Question

Consider a message signal m(t) of bandwidth 10kHz. The power of m(t) is 0.1 . It is used to generate the signal s(t) given by s(t)=m(t)cos(2πfct)− m(t)sin(2πfct)+Acos(2πfct)

where the carrier frequency fc=1MHz. The modulated signal s(t) is transmitted through an AWGN channel with power spectral density of N₀/2. The receiver is as shown below

-→ BPF -→ ⊗ -→ LPF -→
↑
cos(2πfct)

Determine a suitable characteristic of the BPF

Answer 1

The BPF suitable for the transmitted signal should allow the frequency components of the modulated signal to pass, with a passband from 990 kHz to 1010 kHz, covering the carrier frequency and the bandwidth of the message signal.

Step-by-step explanation:

The characteristic of the Band-Pass Filter (BPF) suitable for the receiver in question needs to be adjusted to the bandwidth of the transmitted signal s(t), which is given by s(t) = m(t)cos(2πfct) - m(t)sin(2πfct) + Acos(2πfct), where m(t) is the message signal with a bandwidth of 10 kHz and fc is the carrier frequency at 1 MHz. Since the BPF is placed before the demodulation process, it should allow the frequency components of the modulated signal to pass while rejecting frequencies outside the range. The BPF should have a passband that covers the frequency range of the carrier fc plus and minus the message bandwidth, which means the passband should be approximately from 990 kHz to 1010 kHz.