ROSE HULMAN INSTITUTE OF TECHNOLOGY Department of Electrical and Computer Engineering ECE 300 Signals and Systems Spring 2006 Basic Signal Spectra Lab 6 by Bruce A Ferguson Objectives To become familiar with the signal spectrum as a means to represent and analyze signals To become acquainted with the various tools available for viewing the signal spectrum Equipment Agilent 4402B Spectrum Analyzer Agilent Function Generator Oscilloscope BNC T Connector Background In the previous lab we learned to view the Fourier Series representation of a signal in the frequency domain using a spectrum analyzer We called this display of signal power vs frequency the power spectrum of the signal There are several tools available for viewing the spectrum of the signal which is what we call the display of signal voltage magnitude magnitude spectrum or phase phase spectrum versus frequency In this lab we will combine several of these tools to confirm our understanding of what a signal spectrum tells us about a signal The FFT or Fast Fourier Transform is an estimate of the signal spectrum computed using an algorithm based on the concept of the Fourier Series Technically the FFT is not the same as the Fourier Transform Often however we accept the fft output as a display of the signal s true spectrum although care must be taken that the fft algorithm is set up properly and that it displays results in the units we expect Since those details will be covered in ECE 380 we will focus today on the use of the fft as a means of displaying the signal spectrum and not worry so much about the finer points of its calculation and interpretation Recall that the power spectrum of a periodic signal was found by creating a two sided spectrum with the height of each spectral component equal to the square of the corresponding ak A one sided spectrum was then created by displaying only DC and positive frequencies and doubling the power of each positive frequency component i e 2 ak 2 The same can be done using the FFT of a signal We will be focusing on one sided spectra throughout this lab There is no Prelab for this Lab Page 1 of 3 ECE 300 Signals and Systems Spring 2006 Procedure Visualizing Signal Spectra 1 Calculate the Fourier series coefficients ak k 0 1 2 9 for the signal x1 t 0 2 cos 2 1 106 t V Draw the one sided power spectrum for this signal properly labeled and with correct units indicated The height or level of each spectral component line should be given in both Watts and dBmV 2 Using one of the function generators produce the signal x1 t Display this signal on the oscilloscope and discuss how perfect this sinusoidal waveform is e g are there any features of the waveform which deviate from that expected for a sinusoid Include your display data and comments in your lab notebook Be sure to verify that the signal has proper amplitude offset and frequency 3 Display the signal spectrum for the signal x1 t on the spectrum analyzer Sketch the spectrum in your lab notebook and compare your results to those predicted in the by hand analysis Are there any deviations from what you expect Try setting the reference level to 30 dBmV and the displayed frequency span to 2 3 MHz a If there are deviations of what power level are they in dBmVs b Explain the presence of these anomalous spectral features c Would you consider the deviations harmonics Explain 4 Now vary the amplitude and frequency of x1 t noting the changes in the spectrum in your lab notebook Use precise and accurate language to describe what you see A picture of how to visualize the spectrum of a simple sinusoid should be growing in your mind Using the MATLAB FFT Tools to View Signal Spectra 5 Write a Matlab script to use the provided MATLAB function baf fft m to display the two sided magnitude spectrum of x1 t View the comment lines in the m file to understand the correct usage of the function Simulate the waveform x1 t for 16 periods using 32 samples per period 6 Write a MATLAB function to display a one sided power spectrum given the two sided spectrum calculated by the baf fft m function The level of the terms should be expressed in dBmV Include a call to this function in the script you produced in Step 5 Compare these results to what you measured from the spectrum analyzer in Step 2 Produce a display of the signal power spectrum and include it in your notebook Using the Oscilloscope FFT Tool to View Signal Spectra 7 Use the oscilloscope s built in fft capability to examine the signal spectrum Include a screen capture of the spectral display in your lab notebook specifically indicating that the results match those obtained using the other methods in the previous steps Note that this display is not a power spectrum but rather is a one sided magnitude spectrum a Display the signal on Channel 1 and press autoscale to produce a convenient display All other channel displays should be off Page 2 of 3 ECE 300 Signals and Systems Spring 2006 b Press the math button beside the Channel 1 button This gives access to various math functions available built in to the scope Select FFT to activate the scope s built in FFT feature c When you press the FFT button a second curve will appear on the display It will not be recognizable because the FFT settings are not yet optimized for our signal Press the Settings button to change the FFT display Set the span to 5 MHz This is the range of frequencies which will be displayed on the screen Set the center frequency to 2 5 MHz This defines the frequency of the center of the screen Given this information you should be able to determine the frequencies of any spectral component on the screen d Next adjust the display to be able to read the dBV level of the signal Set the scale to10 dB div vertical The 0 dBV reference level is the center horizontal line of the screen note the change in units The offset moves the signal spectrum up or down relative to the reference level If the offset is adjusted so that the peak of the spectral component of interests touches the reference level line the offset value is equal to the spectral component level in dBV think about this e The final setting to be adjusted is the sampling rate This is set by turning the horizontal time display knob Turn the horizontal display knob until the sampling rate is 10 Msamples sec You may have to readjust the center frequency and span after adjusting the sample rate The time display of the waveform may be less recognizable as a sinusoid but the spectrum is correctly
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