How do I solve this Communications Theory problem? **Problem 1. (a)** This problem involves designing a receiver for 10 kHz wide speech signals in the frequency band of 144 to 148 MHz, using a superheterodyne analog front-end. The diagram shown illustrates the setup. You are to assume a center frequency and bandwidth for the intermediate frequency (IF) amplifier, specifically:- \( f_{IF} = 450 \, \text{kHz} \)- \( W_{IF} = 10 \, \text{kHz} \)The task is to determine the appropriate range for the local oscillator frequency \( f_{LO} \) and identify the requirements for the RF filter.**Diagram Explanation:**- **\( x(t) \):** Represents the incoming signal.- **RF Filter:** This block is responsible for filtering the input signal with parameters \( f_c \) and \( W_{RF} \). It passes specific frequencies while attenuating others.- **tunable \( f_{LO} \):** The local oscillator is tunable, meaning it can adjust its frequency to mix with the incoming signal.- **Mixer (\( \times \)):** Combines the incoming signal with the local oscillator signal, resulting in the output signal \( v(t) \).- **IF Amp:** The intermediate frequency amplifier processes the mixed signal with characteristics \( f_{IF} \) and \( W_{IF} \) before outputting \( y(t) \). This configuration is essential in achieving the desired frequency translation for signal processing within the specified bandwidth.

Given:A superheterodyne receiver, RF signal frequency range = 144 - 148 MHz. bandwidth of RF signal = 10 KHz. and,Intermediate frequency ,bandwidth of IF signal ,we need to determine:range of local oscillator frequency and the requirements on the RF filter. For the given super heterodyne receiver, local oscillator frequency can be computed using the formula (for up-conversion), , Given the range of received signal and so the required range of local oscillator frequency is, As the received signal is being passed through only mixer and IF amplifier not by multiplier so the output signal of IF filter will also have the 10 KHz bandwidth as same as bandwidth of the received signal.The RF filter should cover the entire frequency range of interest for the receiver. Here the required frequency range is 144 to 148 MHz. The RF filter must provide sharp selectivity to minimize interference from nearby frequencies.The filter should be able to reject the image frequencies. In this case, image frequency RF filter should be able to maintain a low passband ripple to ensure uniform signal transmission within the desired frequency range.RF filter should be able to keep insertion loss low to minimize signal attenuation as the signal passes through the filter.It should provide good adjacent channel rejection to filter out signals from adjacent frequency channels, especially in crowded RF environments where multiple channels are in close proximity.By meeting these requirements, the RF filter in a superheterodyne receiver ensures proper signal reception, selectivity, and rejection of unwanted interference, resulting in high-quality demodulated signals.Required range of local oscillator frequency is, RF filter requirements for a super-heterodyne receiver have been explained.