NOTE: This lab exercise is specific to two Frequency analyzers owned by GMI. If you do not have these same analyzers you will have to modify the specific instructions which are meant as a familiarization exercise for our students. However, with local modifications, the concepts covered in the lab exercise should transfer over to any other analyzer.
I. Introduction
This laboratory exercise is intended to be a simple introduction to the two frequency analyzers currently owned by GMI's Center for Acoustics, Noise, and Vibration. These analyzers are the Brüel & Kjær Dual Channel Real-time Frequency Analyzer Type 2133, and the Hewlett-Packard 35670A Dynamic Signal Analyzer. This lab will familiarize you with these analyzers so that you can use them effectively later, demonstrate a few of their features, and display some characteristics of signal analysis in the process. You will have opportunity to use these analyzers in future lab exercises, and you may wish to use them to take measurements for your project.
II. B&K 2133
The B&K Real-Time Frequency Analyzer Type 2133 uses a "recursive digital filter" process to process an input signal over a frequency range of 25Hz -- 20kHz in 1-, 1/3-, 1/12-, and 1/24-octave bands. Octave or 1/3 octave band analysis is used very widely in industry to gain information about the energy of noise or vibration contained in certain frequency ranges. Noise levels in acoustic environments, absorption coefficients of acoustic materials, and reverberation times examples of information which is listed according to octave or 1/3 octave frequency bands. In addition, the behavior of such a frequency-band analysis is in many ways similar to the way our ears process sound data.
The B&K Type 2133 Frequency Analyzer has many very interesting and useful features. Some of these we will use in future lab exercises. The goal of this laboratory is to familiarize you with the use of this analyzer, as well as to help you understand some characteristics of frequency band analysis. To help you become familiar with this analyzer you will analyze pink and white noise, and calibrate a microphone.
The front panel of the analyzer, and the retractible keyboard are shown below, with the more important buttons identified.
Octave Bands, Adding Levels, White and Pink Noise
If a broadband noise has a pressure level that independent of frequency (frequency spectrum is flat), the noise is termed white noise. This kind of noise is characterized as being rather sharp and "hissing." Another type of noise is pink noise, for which equal fractions of an octave contain the same power. The pressure level for pink noise decreases uniformly with increasing frequency with a slope of -3 dB / octave, while the power level for pink noise will be flat. Pink noise is characterized by a "hushing" sound that is less irritating than that of white noise.
A. Pink Noise
- Turn the Frequency Analyzer On.
- Start the Analyzer in its default state by pressing [Reset] [9] simultaneously. There appears to be a glitch in the analyzer, and every so often all of the LED lights on the analyzer front face and keyboard may light up. Just ignore it.
- Use the [Field Select] keys (up/down/left/right arrows) to navigate around the input fields on the screen. Use the [Field Entry] keys (up/down arrows) to change the entry in a highlighted field. A complete list of possible field entries may be obtained by pressing the [Menu] key. To get back to the graphic display, press the [Graph Format] key in the Display region of the keyboard.
- Use the [Field Selector] keys to go to the line just above the spectrum graph. This line should read something like: 97.0 dB re 20.0µPa RMS. Using the [Field Entry] keys, change the RMS field to PWR, so that the spectrum will show the power contained in each frequency band.
- Using the [Field Select] keys, navigate to the bottom half of the screen, to the line which begins: Ch.A : Preamp mV.. Highlight the field Preamp. Using the [Field Entry] keys, change the field entry Preamp to Direct.
- Using the [Field Select] keys move to the Generator field. Select a continuous "Cont." signal with a level of 0.0dB. Select Pink Random.
- Connect a BNC cable between the Generator Output (bottom of front panel) to the Channel A Direct Input.
- Turn on the Generator by pressing the [Generator] key on the upper front panel. A red LED should light up indicating that the generator is on.
- Tell the analyzer to calibrate itself to the input data by pressing the [Input Autorange] key on the keyboard. A red LED will light up while autoranging is in progress.
- Using the [Field Select] keys move to the line which begins "Bandwidth:". Set the bandwidth field to1/1 Oct.. Set the frequency range from 31.5 Hz to 16 kHz.
- Move down to the line beginning "Averaging" and set the averaging type to Exp. This gives an exponentially weighted recursive digital filter analysis which is as close as this analyzer comes to real time data processing.
