Help Topics

Aliasing

Additional Resources Aliasing by Justin Romberg and Don Johnson Signal Processing Firstby McClellan, Schafer, & Yoder - Section 4-2.3 (page 81) Fundamentals of Signals and Systems by Kamen & Heck - Section 5.5 (page 236) Signal Processing and Linear Systems by Lathi - Section 5.3 (page 557)

Simulator Practice Change the Frequency of the Signal to be Acquired spin box to 10 Hz. Set the Sampling Frequency slider to a high value. Notice the sampled signal more closely matches the original as sampling rate increases. Set the Sampling Frequency slider to a low value. Notice the Aliasing LED will turn bright green to indicate that aliasing is present. Change the Sampling Frequency slider and try to obtain 0.5, 1, 1.5, 2, and 2.5 in the Sampling Frequency / Signal Frequency indicator. Observe the changes in the plots.

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Amplitude & Power Spectrum

Additional Resources A Signal's Spectrum by Don Johnson

Simulator Practice Select different wave types and frequencies. Compare the plots.

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Amplitude Modulation

Additional Resources Amplitude Modulation by Don Johnson Signal Processing First by McClellan, Schafer, & Yoder - Section 3-2.3 (page 41) - Section 12-2 (page 358) Fundamentals of Signals and Systems by Kamen & Heck - Section 6.1 (page 252) Signal Processing and Linear Systems by Lathi - Section 4.7-2 (page 282)

Simulator Practice Set the Frequency of Tone slider to 0 Hz and the Frequency of Carrier slider to 50 Hz. Gradually increase the Frequency of Tone slider. Notice how the modulated signal changes. Set the Frequency of Tone slider to 10 Hz and gradually increase and decrease the frequency of the carrier signal. Increase the Modulation Factor slider and observe the amplitude of the signal in the time and frequency domains.

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Autocorrelation

Additional Resources Autocorrelation of Random Processes by Michael Haag Signal Processing and Linear Systems by Lathi - Section 3.2-2 (page 182)

Simulator Practice Set the Noise Amplitude slider to 0 and change the Frequency slider. The Autocorrelation graph displays a clean autocorrelation plot for the respective frequency. Gradually increase the Noise Amplitude slider and observe the changes to the Autocorrelation graph. Try different signals, frequencies, and noise amplitudes. Compare the differences between the autocorrelation plots.

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Bits and Resolution

Additional Resources Bits Resolution

Simulator Practice Set the A/D Conversion Bits slider to 3. Notice the distortion of the acquired sine wave. Change the A/D Conversion Bits slider to a higher value. Notice the resolution of the acquired sine wave is much higher.

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Cepstrum

Additional Resources Cepstrum

Simulator Practice Select different signal frequencies. Compare the plots.

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Clipping

Additional Resources Saturation (Electronics)

Simulator Practice Set the Clipping Level slider to the highest position. Change the Frequency slider. Notice only the input frequency appears in the Frequency Spectrum plot. Gradually decrease the Clipping Level slider. Notice that clipping occurs in the Signal plot. Also notice that there are several harmonics in the Frequency Spectrum plot.

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Constant Percentage Bandwidth Filter

Additional Resources Not available at this time.

Simulator Practice Set the Bandwidth % spin box to 3%. Run an execution cycle and compare the response of both techniques in low and high frequencies using the zoom tool. Change the Bandwidth % spin box to higher and lower values between the range of 0.5 to 23.0% and compare the responses, running a few cycles. Set the Bandwidth % spin box to 0.622%. This obtains the same number of lines as constant bandwidth spectrum (512). Again compare the plots.

More information on constant percentage bandwidth filters Until recently, frequency analyzers had two problems when calculating a spectrum using the Fourier transform (FT). First, the digital processors embedded in frequency analyzers were too slow. Second, the algorithm for calculating the FT was not efficient. Due to this analyzers used analog filters to calculate spectra. Analyzers used two kinds of filters—the constant absolute bandwidth filter and the constant relative (percentage) bandwidth filter. Both are bandpass filters. The difference is that the constant absolute bandwidth filter provides uniform resolution and separation on a linear frequency scale and the constant relative (percentage) bandwidth filter provides uniform resolution on a logarithmic frequency scale.

