for very small (close to zero) values of t in cos(t), cos(t) is almost 1, and sin(t) is almost t. If we assume that p(t), the angle modulating signal message, always has a very small value (nearly zero), we can reasonably simplify the modulated signal to the form:u(t) Ac[ cos(2*pi*fc*t) - p(t)*sin(2*pi*fc*t) ]which, if you compare with the form of the AM signal, is very similar. In fact, this "narrowband" angle modulation, which assumes a narrow range of angles possible, is nearly identical to the functionality of AM and therefore consumes almost the same amount of signal bandwidth and is analyzed in a very similar manner. This is because a first-order approximation (which narrowband is an example of) is linear and therefore is fundamentally the same as AM.Physically speaking, however, using a narrowband angle modulation technique is not reliable and provides little benefit over an AM technique. It consumes the same amount of signal bandwidth as AM and is just as susceptible to noise. (Consider some additive spectral noise variable, taken with our assumption that p(t) was extremely small, will indicate that the received signal will be unrecognizably different than the transmitted signal.)Wide band angle modulation, on the other hand, does not make this simplifying assumption that angles are small (first-order approximation). Without these assumptions, signal analysis is much more complex, and involves solving Bessel functions for multiple values of the message signal across the intended spectrum. However, because of its true nonlinearity, wide band angle modulation is much more resilient to noise than is narrowband/AM and consumes much more bandwidth.


What is the Comparison of frequency modulation and amplitude modulation?

I will answer this in the simplest way I know in the application I use it in; this would be in audio applications. Amplitude modulation is modulation of a carrier source's loudness; Frequency modulation is modulation of a carrier source's pitch; and Phase modulation is modulation of a carrier source's duty cycle/symmetry/timbre. One can often notice that all 3 modulation types relate in some way with another in that when frequency rises and falls it typically makes it favorable for either a rise in loudness or timbre. The most analog way to understand it in nature is typically your small vowel sounds like "iiiiiiiiiiiiii" as in the American-English word 'easy' and 'eeeeeeeeeeee' as in 'edge' are easier to say with loudness at higher pitches; medium vowel sounds like 'uuuuuuuuuuu' as in 'Utter' or 'sOn' and 'aaaaaaaaaaaa' as in 'Awe' *chuckles* are easier to say with loudness at medium pitches; large vowel sounds like 'ooooooooooo' as in 'Oh' and 'uuuuuuuuuuuu' as in 'rUne' are easier to say with loudness at lower pitches. AM is often known as 'tremolo'; FM is often known as 'vibrato'; PM is often known as 'wow'; AM/FM is 'vibremelo' and fill in the blanks for the other sub-variants. Maikel Stellerfield