- Begin collecting data by pressing the [Start] key on the Measurement area of the keyboard. You may have to press the [Autoscale] key to automatically adjust the
spectrum scale. The analyzer should now be analyzing a pink noise signal.
- You can have the analyzer take an average of collected data over a specified time interval by changing the "Averaging" field from [Exp] to [Lin]. Try a measurement with [Lin] and with [T: 8s].
- Press [Start] on the keyboard to take the average of 8 seconds of data.
- ⇒ What does the octave band power (PWR) spectrum of a pink noise signal look like?
- Press the [Cursor] key on the keyboard, and then use the [Field Entry] keys to move the cursor to check the levels of the various octave bands. The level is found at the upper right of the screen. The "X" locates the center frequency of the band, and the "Y" gives the level over that band.
- You can also press the [Table] key in the Display region of the keyboard to see a table showing the levels for each octave band.
- ⇒ Record the PWR levels for each octave band for the pink noise signal. Also include the overall "A" weighted level, and the "L" linear overall level. Include this data as a table (or a bar graph) in your report.
- ⇒ From this data, how does the PWR spectrum of in a pink noise signal
appear to vary with octave frequency bands? Does this match what you expect for a pink noise signal?
- Use the [Field Selector] keys to go to the line just above the spectrum graph, the line that reads something like: 97.0 dB re 20.0µV PWR. Highlight the PWR field, and use the [Field Entry] keys to change this field to PSD for Power Spectral Density. Now the analyzer will display power per unit frequency instead of power per frequency band.
- ⇒ How does the pink noise spectrum change? What is the slope (dB/octave) of the power spectral density display? Does this match what you expect for a pink noise signal?
- ⇒ Record the PSD value for each frequency band. You can use the [Cursor] and [Field Entry] keys to move the cursor, or press the [Table] key to obtain this data. Include this data in your report in an appropriately labelled table or plot.
B. White Noise
- Return to an PWR measurement by using the [Field Selector] keys to go to the line just above the spectrum graph, the line that reads something like: 97.0 dB re 20.0µV PSD Highlight thePSD field, and use the [Field Entry] keys to change this field to PWR.
- Use the [Field Selector] keys to go to the Generator line, and change the type of noise from Pink to White.
- [Start] a new 1/1 Octave measurement.
- ⇒ What does the Octave band PWR spectrum of a white noise signal look like?
- Press the [Cursor] key on the keyboard, and then use the [Field Entry] keys to move the cursor to check the levels of the various octave bands. You can also press the [Table] key in the Display region of the keyboard to see a table showing the levels for each octave band.
- ⇒ Record the PWR levels for each octave band for the white noise signal. Also include the overall "A" weighted level, and the "L" linear overall level. Include this data as a table (or a bar graph) in your report.
- ⇒ From this data, how does the PWR spectrum of in a white noise signal appear to vary with octave frequency bands? What is the slope (dB/octave) of the power spectrum for white noise? If each octave band contains twice as large a frequency range as the previous band, and the white noise power level in each successive frequency band is 3dB higher (double) than the previous band, how would you expect the power spectrum of a white noise signal to vary with linear frequency (not bands)?
- Press the [Graph Format] key to return to the graphical display.
- Change to PSD for Power Spectral Density.
- ⇒ How does the white noise spectrum change? The analyzer is now measuring the power per unit frequency. How does the power contained in a white noise signal vary with (linear) frequency? Does this agree with what you expect?
- ⇒ Record the power in each frequency band. You can use the [Cursor] and [Field Entry] keys to move the cursor, or press the [Table] key to obtain this data.
C. Octave Bands and Adding Levels
- Return fo the PWR spectrum for white noise.
- Using one of the three methods for adding decibel levels, add the levels from each octave band and see how your answer compares with the "L" linear overall level measured by the analyzer.
- For each octave band, convert the level to an A-weighted level using the corresponding A-weighted correction factors. Then add the A-weighted levels from each band and compare your answer with the overall "A" weighted level as measured by the analyzer.
- Press the [Graph Format] key to return to the graphical display.
- Change the bandwidth to 1/3 Octave, and [Start] a new measurement.
- Change the bandwidth to 1/12 Octave, and [Start] a new measurement.