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Convolution Frequency Domain

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder - Section 11-6.2 (page 327) Fundamentals of Signals and Systems by Kamen & Heck - Section 4.4 (page 186) Signal Processing and Linear Systems by Lathi - Section 4.3-6 (page 263)

Simulator Practice Select Square from the Signal Y Type pull-down menu. Now change the Signal Y Frequency slider to different values. Notice how the Convolution window varies with frequency. Select different values from the Signal Y Type pull-down menu. Compare the different Convolution X * Y plots you obtain when using different signal types.

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Convolution Time Domain

Additional Resources Graphical Convolution Algorithm by Richard Baraniuk Signal Processing First by McClellan, Schafer, & Yoder - Section 5-6.1 (page 118) Fundamentals of Signals and Systems by Kamen & Heck - Section 4.4 (page 186) Signal Processing and Linear Systems by Lathi - Section 2.4-1 (page 120)

Simulator Practice Using the spin boxes, select a delta function for both Signal X Type and Signal Y Type. Notice the signals are displayed in both the Signal X and Signal Y plots. Using the slider, slowly move the Convolution Slide to the right. The Signals to Convolve plot shows the sliding of Signal Y, which is flipped horizontally, across Signal X. Notice that the Convolution (X*Y) plot is 0 until there is overlap of the signals in the Signals to Convolve plot. Once there is overlap, the result of the convolution is nonzero. You may view this result in the Convolution (X*Y) plot. Using the slider, move the Convolution Slide back to the far left. Repeat steps 1 and 2 with different combinations of signals.

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Crosscorrelation

Additional Resources Crosscorrelation of Random Processes by Michael Haag Signal Processing and Linear Systems by Lathi -Section 3.2 (page 177)

Simulator Practice Set the frequency of each signal to the same value. Notice that the Crosscorrelation plot displays a clear waveform. Change the input signal type for each signal and notice how the Crosscorrelation plot continues to display a clear waveform. Add noise to the signals and notice how the crosscorrelation eliminates it. Change the frequency of Signal 1 gradually. Observe the Crosscorrelation plot. Select different kinds of signals with different frequencies and observe the results in the Crosscorrelation plot.

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Deconvolution

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 7-5.3 (page 175)

Simulator Practice Select Square from the Original Signal X spin box. Select Hanning from the Weight Y spin box. Observe how the signal in the Acquired Signal (Convolution X * Y) plot has rounded edges. This is due to the weight function. Notice the deconvolved signal in the Deconvolved Signal X plot is squared again. Try different signals and frequencies and observe how well deconvolution works in each case.

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Delta Function

Additional Resources Useful Signals by Melissa Selik and Richard Baraniuk Signal Processing First by McClellan, Schafer, & Yoder -Section 5-3.2.1 (page 107) Fundamentals of Signals and Systems by Kamen & Heck -Section 1.3 (page 20) Signal Processing and Linear Systems by Lathi -Section 2.3 (page 115)

Simulator Practice Set the Delay When Cycling Through Frequencies dial to a high value so that the plots can be easily observed. Notice that no matter where the delta function is located, the frequency spectrum remains the same. Watch the 3D plots. The point representation displays the vector ending points. The vector representation displays the entire vectors. Click the Pause button to pause the execution of the simulator. Use the zoom tool to view different sections of the plots in detail.

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Even & Odd Signals

Additional Resources Even and Odd Signals by Harika Basana Signal Processing First by McClellan, Schafer, & Yoder -Section 2-2 (page 10) Fundamentals of Signals and Systems by Kamen & Heck -Section 4.3 (page 172) Signal Processing and Linear Systems by Lathi -Section 1.5 (page 75)

Simulator Practice Set the Phase slider to 90° and –90° to obtain even functions. Change the Phase slider to 0° and 180° to obtain odd functions. Compare the plots.

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FFT 2-D

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Chapter 11 (page 307) Fundamentals of Signals and Systems by Kamen & Heck -Section 4.3 (page 181) Signal Processing and Linear Systems by Lathi -Chapter 4 (page 235)

Simulator Practice Select different values using the width and delay sliders for the two-dimensional square function. Observe the Magnitude of 2D FFT plot. Set both the Width X and Width Y sliders to 1. Can you determine what happened with the Magnitude of 2D FFT plot? (Clue: Delta function).

