This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Exercises 3.1 Find an expression for and sketch the frequency spectrum of a sine wave of angular frequency ϖ = 2π / T . Obtain an expression for the energy and power of this sinewave. 3.2 Obtain and sketch the frequency spectrum the following signal ) 4000 sin( 2 ) 3000 sin( 5 ) 1000 sin( 10 ) ( t t t t x π π π + + = Calculate the total signal power and the power at each individual frequency, and hence deduce the Parseval’s theorem. 3.3 Find the frequency spectrum of a periodic train of pulses with a period of 10 kHz and a pulse 'on' duration of 0.04 milliseconds. Write the formula for synthesising the signal up to the 10 th harmonic, and plot a few examples for the increasing number of harmonics. 3.4 Find the spectrum of a shifted impulse function defined as ∆- ∆ ≤- ∆ = =- → ∆ 2 / 2 / / 1 ) ( limit ) ( T t T t t p T t δ (3.26) and hence deduce the relationship between the time-delay and the phase of a signal. 3.5 Obtain and sketch the spectrum of the rectangular pulse given by ≤ = otherwise T t t x 2 / | | 1 ) ( Find an expression relating the bandwidth of the main lobe of the spectrum to the pulse duration. Calculate the percentage of the pulse power concentrated in the main lobe of the pulse spectrum....
View Full Document