- Change the bandwidth to 1/24 Octave, and [Start] a new measurement.
- ⇒ Is there any change in the spectra when a smaller bandwidth is used? What happens to the frequency range when you change to smaller bandwidths? Do the overall A and L levels change? Can you explain why the overall levels do or don't change?
D. Calibration of a Microphone
- Turn off the Generator by pressing the [Generator] key on the front panel
- Change the data type back to RMS.
- Disconnect the BNC cable from the Channel A Direct Input.
- Connect the B&K condenser microphone to the Preamp Input. This microphone is a capacitor microphone, and the B&K analyzer has a charge preamp to maintain a constant charge on the capacitor. Using this microphone with another analyzer would require the use of a preamp between the microphone and the analyzer. Please be careful with the microphone. \underbar{\it It is very sensitive, and quite expensive.}
- Use the [Field Selector] and [Field Entry] keys to change the Ch.A field entry from Direct V to Preamp mV. Once a new measurement is started, the field line just above the spectrum graph should read "dB re 20µPa".
- Insert the microphone into the B&K pistonphone. This pistonphone produces a constant 124 dB at 250 Hz. Switch the pistonphone to "On". You can check the battery by switching to "batt", but do not make a measurement at this position.
- Set the analyzer bandwidth to 1/1 Octave. Set the Averaging to Expand [Start] a measurement. Adjust the input range for the microphone by pressing [Input Autorange]. Press the [Autoscale] key if necessary to adjust the scale of the spectrum plot.
- Move the cursor to the 250 Hz octave band.
- Find the line which reads Ch.A Preamp mV 50.0mV/Pa. Highlight the field 50.0m. This field indicates the sensitivity of the microphone --- 50 mV of electrical output for one Pascal of pressure.
- Using the numeric keypad on the keyboard, change this value until the cursor reads "Y : 124.0 dB" or as close as you can get. For example, to enter 30.0mV you would press [3] [0] [m] [ENT] on the numeric keypad.
- ⇒ What is the sensitivity of the microphone for 124 dB at 250 Hz? Did you have to decrease or increase the number to get 124 dB? Why?
- Remove the microphone from the pistonphone, and turn the pistonphone off.
- Calibrate the Radio Shack Sound Level Meter \#33-2050 by inserting it into the pistonphone and reading the level. (You may have to remove the black plug from the pistonphone first.) Does the sound level meter read 124 dB? If not, how much is it off?
- Hold the microphone and the sound level meter parallel to each other, and near some noise source (connect the horn loudspeaker through the amplifier to the noise generator of the analyzer). Switch the sound level meter to "A" weighting, and "Slow" averaging.
- ⇒ Move the cursor on the analyzer all the way to the right to the spectral line labelled "A". This spectral line gives the A-weighted level for the input signal. What is the A-weighted sound pressure level recorded by the microphone on the analyzer?
- ⇒ What is the A-weighted sound pressure recorded by the Radio Shack sound level meter? What adjustment to the sound level meter reading, if any, is necessary to give a measurement which matches the B&K microphone? How does this adjustment compare with the sound level calibration result?
- When you are finished, disconnect the microphone from the Preamp Input of the analyzer, and turn the analyzer off.
III. HP 35670A
The Hewlett-Packard 35670A Dynamic Signal Analyzer is a digital frequency analyzer which samples a "chunk" of data (a time record) and then analyzes it via a Fast Fourier Transform algorithm. Depending on the length of the time record (or the desired range of frequencies) the data processing may be fast enough to appear real time. This analyzer may be used to analyze rotating machinery, structural vibration (including frequency response to transient impulse excitation), sound (including frequency bands), and to analyze control systems. In order to gain some familiarity with this analyzer you will investigate the problem of "leaking" and the effects of different windowing techniques, as well as observing the frequency content of several standard waveforms.
The front panel of the HP FFT analyze is shown in the figure on the below, with the more important buttons identified.
A. Leakage and Windows
- Connect the Signal output of the HP 33120A Waveform Generator to the Channel 1 input of the HP 35670A Analyzer with a BNC cable. Turn the generator and analyzer on. The waveform generator should power up with a 100 mV sine wave at 1000 Hz.
