mae 3113 in class problems set fall 2014 (sampling, fft and filtering)

8/9/2019 MAE 3113 in Class Problems Set Fall 2014 (Sampling, FFT and Filtering)

1/10

1

MAE 3113

MEASUREMENTS AND INSTRUMENTATIONS

Fall 2014

Sampling, FFT, and Filtering Review Questions

Given: A pressure transducer is used to measure the periodicity of a fluid flow.The transducer output ranges from -5 to 5 volts, and the maximum frequency of

interest is 10 Hz. Superimposed on the signal is some pesky electronic noise at 60Hz with an amplitude of 0.1 volts (the noise ranges from -0.1 to + 0.1 V). The

noise must be reduced by at least a factor of 10 (a gain of 0.1 or less). The cutoff

frequency to be used by the filter is 10 Hz.

(a)

To do: Assuming that the only filters available are first, second, and fourth-

order (n = 1, 2, or 4) Butterworth filters, select the lowest order filter that willdo the job

(b)

To do: For the filter selected in Part (a), calculate the gain in dB right at thecutoff frequency.

(c)

To do: Notice from the problem statement that the cutoff frequency of the filteris equal to the frequency of the signal. As calculated in Part (b), the amplitude

of the signal itself is therefore attenuated somewhat. To correct this problem,you decide to use a second-order low-pass Butterworth filter, but with a higher

cutoff frequency. Calculate the highest cutoff frequency that can be used such

that it still provides the desired attenuation of the high frequency noise.(d)

To do: What is the minimum sampling frequency that should be used to avoidaliasing (of the desired signal, not the noise)?

(e)

To do: If we sample at 25 Hz, at what frequency will a small peak appear in thespectrum due to the electronic noise?

Solution:


2/10

2

Given: A voltage contains a strong component at 1000 Hz (the desired signal),

along with some undesired noise at 12,000 Hz. Samantha puts in a first-order, low-pass, anti-aliasing filter with a design cutoff frequency of 2000 Hz, and then

digitally samples the voltage at a sampling frequency of 10,000 Hz.

(a)

To do: Assuming Calculate the gain and decibel gain of the filter at both the

signal frequency and the noise frequency.(b)

To do: In order to meet specifications, the noise must be attenuated by at least

45 dB. What is the lowest-order filter that Samantha could buy to satisfy therequirements: second-order, fourth-order, sixth-order, or eighth-order?


3/10

3

Given: A voltage signal ranges from -1.1 to 1.2 volts. A digital data acquisition

system is to be chosenfour choices are available:

(a) 12 / = 10 10

(b) 8 / = 2 2

(c)

10 / = 5 5 (d)

14 / = 1 1 To do: Determine which system is the best choice for this application, assuming

that cost is irrelevant (all four are available in the lab).Solution:


4/10

4

Given: A voltage signal contains frequency components at 150, 350, and 700 Hz.

It also contains some electronic noise at 60 Hz. We sample the data digitally at asampling frequency of 400 Hz.To do: Is there any aliasing? If so, what frequencies will we see (perceive)?

Solution:


5/10

5

Given: Andy collects data with a digital data acquisition system that is 14-bit and

has a range of -5 to 5 V. He samples at a sampling frequency of 200 Hz.(a)

To do: Calculate the quantization error in millivolts.(b)

To do: For each case, will Andys signal be clipped? Is there any aliasing? If

so, what frequencies will he see (perceive)?(a)

Signal has a frequency of 40 Hz with a range of3 to 3 V.

(b)Signal has a frequency of 120 Hz with DC offset =4.5 V and amplitude =1.0 V.

(c)Signal is () = 3.5(700 ) + 1.0 Volts.


6/10

6

Given: Voltage data are acquired with a digital data acquisition system. A FFT is

performed, and a frequency spectrum plot is generated.To do: Which of the following has the better frequency resolution?

Case a: Data are sampled atfs = 100 Hz, and 512 data points are taken.

Case b: Data are sampled atfs = 200 Hz, and 256 data points are taken.


7/10

7

Given: Voltage data are acquired with a digital data acquisition system at =

1000 2048 data points are taken, a FFT is performed, and a frequencyspectrum plot is generated.

(a)To do: Calculate the total sampling time

(b)

To do: Calculate the folding frequency of the resulting frequency spectrum(c)

To do: Calculate the frequency resolution of the resulting frequencyspectrum


8/10

8

Given: A voltage signal has a 1.50 V DC component and two periodic

components:

Frequencyf1 = 115 Hz, amplitudeA1 = 2.00 V

Frequencyf2 = 540 Hz, amplitudeA2 = 0.500 V

There is also some noise.The signal is sampled at 1000 Hz, taking 256 data points.(a)To do: Sketch the ideal frequency spectrum assuming sampling rate is not an

issue.(b)To do: Is there any aliasing? If so, calculatefa.

(c)

To do: Calculate the frequency resolution and sketch the frequency spectrum.

Solution:


9/10

9

Given: A voltage signal contains useful data up to about 1000 Hz. There is also

some unwanted noise at frequencies greater than 3000 Hz. We want to use a low-pass filter so that the noise is attenuated by at least 95%. We plan to use a cutoff

frequency of 2000 Hz so that there is minimal attenuation of the 1000 Hz

component of the signal.To do: Calculate the required order of the low-pass filter.

Solution:


10/10

10

Given: Vibrations around 90 Hz with an amplitude of about 5 V are measured with

a DAQ. Data is sampled atfs = 500 Hz. Unfortunately, there is also some electronicinterference noise at 3600 Hz, with an amplitude of about 1 V.

(a)To do: Sketch the frequency spectrum that you would expect to see if there is nofiltering.

(b)To do: Sketch the frequency spectrum that you would expect to see after the

signal is filtered with a 4-order low-pass anti-aliasing filter set to a cutoff

frequency of 200 HzSolution:

mae 3113 in class problems set fall 2014 (sampling, fft and filtering)

Documents