1. Recall that the Nyquist-Shannon theorem states that the minimum sampling rate fs necessary to faithfully...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Recall that the Nyquist-Shannon theorem states that the minimum sampling rate fs necessary to faithfully resolve a signal of interest with frequency f is given by: fs 2f (a) Consider the following 1D 13C NMR spectrum, given as the Fourier transform in the frequency domain. Note that the y axis units are arbitrary, and the x axis represents the frequency in kHz, increasing right to left. Identify the highest frequency signal in this dataset, and determine whether or not the actual sampling frequency (59.524kHz) was sufficient to faithfully render all resonances in the spectrum. What is the maximum frequency of a resonance that can be faithfully rendered at this sampling rate? 25 25 - 21442.075 - 17560.276 15423.241 9718.133 9686.150 9654.128 9303.159 7129.056 7060.676 6292.448 5321.362 5303.375 4997.101 4970.318 4794.607 4653.003 4601.200 4551.400 4502.794 4011.554 4007.107 3550.974 3523.137 3504.844 3492.921 3054.328 2998.199 2870.221 2838.189 2694.008 20 20 15 2 10 10 2645.336 2428.483 15 20 [rel] 5 0 [kHz] 10 10 55 0 (b) Assuming the ADC for the spectrometer used to acquire this data operates at 16 bit, what is the minimum data transfer rate demanded of this ADC for the above dataset, if the data is generated in 1.101s and must be converted in the same time? (c) Consider the case in which the sampling rate is 30.0kHz. Which of the signals in the above spectrum would not be faithfully rendered, and at what frequencies would their aliases appear? (Hint: Drawing out a Nyquist zone diagram can be helpful). 3 1. Recall that the Nyquist-Shannon theorem states that the minimum sampling rate fs necessary to faithfully resolve a signal of interest with frequency f is given by: fs 2f (a) Consider the following 1D 13C NMR spectrum, given as the Fourier transform in the frequency domain. Note that the y axis units are arbitrary, and the x axis represents the frequency in kHz, increasing right to left. Identify the highest frequency signal in this dataset, and determine whether or not the actual sampling frequency (59.524kHz) was sufficient to faithfully render all resonances in the spectrum. What is the maximum frequency of a resonance that can be faithfully rendered at this sampling rate? 25 25 - 21442.075 - 17560.276 15423.241 9718.133 9686.150 9654.128 9303.159 7129.056 7060.676 6292.448 5321.362 5303.375 4997.101 4970.318 4794.607 4653.003 4601.200 4551.400 4502.794 4011.554 4007.107 3550.974 3523.137 3504.844 3492.921 3054.328 2998.199 2870.221 2838.189 2694.008 20 20 15 2 10 10 2645.336 2428.483 15 20 [rel] 5 0 [kHz] 10 10 55 0 (b) Assuming the ADC for the spectrometer used to acquire this data operates at 16 bit, what is the minimum data transfer rate demanded of this ADC for the above dataset, if the data is generated in 1.101s and must be converted in the same time? (c) Consider the case in which the sampling rate is 30.0kHz. Which of the signals in the above spectrum would not be faithfully rendered, and at what frequencies would their aliases appear? (Hint: Drawing out a Nyquist zone diagram can be helpful). 3
Expert Answer:
Related Book For
Digital Signal Processing
ISBN: ?978-0133737622
3rd Edition
Authors: Jonh G. Proakis, Dimitris G.Manolakis
Posted Date:
Students also viewed these physics questions
-
Consider the following context-free grammar of expressions E ::= n | (E, E) where n ranges over integers. (a) Present a right-most derivation of the expression ((21, 18), 17). [2 marks] (b) List the...
-
A company purchased merchandise to be resold at increasing cost during the year 2017. The purchases were made at the following costs. January 1, 2017 (carried over from 2016) - 20 units at $10...
-
Consider again examples 9.2 and 9.3 , and once again assume that there are two states of the world for each random variable, denoted by V L j , V H j and n L , n H . Denote the probabilities for...
-
Customers arrive at an automated coffee vending machine at a rate of 4 per minute, following a Poisson distribution. The coffee machine dispenses a cup of coffee at a constant rate of 10 seconds. (a)...
-
A psychologist records the duration of natural labor (in hours) in a sample of 36 first-pregnancy mothers. Based on the duration data given in the following table, which measure of central tendency...
-
Assume you have been tasked to describe a context diagram to someone unfamiliar with it. Write a brief description of its elements, how to construct it, and what information should be depicted.
-
The TransCanada Lumber Company and Mill processes 10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging companys supplier begins delivery to the lumber...
-
5 Kayak Company budgeted the following cash receipts (excluding cash receipts from loans received) and cash payments (excluding cash payments for loan principal and interest payments) for the first...
-
Calculate the required rate of return for Mars Inc.'s stock. The Mars beta is 1.2, the rate on a T-Bill is 4 percent, the rate on a long-term T-Bond is 6 percent, the required return on the market is...
-
Explain how having a single type of aircraft in a fleet affects an airlines ability to recover from irregular operations, such as diversion recovery or an extended airport shutdown due to bad weather?
-
Explain why airlines originally formed alliances with foreign carriers.
-
What do you conclude about the gains from trade when you compare the sum of producer surplus and government gain to the loss of consumer surplus?
-
From time to time, when purchasing certain items such as jewelry, the salesperson will ask the customer what price the customer has in mind. What do you suppose is the purpose of this question?
-
Explain why it is often said that trade is always good, but not always good for everybody.
-
Windows wear museum n brands invest millions in their displays which are very artistic and creative and showcased on store floors and retailers windows, n window displays are often thrown away,...
-
Floyd Distributors, Inc., provides a variety of auto parts to small local garages. Floyd purchases parts from manufacturers according to the EOQ model and then ships the parts from a regional...
-
(a) Describe the distinguishing characteristics of production systems where: (i) job costing techniques would be used, and (ii) process costing techniques would be used. (b) Job costing produces more...
-
(a) While the ascertainment of product costs could be said to be one of the objectives of cost accounting, where joint products are produced and joint costs incurred, the total cost computed for the...
-
South Africa is one of the top gold producers in the world, holding about 40 per cent of global reserves. According to Statistics South Africa, a government statistics agency, the value of gold sales...
Study smarter with the SolutionInn App