- Once the analyzer has come up in its default state, press the [System Utility] button (underneath screen), select [F2] Calibration, [F1] Auto Cal OFF. This will prevent the analyzer from autocalibrating itself every 5 minutes.
- Create a 2 panel display on the analyzer --- Display [Disp Format] [F3] "upper/lower"
- Select the upper trace to be active --- Display [Active Trace] [F1] "A"
- Select the upper trace to show the power spectrum for channel 1 --- Display [Meas Data] [F1] "Channel 1" - highlighted --- [F3] "Power Spectrum Channel 1"
- Select the lower trace to show the time signal for channel 1 --- Display [Active Trace] [F2] "B" --- Display [Meas Data] [F1] "Channel 1" --- [F5] "Time Channel 1"
- Select the frequency range for the measurement --- Measurement [Freq] [F1] "Span" --- use ⇑ and ⇓ keys on keypad to set frequency span to 12.8 kHz
- Set the trigger to channel 1 --- Measurement [Trigger] [F3] "Channel 1"
- Make the upper the trace active --- Display [Active Trace] [F1] "A"
- Move the marker (cursor) to the 1000Hz peak --- Marker [Marker] --- use the ⇑ and ⇓ keys or the marker knob to move the marker to the peak.
- ⇒ What is the frequency spacing Δf between adjacent marker positions? This frequency spacing equals the width of a "frequency bin" over which the analyzer performs an FFT on the time signal. How is this Δf related to the length of the time signal displayed in the lower trace? (the time length is located in the lower right corner of the screen)
- Change the FFT resolution --- Measurement [Frequency] [F9] "Resolution" and use the ⇑ and ⇓ keys to change the resolution to 200 and then to 800 lines.
- ⇒ How do Δf and the sample time change? Does the relationship between the two change or remain the same?
- Return to 400 lines of resolution.
- Adjust the waveform generator so that the frequency of the sine wave is 480 Hz.
- Select a Uniform window for the time record --- Measurement [Window] [F3] "Uniform"
- Move the cursor to the 480 Hz peak --- Marker [Marker] --- use the ⇑ and ⇓ keys or the marker knob to move the marker to the peak.
For a 0 to 12.8 kHz frequency range, with 400 frequency points of resolution, there is a frequency bin centered at 480 Hz.
- Change the frequency of the sine wave by 1 Hz increments from 480 Hz. to 512 Hz.
- ⇒ What happens to the frequency spectrum? Sketch (Plot?) the frequency spectrum for 481 Hz. There is not a frequency bin centered at 481 Hz; the closest bin is 480 Hz. Do you see any evidence that the 481 Hz signal "leaked" into the neighboring frequency bins? How might this "leakage" affect a measurement if a measured signal does not exactly match a frequency at which the analyzer can make an exact analysis?
- ⇒ Look carefully at the time record (you may want to change the active trace, and move the cursor across the time data, paying close attention to the phase at the beginning and the end of the signal) as you change the frequency. From the supplementary material handed out with the lab, can you explain why this leaking occurs?
- ⇒ Save to disk, for later plotting, the frequency spectrum for the 480 Hz signal and for the 481 Hz signal. (See the appendix for the steps to save data to a disk)
- Set the frequency of the sine wave back to 480 Hz.
- Change to a Hanning window --- Measurement [Window] [F1] Hanning.
- ⇒ Save to disk, for latter plotting, the frequency spectrum of the 480 Hz sine wave with a Hanning window.
- Change the frequency of the sine wave by 1 Hz increments.
- ⇒ What happens to the frequency spectrum? Save to disk, for latter plotting, the frequency spectrum for 481 Hz. How does the leakage with a Hanning window compare to that for a Uniform window? Which might be better for a measurement where several frequency components of a signal might not exactly match a frequency bin?
- Set the frequency of the sine wave back to 480 Hz.
- Change to a Flat Top window --- Measurement [Window] [F2] "Flat Top"
- ⇒ Save to disk the frequency spectrum of the 480 Hz sine wave with a Flat Top window. Include a plot of this spectrum in your report. How does this frequency spectrum compare to those for the Uniform and Hanning windows?
- ⇒ Change the frequency of the sine wave by 1 Hz increments. What happens to the frequency spectrum?
- Save to disk the frequency spectrum for 481 Hz. Include a plot of this spectrum in your report.
