Note: Nyquist sampling rate is the minimum sampling frequency according to the sampling theorem In the sampler system shown below, the FT X(w) of the input signal x(t) is as shown below. If this signal is sampled using Nyquist sampling rate, then the spectrum Xs(@) of the sampled signal x-(t) is: X(@) 1 x(t) Sampler -100 n 100 я A. В. (@}sx* AA 100 hoo '-100n 100n - 400n 400n 800n w С. 4 Xs(@) D. Xs() NAKAA 100 100 -200n 200n 400x w -200n 200n 400n

Note: Nyquist sampling rate is the minimum sampling frequency according to the sampling theorem In the sampler system shown below, the FT X(w) of the input signal x(t) is as shown below. If this signal is sampled using Nyquist sampling rate, then the spectrum Xs(@) of the sampled signal x-(t) is: X(@) 1 x(t) Sampler -100 n 100 я A. В. (@}sx* AA 100 hoo '-100n 100n - 400n 400n 800n w С. 4 Xs(@) D. Xs() NAKAA 100 100 -200n 200n 400x w -200n 200n 400n

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...

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6.1 A 1 kHz sine wave is sampled at frequency of 5 kHz.(a) What is the Nyquist frequency of the sampling system in this case? Showyour work.(b) What is the Nyquist rate of the signal? Show your work.(c) Is the signal properly sampled; that is, will there be aliases in the digitallyrecorded signal? Explain.(d) What if the original analog signal included both even and odd harmonics of itsprimary frequency; that is, 2, 3, 5 kHz, etc. What would be the highest harmonicthat will be faithfully represented in the discrete-time version of the analogsignal?(e) Following on with the previous step, what is the lowest harmonic that will bealiased and what would be resulting alias frequency?
Consider the following amplitude modulated signals(t)= cos(2000t) 4cos(2400t) cos(2800t). If this signal is sampled, then what will be Nyquist's sampling frequency of this signal s(t)?
A continous - time analog signal is represented by x(t) = cos(2000πt). This signal is sampled at different sampling frequencies with the first sample taken at t=0. E. From the results of b, c, and d, which sampling frequency would yield samples which resembles closely to a? Which sampling frequency would produce the worst result?
A digital communication link carries binary-coded words representing samples of an input signal, xa(t)=3cos⁡(600πt)+2cos⁡(1800πt)The link is operated at 1,000 samples/s. (a) What is the folding frequency? (b) What is the Nyquist rate for the signal xa(t)? (c) What are the frequencies in the resulting discrete-time signal x(n)? (d) Will there be any aliasing here? (e) Which frequency will alias to what frequency
Given that sampling frequency (fs) is equal to 250Hz and Nyquistfrequency (fN) is equal to two times of the alias frequency, find the aliasfrequency.
2) An analog signal Xa(t) = sin(480pit)+3sin(720pit) is sampled 600 times per second . a) determine the nyquist sampling rate for Xa(t) and the folding frequency ? b)what are the frequencies in radians, in the resulting discrete time signals x(n) ? c)if x(n) is passed through an ideal D/A converter , what is the reconstructed signal Ya(t) ?
An analog signal, with an absolute bandwidth of 10 KHz, is to be converted to a digital signal usingan A/D converter and stored in a PC. If the quantization error must be within ±0.05% of the peak-to-peakvalue of the analog signal, determine the storage requirement. Please assume that we are going to record 8seconds of data, sampled at 1.5 times the Nyquist rate.
For the CT signal x(t)=12cos (4000nt) %31 -Find all the frequency components (frequency & voltage values for each) of x(t). Hint: simplify cos first to be cos of power one only before finding frequencies. -Convert the CT signal to digital PCM signal so that SNqR=40 dB and 150 kbps. What are m and fs values, and which type of sampling? Calculate and justify. -How many minutes of PCM signal can be saved in one CD disk (700 Mbyte).
3、The relationship between the signal frequency fc and sampling rate Ts is ( ) according to the Nyquist sampling law A、 fcTs>1 B、 2fcTs>1 C、 3fcTs>1 D、 4fcTs>1
Q 5. A television signal (video and audio) has a bandwidth of 4.5 MHz. The signal is sampled,quantized and binary coded to obtain a Pulse Coded Modulated (PCM) signal.(a) Determine the sampling rate if the signal is to be sampled at a rate of 20% above theNyquist rate.(b) If the samples are quantized into 1024 levels, determine number of binary pulses (ordigits) required to encode each sample.(c) Determine the binary pulse rate (bits per second) of the binary coded signal.(d) Calculate minimum bandwidth required to transmit this signal.
Calculate: - the total sampling time - the time increment between sampled data points - the frequency resolution of the frequency spectrum - the Nyquist frequency
2.A music signal with bandwidth Bx=20kHz has to be converted through an analog-to-digital converter with resolution 16 bit (this is the number of bits used to represent each real sample extracted from the analog waveform). The sampling frequency chosen is the least required to satisfy the sampling theorem. The stream of bits is transmitted digitally, one bit at the time, through a binary antipodal modulator. It is known that the probabilities of the bits emitted are p1=0.5 and p0=0.5. If the power spectral density of the Additive Gaussian Noise is No/2 with No=10-4 W/Hz, find the amplitude A of the modulator pulses that is required to achieve a bit error probability of 10^-5.