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FFT Bandwidth References Signal Processing First by McClellan, Schafer, & Yoder -Section 11-4.1.1 (page 173) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.3 (page 173)

Simulator Practice Select different values in the FFT Size spin box and compare the plots. Notice that the lower the FFT Size, the lower the resolution. Reduce the execution speed using the Seconds to Wait slider or the Pause button to analyze the plots. Use the zoom tools to examine specific frequencies in the spectra.

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FFT Even & Odd

Additional Resources Symmetry Properties of the Fourier Series by Justin Romberg Signal Processing First by McClellan, Schafer, & Yoder -Section 11-5.2 (page 325) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.3 (page 172) Signal Processing and Linear Systems by Lathi-Section 3.5 (page 213)

Simulator Practice Change the Real Part of Signal and Imaginary Part of Signal spin boxes. Notice the type of signal composed of the parts you selected. Compare the plots of the different types of signals.

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FFT Linearity

Additional Resources Fourier Series Properties by Justin Romberg and Benjamin Fite Signal Processing First by McClellan, Schafer, & Yoder -Section 11-4.5 (page 318) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 175) Signal Processing and Linear Systems by Lathi-Section 4.1 (page 240)

Simulator Practice Using the Frequency of Signal 1 and Frequency of Signal 2 sliders, select different frequency values for Signal 1 and Signal 2. Compare the frequency spectra plots. Using the Frequency of Signal 1 and Frequency of Signal 2 sliders, set equal frequency values for Signal 1 and Signal 2. Observe how the amplitude of the combined signals is double the frequency spectrum of the original signals.

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FFT Time Scaling

Additional Resources Properties of the Continuous-Time Fourier Transform by Melissa Selik and Richard Baraniuk Signal Processing First by McClellan, Schafer, & Yoder -Section 11-5.1 (page 322) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 177) Signal Processing and Linear Systems by Lathi-Section 4.3-3 (page 255)

Simulator Practice Gradually increase the width of the sine wave cycle using the Impulse Width slider. For example, gradually change the Impulse Width slider from 10 to 128. Observe the changes in the frequency spectra. Use the zoom tools to analyze the plots in further detail.

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FFT Time Shifting

Additional Resources Fourier Series Properties by Justin Romberg and Benjamin Fite Signal Processing First by McClellan, Schafer, & Yoder -Section 11-7.1 (page 332) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 176) Signal Processing and Linear Systems by Lathi-Section 4.3-4 (page 257)

Simulator Practice Select different values using the Phase slider. Observe the effect on the real and imaginary components of the signal in the Frequency Spectrum plot. Try selecting phase values of 0°, 45°, 90°, -90°, and 180° in the Phase slider. Now select different frequency values using the Frequency slider. Notice the effect on the real and imaginary components of the signal.

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FIR (Finite Impulse Response) Windowed Filter

Additional Resources Filter Design by Windowing by Hyeokho Choi Signal Processing First by McClellan, Schafer, & Yoder -Section 5-3 (page 105) Fundamentals of Signals and Systems by Kamen & Heck-Section 12.4 (page 639) Signal Processing and Linear Systems by Lathi-Section 4.9 (page 300)

Simulator Practice For the same type of filter, change the value of the Low Frequency Cutoff and High Frequency Cutoff sliders and observe the behavior. Keeping all else constant, change the Window spin box to different window types. Notice the effect the different windows have on the Frequency Spectra and Phase Spectra plots. Keeping the window constant, change the value of the Taps spin box. Notice that the number of poles increases when the number of taps are increased and vice versa. Compare the Frequency Spectra plots in both linear and logarithmic scales by switching the Magnitude Display.

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Filter Response Time

Additional Resources Not available at this time.

Simulator Practice Select different filter types using the Type spin box. Vary the value of the cutoff frequencies by changing the Lower Cutoff Frequency and Upper Cutoff Frequency sliders. Observe the filter response. Compare the filter responses when different filter orders are selected.

