The input to a linear delta modulator having a step size $$\Delta $$ = 0.628 is a sine wave with frequency f_m and peak amplitude E_m. If the sampling frequency f_s = 40 KHz. the combination of the sine-wave frequency and the amplitude, where slope overload will take place is

Let $$m\left(t\right)\;=\cos\left[\left(4\mathrm\pi\times10^3\right)t\right]$$ be the message signal and $$c\left(t\right)\;=5\cos\left[2\mathrm\pi\times10^6t\right]$$ be the carrier.

c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM singal, then the coefficient of the term $$\cos\left[2\mathrm\pi\left(1008\times10^3\right)t\right]$$ in the FM signal (in terms of the Bessel coefficients) is

Let $$m\left(t\right)\;=\cos\left[\left(4\mathrm\pi\times10^3\right)t\right]$$ be the message signal and $$c\left(t\right)\;=5\cos\left[2\mathrm\pi\times10^6t\right]$$ be the carrier.

c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity $$\frac{Total\;sideband\;power}{Carrier\;power}$$ is

A DSB-SC signal is to be generated with a carrier frequency f_c = 1MHz using a nonlinear device with the input-output characteristic $$v_0=a_0v_i\;+\;a_1v_i^3$$.where a₀ and a₁ are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter. Let $$v_0=A_c'\;\cos\left(2{\mathrm{πf}}_\mathrm c'\mathrm t\right)\;+\;m\left(t\right)$$ where m(t) is the message signal. Then the value of $$f_c'$$ (in MHz) is