An analog signal xa(t) = 3 cos 480nt · sin 700nt – 5 sin 1100nt · cos 2180nt is to be sampled and converted to a digital signal. What is the Nyquist rate for sampling xa(t)? If xa(t) is sampled at twice the Nyquist rate, what is the resulting discrete-time signal? If xa(t) is sampled at F, = 1000 samples/sec, what is the resulting discrete-time signal? Show that aliasing has occurred in this case. Finally, what would be the reconstructed analog signal if the discrete-time signal is passed thru an ideal D/A conversion.

An analog signal xa(t) = 3 cos 480nt · sin 700nt – 5 sin 1100nt · cos 2180nt is to be sampled and converted to a digital signal. What is the Nyquist rate for sampling xa(t)? If xa(t) is sampled at twice the Nyquist rate, what is the resulting discrete-time signal? If xa(t) is sampled at F, = 1000 samples/sec, what is the resulting discrete-time signal? Show that aliasing has occurred in this case. Finally, what would be the reconstructed analog signal if the discrete-time signal is passed thru an ideal D/A conversion.

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

1. The CT signal x(t)=3cos (600πt) + 6cos2(mπt) is critically sampled (Nyquist rate) by fs=4000 Hz. Find:i. The value of m.ii. The frequency components of the signal.iii. The frequency resolution (∆f) of the output spectrum if the sampled signal is processed by 64 point-DFT.iv. Define frequency resolution.
An analog signal is given as x(t) = 5 + 2 cos(20πt) + 3cos(400 πt). a) What is the bandwidth of x(t)? Determine the Nyquist sampling frequency for x(t), both in radian/sec (ws), and in Hz (Fs).b) Formulate Xp (jw), the signal sampled with the Nyquist frequency. c) Plot frequency spectrum of the the sampled signal, Xp (jw). d) Determine the filter to reconstruct the signal x(t). e) Is it possible to reconstruct the signal x(t) for Ts =0.004 [s]? State that if aliasing error occurs or not.
(can you solve it fast?) Which ones are correct about Nyquist's Theorem in sampling? I. Relates the conditions on the time and frequency planes ii. Helps quantize iii. They determine the bandwidth requirement iv. Returns the spectrum of the sign
Use the signal flow graph method for finding the transfer function Y(S)/R(S)
The signal s(n)s(n) is recorded with frequency sampling Fs=500HzFs=500Hz. What's the duration of the following part s1(n)s1(n) of the signal s(n)s(n) where s1=s(601:4:5000)
The speech signal xa(t) is bandlimited to |F| < 8kHz. It is desired to filter the analog signal with a bandpass filter that will pass all frequencies between 200 Hz and 6kHz. This is done by the set up in the image where h[n] is a discrete time filter. A) What is the Nyquist rate for the input signal? B) Sketch the necessary H(w) if the sampling rate Fs is equal to the Nyquist rate. C) For this problem, it's possible to sample below the Nyquist rate and still produce the desired output ya(t). What is the lowest sampling rate Fs that makes this possible and what is the corresponding H(w)?
A robotic system with transfer function ?(?) =(100)/(s(0.1s+1)(0.1s +1)) is controlled with gain K as shown in the figure. A)To analyze the frequency response of this system, draw the Nyquist graph. B)Apply the Nyquist stability criterion. C)Verify the stability analysis you made in part (b) by plotting root locus plots for the positive and negative values of the K gain. D)Calculate the gain value that makes this system borderline stable and show it on Nyquist and Root locus graphs. E)Calculate the gain margin, phase margin, gain crossover frequency and phase crossover frequency values. F)Explain whether the system is stable over the gain margin and phase margin values. WE NEED TO SOLVE THE PROBLEM IMMEDIATELY. PLEASE HELP.
1. Given an analog signal x(t)=10 cos(2π.5500t)+5 cos(2π.7500t) is sampled at a rate of 8,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal low pass filter with a cutoff Frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal; c. determine the frequency/frequencies of aliasing noise.
Q3 in a digital telephony network, the signal of human voice needs to be sampled and digitized before transmission. it is found that limiting the bandwidth of human voice to 3000 hz would be enough to ensure good-quality phone calls. a. Human voice contains frequency components above 3000 Hz. How canwe ensure that the voice signal will only occupy a bandwidth of 3000Hz? b. The sampling rate is determined to be 50% higher than the Nyquistsampling rate. Determine the sampling rate c. A pulse-code modulation (PCM) scheme is used to represent thedigitized voice signal, where 10 bits are used for each sample.Determine the data rate of a single voice call. d. Time-division multiplexing (TDM) is used to aggregate a maximum of 40voice calls in a telephone line. Determine the maximum data rate thatyou can observe over a telephone line. e. Determine the minimum required bandwidth of the telephone line thatcan support a maximum of 40 phone calls.- d. Explain what…
TRUE or FALSE 1.) In time domain represenatation of a signal, a signal with an expression of 220 cos (377t -180) is also equal to -220 cos (377t) 2.) In time domain represenatation of a signal, a signal with an expression of 220 sin (377t +90) is also equal to -220 cos (377t)
Scale the inductor and capacitor so that themagnitude and the phase angle of the output current do not change whenthe input frequency is changed from 20 krad/s to 500 rad/sec.1. What are the scaled values of the inductor and capacitor?2. What is the steady-state value of the output current, io, when theinput current is 400 cos 500t mA?
A signal m(t) = sin(2*pi*f*t) with f =2Hz and has a duration of 1 second. If m(t) is sampled at a frequency of 8Hz, using ideal sampling, determine the values of each sampled value and plot ms(t). Also using the sampling theorem, find the value of the reconstructed signal at time t = 0.001s. Answer is 1.073