More help on filter response time Every filter, regardless of type or characteristics, requires time to respond when a signal is passed through it. This is necessary because of the need to perform calculations over the input signal in order to do the filtering. During this response time, the filter output contains errors. These errors gradually disappear until the expected response is achieved.

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Frequency Domain Averaging

Additional Resources Frequency Spectrum

Simulator Practice Set the Noise slider to 10. Select different values in the Number of Averages spin box. Notice that fewer averages produces a large difference between the Frequency Spectrum and Averaged Frequency Spectrum plots. Change the Noise slider again. Notice the variation in the Averaged Frequency Spectrum plot.

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Frequency Modulation

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 3-8 (page 61) Fundamentals of Signals and Systems by Kamen & Heck-Section 6.1 (page 257) Signal Processing and Linear Systems by Lathi-Section 4.8 (page 289)

Simulator Practice Set the Frequency of Tone slider to 10 Hz, the Frequency of Carrier slider to 60 Hz, and the Modulation Index slider to 0.50. Gradually change the Frequency of Carrier slider to different values. Notice the change in the Frequency Spectrum plot. Select different values for the Modulation Index slider. Compare the plots obtained. Select different values for the Frequency of Tone slider. Again, compare the plots obtained.

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Frequency Shift

Additional Resources Amplitude Modulation by Don Johnson Signal Processing Firstby McClellan, Schafer, & Yoder -Section 12-2 (page 358) Fundamentals of Signals and Systems by Kamen & Heck-Section 6.1 (page 252) Signal Processing and Linear Systems by Lathi-Section 4.7 (page 277)

Simulator Practice Set the Signal 1 Frequency slider to 100 Hz. Set the Signal 2 Frequency slider to 0 Hz. Notice that only Signal 1 is shown in the Signal 1 x Signal 2 and Frequency Spectrum (Signal 1 x Signal 2) plots. Gradually increase the Signal 2 Frequency slider and observe the Signal 1 x Signal 2 and the Frequency Spectrum (Signal 1 x Signal 2) plots.

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IIR (Infinite Impulse Response) Filter Design

Additional Resources IIR Filtering: Introduction by Douglas Jones, et al. Signal Processing First by McClellan, Schafer, & Yoder -Chapter 8 (page 196) Fundamentals of Signals and Systems by Kamen & Heck-Section 12.2 (page 618)

Simulator Practice Keeping all other settings the same, compare different filter designs. For the same filter design, change the Order spin box and observe the behavior. Using the Sideband Attenuation slider, select different filter attenuations and compare the responses. Switch the Magnitude Display and between the Linear and Logarithmic scales and observe the differences.

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Leakage

Additional Resources Fundamentals of Signals and Systems by Kamen & Heck-Section 7.2 (page 319) Signal Processing and Linear Systems by Lathi-Section 4.9 (page 302)

Simulator Practice Set the Frequency slider to 10. Notice that there is no jump in the Signal Sampled plot and the Frequency Spectrum is a single line. Slowly decrease the Frequency slider. Notice the jump in the Signal Sampled plot and the change in the Frequency Spectrum plot. Change the Phase slider and notice its effect on the plots.

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Linear & Log Frequency Scales

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 10-1.1 (page 288) Fundamentals of Signals and Systems by Kamen & Heck-Section 9.5 (page 475) Signal Processing and Linear Systems by Lathi-Section 7.2 (page 477)

Simulator Practice Compare the Linear Frequency Plot and the Logarithmic Frequency Plot. Using the zoom tool, better examine the higher and lower frequencies.

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Lowpass Filter

Additional Resources Filter Types by Anders Gjendemsjo Signal Processing First by McClellan, Schafer, & Yoder -Section 10-3.2 (page 296) Fundamentals of Signals and Systems by Kamen & Heck-Section 5.4 (page 223) Signal Processing and Linear Systems by Lathi-Section 7.4-2 (page 500)

Simulator Practice Set the Signal Frequency slider to 5 Hz. Start with a low value for the Noise Amplitude slider. Gradually increase the slider and notice the effect on the original signal. Change the Lowpass Filter Frequency slider to 0 Hz, 5 Hz, 10 Hz, 15 Hz, and 20 Hz. Observe the filtered signal in the time and frequency domains.

