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

Answer 1

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 identity

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

we can rewrite u(t) in its in-phase quadrature form

u(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.

Answer 2

Commercial FM broadcasting carries 'baseband' information (modulating frequencies) up to

about 70 KHz, has a peak deviation of 75 KHz, and can occupy a bandwidth of up to 300 KHz.

Channels in the FM broadcast band are spaced on 200 KHz centers.

"Narrow band" FM limits the modulating frequency to voice ... 4 KHz or less ... and uses a

smaller peak deviation and modulation index. It occupies a bandwidth of 10 KHz or less.

Channels for analog mobile NBFM are spaced on 12.5 KHz centers.