Explore BrainMass
Share

# Examining frequency to time domain signals

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

A spectrum analyzer is connected to an unknown signal. The spectrum analyzer displays the power level of signals in dBm vertically and frequency horizontally. The spectrum of the unknown signal creates the following display:
A continuous spectrum that is completely filled so no lines are visible.
The spectrum has a sin X / X (sinc X) shape. The spectrum has maximum power spectral density at 0 Hz and falls to zero at 2 kHz, 4 kHz, 6 kHz and other even kHz frequencies.

a. What is the input waveform?
b. Is the input signal periodic or non-periodic?
c. What is the pulse width?
d. If the spectrum suddenly changes to have zeroes at 5 kHz, 10 kHz, 15 kHz, etc, what is the new pulse width?

https://brainmass.com/engineering/electrical-engineering/424280

#### Solution Preview

(a)

The Sin(x)/x type waveform (also known as Sinc(x) function) in the frequency domain is charactristic of a stream of pulses. The zero crossing points (nulls) in the Sinc(x) = Sin(x)/x waveform occur at points denoted by

1/t, 2/t, 3/t.......n/t (n an integer ranging from 1 to infincity) where t represents the pulse width (time duration) of the pulses. In addition with the Sinc(x) function if there is any periodicity in the pulse stream (ie repeated data patterns) then this ...

#### Solution Summary

In this solution from a description of a Sinc function we back engineer the signal to its tiime domain representation to answerthe following

A spectrum analyzer is connected to an unknown signal. The spectrum analyzer displays the power level of signals in dBm vertically and frequency horizontally. The spectrum of the unknown signal creates the following display:
A continuous spectrum that is completely filled so no lines are visible.
The spectrum has a sin X / X (sinc X) shape. The spectrum has maximum power spectral density at 0 Hz and falls to zero at 2 kHz, 4 kHz, 6 kHz and other even kHz frequencies.

a. What is the input waveform?
b. Is the input signal periodic or non-periodic?
c. What is the pulse width?
d. If the spectrum suddenly changes to have zeroes at 5 kHz, 10 kHz, 15 kHz, etc, what is the new pulse width?

\$2.19

## Root Raised Cosine (RRC) Filters, Inter Symbol Interference (ISI), Noise Bandwidth

A digital communication system transmits binary data using polar NRZ pulses of current over a baseband link with a bandwidth of 20 kHz. The transmitter and receiver have ideal "Root Raised Cosine" (RRC) filters with roll off factor = 0.5.

a. What is the minimum bandwidth that the link must provide to avoid generating ISI (inter symbol interference) at the receiver?

b. What transfer function must the link have over this bandwidth to avoid the generation of ISI?

c. A radio link has a bandwidth of 15 kHz. What is the maximum bit rate at which binary data can be transmitted without ISI if the transmitter and receiver have ideal RRC filters with roll off factor = 0.5 using BPSK modulation?

d. What is the noise bandwidth of the receiver?

e. What is the requirement for the phase response (transfer function) of each of these links to avoid distortion of the transmitted waveform?

View Full Posting Details