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Median Filter

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 5-2 (page 102)

Simulator Practice Set the Pulse Amplitude slider to 10 and the Pulse Width slider to 15. Observe the estimated parameters of Amplitude, Width, and Delay. Set the Noise Level slider to 0, 1, and 2. Observe how it affects the original signal (green signal) and the estimated parameters of Amplitude, Width, and Delay. Set the Filter Rank slider to 1, 5, 10, 15, and 20. Observe the change in the filtered signal (red signal) and the estimated parameters of Amplitude, Width, and Delay.

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Orbits

Additional Resources Not available at this time.

Simulator Practice Set the Vibration Frequency slider to 1000 Hz. This will result in a Vibration Frequency / RPM of 1, because the object is vibrating at the same frequency as its rotation speed, which causes a circle in the plot. Gradually increase and decrease the value in the Vibration Frequency slider. Observe the changes in the plot. For a complete orbit, set the Vibration Frequency / RPM to an integer value.

More information on orbits The pattern formed by graphing the x and y coordinates of a point on a rotating object is an orbit. Orbits are commonly used in the alignment of rotating shafts.

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Parseval's Theorem

Additional Resources Parseval's Theorem by Don Johnson Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 187) Signal Processing and Linear Systems by Lathi-Section 4.6 (page 275)

Simulator Practice Allow the simulator to run for a few seconds. Observe Parseval's Theorem and notice that the two values are equal. Click the Pause button to examine the simulation in more detail. Change the Frequency slider and Input Signal spin box. Notice that these changes have no effect Parseval's Theorem. The two values are still equal.

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Phase In Time & Frequency

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Chapter 11 (page 307) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.3 (page 181) Signal Processing and Linear Systems by Lathi-Chapter 4 (page 235)

Simulator Practice Set the Frequency of Sine 1 slider to 2 Hz and the Frequency of Sine 2 slider to 4 Hz. Move the Phase of Sine 1 slider to different values and observe the plots. Now set the Frequency of Sine 1 slider equal to the Frequency of Sine 2 slider. If the frequencies are equal, the Sum of Signals plot should be a sine wave. Set the Phase of Sine 1 slider to 0. Notice that the amplitude in the Frequency Spectrum plot greatly increases. Now select different values for the Phase of Sine 1 slider and observe the plots. Notice that the sine waves cancel each other out due to deconstructive interference when Phase of Sine 1 is 180°.

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Picket Fence Effect

Additional Resources Signal Processing and Linear Systems by Lathi-Section 5.2 (page 340)

Simulator Practice Set the Window spin box to None. Change the Frequency slider and observe the plots and Line Magnitude indicators. Compare the 100 Hz and 101 Hz peak amplitudes when the frequency is near to 100 Hz, 100.5 Hz, and 101 Hz. Move the Phase slider and observe how it affects the plots. Repeat steps 1 through 3 selecting different windows in the Windows spin box. Set the Frequency slider to 100 Hz and the Window spin box to None. Observe the single large pulse at 100 Hz in the Enhanced Frequency Spectrum plot. Now change the Window spin box, and observe the noise introduced because of the equivalent noise bandwidth value of that window.

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RMS – Peak

Additional Resources RMS

Simulator Practice Set the Signal spin box to Gaussian Noise. Click the Pause button to pause the execution and analyze the parameters of the signal. Change the Signal spin box and observe the parameters of different signals.

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Resonance

Additional Resources Fundamentals of Signals and Systems by Kamen & Heck-Section 9.5 (page 472)

Simulator Practice Select different values for C/Cc. Observe the plots.

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Riding and Beating

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 3-2.2 (page 40)

Simulator Practice Set the Frequency Signal 1 slider to 30 Hz, the Frequency Signal 2 slider to 35 Hz, and both the Amplitude Signal 1 and Amplitude Signal 2 sliders to 1. Observe the beating affect in the Signal 1 + Signal 2 plot. Set the Frequency Signal 1 slider to 5 Hz, the Amplitude Signal 1 slider to 1, the Frequency Signal 2 slider to 40 Hz, and the Amplitude Signal 2 slider to 0.5. Observe the riding affect in the Signal 1 + Signal 2 plot.

