Question

A digital communication link carries binary coded words representing samples of an input signal x(n)=5cos2000πt+2cos6000πt+4sin10000πt which is sampled at a rate of 8kHz. Each input sample is quantized to achieve a minimum SQNR of 40 dB.

a) Obtain an expression for the resulting discrete time signal x(n).

Answer 1

The resulting discrete time signal x(n) can be obtained by sampling the input signal x(t) at a rate of 8kHz. The samples of x(n) can be obtained by evaluating x(t) at multiples of Ts, which is 125 microseconds in this case.

Step-by-step explanation:

The resulting discrete time signal x(n) can be obtained by sampling the input signal x(t) at a rate of 8kHz. The sampling rate is given by fs = 1/Ts, where Ts is the time between samples. In this case, Ts = 1/8kHz = 125 microseconds. The samples of x(n) can be obtained by evaluating x(t) at multiples of Ts. Thus, x(n) = x(nTs) = 5cos(2π(2000nTs)) + 2cos(2π(6000nTs)) + 4sin(2π(10000nTs)). Substituting the value of Ts, we get:

x(n) = 5cos(2π(2000n(125e-6))) + 2cos(2π(6000n(125e-6))) + 4sin(2π(10000n(125e-6)))