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c) A continuous time periodic signal x(t) is sketched in Figure 1c below. Calculate the energy in a single cycle of this waveform.

c) A continuous time periodic signal x(t) is sketched in Figure 1c below. Calculate the energy in a single cycle of this waveform.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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question C please 

Lecture name signals adn informations 

Question 1 a) A discrete time signal is described by the formula: x[n] = cos(TT.n) for all negative and positive integer values of 'n'. i) Sketch the signal from n= -2 to n=2 and state whether it is even or odd. ii) Find the energy in the signal over the period n=0 to n=9. iii) If the signal x[n] = cos(π.n) is multiplied by the signal z[n] = sin(π.n). What is the resultant sequence y[n] = x[n].z[n]? (Evaluate y[n] for the values n=0 to n=4 only.) b) A continuous time periodic sawtooth signal, x(t), is described over a single period as follows: for - < t < 1/2 x(t)=t ('t' is in seconds) The period of the signal is 1 second. Sketch the signal x(t). With respect to the Fourier Series, evaluate ao. Find (or state) expressions for an, and bn. HINT: x.sin(a.x) dx = (). (sin (ax)) - () (x.cos(ax)) c) A continuous time periodic signal x(t) is sketched in Figure 1c below. Calculate the energy in a single cycle of this waveform. With respect to the Fourier Series, find an expression for ao for the signal x(t); state which of an, and bn is zero by observation. The signal x(t) is now passed into an Ideal Low Pass Filter (ILPF) with cut-off frequency fc=1.5Hz. Sketch the output signal of the ILPF in the time and frequency domains. -1 0 x(t) Figure 1c 1 2... t, seconds
Transcribed Image Text:Question 1 a) A discrete time signal is described by the formula: x[n] = cos(TT.n) for all negative and positive integer values of 'n'. i) Sketch the signal from n= -2 to n=2 and state whether it is even or odd. ii) Find the energy in the signal over the period n=0 to n=9. iii) If the signal x[n] = cos(π.n) is multiplied by the signal z[n] = sin(π.n). What is the resultant sequence y[n] = x[n].z[n]? (Evaluate y[n] for the values n=0 to n=4 only.) b) A continuous time periodic sawtooth signal, x(t), is described over a single period as follows: for - < t < 1/2 x(t)=t ('t' is in seconds) The period of the signal is 1 second. Sketch the signal x(t). With respect to the Fourier Series, evaluate ao. Find (or state) expressions for an, and bn. HINT: x.sin(a.x) dx = (). (sin (ax)) - () (x.cos(ax)) c) A continuous time periodic signal x(t) is sketched in Figure 1c below. Calculate the energy in a single cycle of this waveform. With respect to the Fourier Series, find an expression for ao for the signal x(t); state which of an, and bn is zero by observation. The signal x(t) is now passed into an Ideal Low Pass Filter (ILPF) with cut-off frequency fc=1.5Hz. Sketch the output signal of the ILPF in the time and frequency domains. -1 0 x(t) Figure 1c 1 2... t, seconds
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