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Signal Differentiation

Additional Resources Properties of the Continuous-Time Fourier Transform by Melissa Selik and Richard Baraniuk Signal Processing First by McClellan, Schafer, & Yoder -Section 11-7.2 (page 333) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 183) Signal Processing and Linear Systems by Lathi-Section 4.3-7 (page 264)

Simulator Practice Click the Pause button to pause the execution. Use the zoom tools to compare the random and differentiated signal plots. Resume the simulation and repeat step 1 for different signal types.

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Signal Integration

Additional Resources Fundamentals of Signals and Systems by Kamen & Heck-Section 4.4 (page 184) Signal Processing and Linear Systems by Lathi-Section 4.3-7 (page 264)

Simulator Practice Click the Pause button to pause the execution. Use the zoom tools to compare the random and integrated signal plots. Resume the simulation and repeat step 1 for different signal types.

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Single Pole Lowpass Filter

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 5-4.2 (page 111) Signal Processing and Linear Systems by Lathi-Section 6.7 (page 426)

Simulator Practice Set the Input Signal Frequency slider to 10 Hz. Notice that the simulation computes 500 samples and then updates the Signal In plot based on the value of the Input Signal Frequency slider. Therefore, when the Input Signal Frequency slider is changed, there is a delay before the Signal In plot updates. Change the value of Constant A to 0.1. Observe how the value of Constant A changes the value of Constant B. Change Constant A to 0.001, 0.010, 0.1 and 1. Observe the change in Output. Set the Input Signal Frequency slider to 20 Hz, 30 Hz, 40 Hz, and 50 Hz. Observe the change in Output. Turn on Step by step. Using the Next button, analyze the values of the filter at each step.

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Square & Sinc Functions

Additional Resources Square Pulse / Box Car / Unit Gate / Square Window by Richard Baraniuk Signal Processing First by McClellan, Schafer, & Yoder -Section 11-4.2 (page 315) Fundamentals of Signals and Systems by Kamen & Heck-Section 4.3 (page 166) Signal Processing and Linear Systems by Lathi-Section 4.2 (page 246)

Simulator Practice Toggle between the Square and Sinc functions. Observe the Time Domain and Frequency Domain plots for both. Modify the width of the functions by changing the Width slider. Observe the plots.

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Stroboscope

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 4-3 (page 84)

Simulator Practice Set the Strobe Frequency and Bar Rotation sliders to 50. The bar remains still because the strobe and the bar are at the same speed. Using the Strobe Frequency slider, select different strobe frequencies. For example, select 49 Hz, 51 Hz, 25 Hz, and 100 Hz. Compare the behavior of the bar. Can you explain why there are two images of the bar at a Strobe Frequency value of 100 Hz?

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Time & Frequency Resolution

Additional Resources Aliasing by Justin Romberg and Don Johnson Signal Processing First by McClellan, Schafer, & Yoder -Section 4-2.3 (page 81) Fundamentals of Signals and Systems by Kamen & Heck-Section 5.5 (page 236) Signal Processing and Linear Systems by Lathi-Section 5.3 (page 557)

Simulator Practice Click the Pause button to pause the execution of the simulation in order to better observe the plots. Use the zoom tools to further compare the plots in the time and frequency domains. Which sampling rate has better resolution in the time domain? Which sampling rate is better in the frequency domain?

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Time Domain Average Noise

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder - Section 5-2 (page 102)

Simulator Practice Set the Number of Averages slider to 1. Click the Run Cycle button. Compare the Signal + Noise plot with the Average (Signal + Noise) plot. Also compare the Spectrum (Signal + Noise) plot with the Spectrum of Average (Signal + Noise) plot. Gradually increment the the Number of Averages slider and repeat steps 2 and 3. Select different frequencies using the Signal Frequency slider and repeat steps 1 to 4.

