A signal f(t) is sampled at a rate of wo rad/s to give a sampled signal fs(t). The Fourier transform of f(t) is F (w) is shown graphically in Figure A1. Sketch the spectrum of the sampled signal, denoted by F(w), for the cases: wo > 2wm, wo = 4wm/3, and wo = wm. In each case, indicate the spectrum that appears at the output of an ideal reconstruction filter. 1 F(w) -@m -0/3 0 00/3 Figure A1: Fourier transform of f(t). @ m 3 (0) C

A signal f(t) is sampled at a rate of wo rad/s to give a sampled signal fs(t). The Fourier transform of f(t) is F (w) is shown graphically in Figure A1. Sketch the spectrum of the sampled signal, denoted by F(w), for the cases: wo > 2wm, wo = 4wm/3, and wo = wm. In each case, indicate the spectrum that appears at the output of an ideal reconstruction filter. 1 F(w) -@m -0/3 0 00/3 Figure A1: Fourier transform of f(t). @ m 3 (0) C

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

4. A 70 year old man was taken to hospital due to chest pain the doctors immediately took him to ICU and did the ECG. The ECG signal is analyzed on spectrum analyzer to find the problem. Assuming that spectrum analyzer internally contains DSP system to do the given task. The ECG signal taken from the patient has bandwidth of 70Hz in that the required signal bandwidth is only 60Hz remaining part of the signal represent the noise. Design a DSP system that accepts only the required signal and samples it and the sampled spectrum contains 40Hz separation between neighboring spectral components and this discrete time signal is transformed into frequency domain using 16 point DFT find the following.i. Find the cutoff frequency of the antialiasing filterii. Find the sampling frequency of the sampler usediii. Find the Frequency of X(4) and X(8) iv. Draw the block diagram of the designed system
The plot in the figure below shows the magnitude frequency content of a signal. Determine the approximate frequency, in Hertz, of the largest sinusoid present in the signal given that the sampling frequency (fs) is 458 Hz. DFT (Magnitude Spectrum) of a Signal Magnitude See 140 120 100 80 60 40 20 G Answer: 916 The correct answer is: 134.7059 G G Frequency Bins 10 12 14 16 for more info on this problem.
Fourier theory states that any sinusoidal signal may be represented or analyzed as the sum of a fundamental sine wave at the signal frequency plus odd, even, or odd plus even nonharmonic sine waves of different phases and amplitudes. True False
A signal with real components at 25, 70, 160 and 510 Hz is sampled at 100 Hz. represent the magnitude spectrum?
Determine the Nyquist rate of a signal whose frequency spectrum is given by ¤(f) = r(f) – 2r(f – 1000) + 2r(f – 3000) – r(f – 4000), where r(f) is the unit ramp function in the frequency domain. O a. 6 kHz O b. 12 kHz O c. 3 kHz O d. 2 kHz O e. 4 kHz Of. 8 kHz A sampling process uses a sampling rate of fg. Determine which of the following input signal frequencies will not be aliased to 0.4f, if it undergoes the said process. О а. 1.6f, оБ. 2.4f. Ос. 1.4f. O d. 1.8f, A continuous-time signal is composed of in-phase sinusoids with periods of 1 ms, 2 ms, and 4 ms. Determine the maximum sampling period allowed to avoid aliasing. O a. 0.4 ms O b. 0.5 ms Oc. 0.2 ms O d. 0.1 ms O e. 0.8 ms Of. 1.0 ms
Consider the following continous time signal x(t). Assume that the signal was sampled at a sampling frequency of 20 Hz. Plot the magnitude spectrum of the sampled signal as a function of cyclic frequency. Be sure to include n values of up to +-2. Label x and y axis. Did aliasing occur? If so, what is the aliased frequency? x(t) = 1 + 2cos(2pi25t)
A sequence of alternating 1s and 0s is transmitted as a square wave. What is the fundamentalfrequency and how many harmonics can be used if the available BW is 100 MHz and a data rate of 56Mbps is desired? Express the signal as a mathematical function of time (s(t)) and sketch the resultingsignal in both the time and frequency domains. Is this a “good enough” representation of the squarewave? Why or why not?
1) For the signals shown in below, a) Find the Fourier transform of the half-cosine pulse in figure (a). Sketch amplitude spectrum of the G(f). b) Apply the time-shifting property to the result obtained in part (a) to evaluate the spectrum of the half-sine pulse shown figure (b). Sketch amplitude spectrum of the G(f). c) What is the spectrum of a half-sine pulse in figure (b) having a duration equal to aT ? Sketch amplitude spectrum of the G(f). d) What is the spectrum of the negative half-sine pulse shown in figure (c) ? Sketch amplitude spectrum of the G(f). e) Find the spectrum of the single sine pulse shown in figure (d). Sketch amplitude spectrum of the G(f). g(t) g(f) -T/4 0 T/4 T/2 (b) g(f) g(t) -T/2 -T/2 0. 0. T/2 -A -A (d)
as can be seein in the figure below, the x1(t) and x2(t) signals are multiplied by the continuous time singal and the w(t) signal is sampled with the periodic unit pulse signal p(t).As stated below, the x1(t) signal is considered to be band-limited with the w1 frequency and the x2(t) signal is considered to be band-limited with the w2 frequency ----------------------------------------------------------------------------- Calculate the maximum sampling interval T to recover the w(t) signal from the ??(?) signal using a low-pass filter
use inverse Fourier trans form formula to Prove this go t EscW- Wo) + scw+ Wo)] CS Scanned with CamScanner
An FM signal has a deviation of 3 kHz and a modulating frequency of 1 kHz. Its total power is 5 W, developed across a 50 2 resistive load. The carrier fre- quency is 160 MHz. (a) Calculate the RMS signal voltage. (b) Calculate the RMS voltage at the carrier frequency and each of the first three sets of sidebands. (c) Calculate the frequency of each sideband for the first three sideband pairs. es Falerna avlop (d) Calculate the power at the carrier frequency, and in each sideband, for the first three pairs.
A discrete time signal is represented as in the figure below.What is the fundamental frequency?a. pi/6b. pi/3c. 2pi/8d. pi