- ⇒ How does the leakage with a Flat Top window compare to that for Uniform and Hanning windows? What are some advantages and disadvantages of each type of window? Can you think of a possible drawback to using a Flat Top window when you are able to match the signal frequency to a frequency bin? (compare spectra for the three windows at 480Hz and 481Hz)
B. Frequency Spectra for Different Waveforms
- Set the sine frequency back to 480 Hz.
- Change the wave type to a square wave, and observe the frequency spectrum. If you wish you can save both the frequency spectrum and the time signal to disk for inclusion in your report. (Be sure to set the active trace to be the data you want to save)
- Try increasing the frequency to 481Hz and changing the window type --- this may help you see how some frequency peaks may be hidden by the leakage effect. Reset the frequency to 480Hz.
- Add Harmonic markers to the cursor --- Marker [Marker Fnct] [F2] "Harmonic Marker" [F1] "Fundamental Frequency" [F1] --- enter the fundamental frequency (480) from the keypad --- press [F2] for "Hz".
- There should now be little arrows above each peak in the frequency spectrum. If you move the cursor (marker) from peak to peak you will see that each peak above 480 Hz is an integer multiple of 480. This harmonic cursor is useful for identifying harmonics in a signal, or for order tracking analysis.
- Change the wave type to a triangle save, and a sawtooth wave ("burst"), and observe the different wave shapes and the different spectra. Again, you can save data to disk for including plots in your report.
- What similarities or differences in frequency spectra can you observe for square, triangle, and sawtooth waves?
- Change the wave type to noise, and observe the time signal and frequency spectra.
- ⇒ From your work with the B&K frequency analyzer, would you classify this noise as "white" or "pink"? Why?
- When you are finished, disconnect the cables, and turn the analyzer and generator off.
IV. References
- R. B. Randall, Frequency Analysis, 3rd Edition, (Brüel & Kjær, 1987).
- R. B. Randall, Chapter 13 of Shock & Vibration Handbook, Third Edition, C. M. Harris, Ed., (McGraw-Hill, 1988).
- Manuals for the B&K and HP analyzers.
Appendix: Saving Data to Disk from HP Analyzer
- Insert a floppy disk (DOS format) into the disk drive. If the disk is not formatted you will have to format it --- Press [Disk Utility]; [F?] "Format Disk"
- If you are taking a continuous measurement, [Pause] the measurement
- Set the active trace to correspond to the data you want to save. If you want to save the frequency information in the top trace A, then set the active trace to A --- Measurement [Active Trace], [F1] "A". To save the time data in trace B, do the same thing only for trace B.
- Press [Save/Recall] under the screen
- [F1] "Save Data"
- [F1] "Save Trace" --- save data in ASCII format (not SDF)
- [F9] "Into File" --- type file name {\it filename}{\tt .txt} and press [F1] "Enter"
- Press [Start] to begin the next measurement
- Four files will be written to the disk:
- filename.txt --- contains the amplitude values for each frequency bin
- filename.x --- contains the frequency of each frequency bin
- filename.z --- contains the range of values on the vertical axis
- filename.hdr --- contains header and screen information
- To plot the data using a spreadsheet (like Excel) you can import the
filename.x file as the horizontal data and the filename.txt file as the vertical data. This will result in a plot of amplitude versus frequency. You may have to use a log scale on the vertical axis to make the data look like it did on the analyzer.
V. Sample Student Data
This laboratory exercise has been used very successfully in a rather popular senior level course, "PHYS-580/ME-530, Acoustics, Noise, and Vibration," which serves as an elective for Mechanical Engineering, Electrical Engineering, and Applied Physics majors at GMI Engineering & Management Institute. Students investigate the phenomenon of "leakage" and investigate the usage of windows to minimize leakage. The plot below shows data taken by students.
1/1 Octave Power Spectrum of Pink and White Noise
1/1 Octave Power Spectral Density of Pink and White Noise
Leakage from a Uniform Window for 480Hz and 481 Hz signals (FFT bin at 480 Hz)
Leakage from a Hanning Window for 480Hz and 481 Hz signals (FFT bin at 480 Hz)
Leakage from a Flat-Top Window for 480Hz and 481 Hz signals (FFT bin at 480 Hz)