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Time Domain Averaging - Out-of-Phase Signals

Additional Resources Averaging

Simulator Practice Set the Signal Frequency slider to 10 Hz, the Number of Averages slider to 30, and the Delay in Seconds slider to 0.2 s. Click the Run Cycle button and watch the plots. Notice that the disturbing signal (orange) disappears from the plots while the averaging process runs. The disturbing signal's frequency is 25.6 Hz. Use a close Signal Frequency (27 Hz) in order to observe the beating effect and how it disappears as a result of averaging.

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Total Harmonic Distortion

Additional Resources Total Harmonic Distortion (THD)

Simulator Practice Set the Signal Frequency slider to an integer value, the Noise Amplitude slider to 0, and the Clipping Level slider to its upper position. Observe the plots, %THD, and %THD + Noise. Add noise, clipping, and fractional fundamental frequencies. Compare the plots, %THD, and %THD + Noise.

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Transfer Functions

Additional Resources Transfer Functions by Don Johnson Fundamentals of Signals and Systems by Kamen & Heck-Section 8.4 (page 395) Signal Processing and Linear Systems by Lathi-Section 2.4-3 (page 138)

Simulator Practice Select different values for Input Signal and Output Signal using the spin boxes. For each signal combination, observe the differences in the Transfer Function plot.

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Transients and Windows

Additional Resources Transient

Simulator Practice Set Window Type to None and select different transient signal frequencies. Select different windows and observe how each window affects the transient signal. Pay careful attention to the Transient x Window and Frequency Spectrum plots.

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Transmissibility

Additional Resources Transmissibility

Simulator Practice Select different values for C/Cc. Observe the plot.

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Waves & Spectra

Additional Resources Fundamentals of Signals and Systems by Kamen & Heck-Section 9.5 (page 465) Signal Processing and Linear Systems by Lathi-Section 7.2 (page 477)

Simulator Practice Using different signals, frequencies, and phase values, compare the plots. Set the Frequency slider to a non-integer number of cycles. The drop observed in the Frequency Spectrum plot is due to the leakage effect. Change the Phase slider. Observe the effect this has on the Phase Spectrum plot.

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Window Amplitude

Additional Resources Signal Processing First by McClellan, Schafer, & Yoder -Section 13-3 (page 393)-Section 13-4 (page 397) Fundamentals of Signals and Systems by Kamen & Heck-Section 12.4 (page 639) Signal Processing and Linear Systems by Lathi-Section 12.8-1 (page 762)

Simulator Practice Set the Fine Frequency slider to 0 Hz and set the Window spin box to None. Setting the Fine Frequency slider to 0 Hz avoids leakage. Increase the Fine Frequency slider and notice the decrease in the Amplitude. Select different window types in the Window spin box. Compare Amplitude and % Error.

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Window Comparison

Simulator Practice Select different characteristics for the amplitude and frequency of the two signals. Select different pairs of windows and compare both their amplitude and resolution. Try signals with leakage (non-integer frequencies) and without leakage (integer frequencies). Set the Signal 1 Frequency and Signal 2 Frequency sliders to similar values. Use the zoom tool to analyze the resolution.

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Window Noise Floor

Simulator Practice Select different window functions using the Window spin box. Compare the RMS Value of Noise in the Spectrum for the different window types.

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Window Overlap

Simulator Practice Set the Window spin box to None and the Percentage of Overlap slider to 0. Observe that the windows are not overlapped and the result is a straight line. Change the Window spin box to Hanning and notice the difference. Gradually increase the percentage of overlap and observe the plot. Notice what happens to the amplitude of the yellow line when the Percentage of Overlap is over 50%. Try different windows and compare the results.

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Window Resolution

Simulator Practice Separate the frequencies of the Signal 1 and Signal 2 sliders by 1 Hz, 2 Hz, 3 Hz, and 4 Hz. Select different window types from the Windows spin box for each frequency value. Observe the Equivalent Noise Bandwidth for each window. Which windows have better resolution?

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Windows for Frequency Analysis

Simulator Practice Set the Frequency slider to 10.4 Hz. Change the Window spin box and compare the plots. Also compare the Equivalent Noise Bandwidth and Coherent Gain values. Use the zoom tools to view the frequency spectrums near the 10.4 Hz peak. Compare the peak width when using different windows. Which window produces the best resolution (less width) in the peak?

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