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11 Pages

### a5_0229436_oneil

Course: ELEC 484, Fall 2009
School: Virgin Islands
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Word Count: 1006

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484 ELEC Assignment 5 BY: Lucas O'Neil (0229436) and David Beckstrom (0430242) Part 1 When we squared and cubed the 1 kHz sine wave we got the following time domain output, shown below in figure 1. Figure 1 When we implemented the squaring of the 1 kHz sine wave we got a sum and difference of frequency of the sine wave, observable in the frequency spectrum. When the fourier transform was taken and the spectral...

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484 ELEC Assignment 5 BY: Lucas O'Neil (0229436) and David Beckstrom (0430242) Part 1 When we squared and cubed the 1 kHz sine wave we got the following time domain output, shown below in figure 1. Figure 1 When we implemented the squaring of the 1 kHz sine wave we got a sum and difference of frequency of the sine wave, observable in the frequency spectrum. When the fourier transform was taken and the spectral response observed, it is clear to see frequency at 2 kHz and 0 Hz. When we cubed the sine wave and repeat the same procedure we observe that frequency content is present at the frequency of the sine wave and at triple the frequency of the sine wave. These graphs are shown below in Figure 2. Figure 2 We repeated the squaring and cubing with a 2.5 kHz sine wave to observe the aliasing. The time domain responses are shown below in Figure 3. Figure 3 Because we are sampling at 8 kHz, we have a Nyquist frequency of 4 kHz and thus we have aliasing at freqencies above that. When the sine wave is squared, a frequency component at 5 kHz is aliased down to 3 kHz, and when the sine wave is cubed, a frequency component at 7.5 kHz is aliased down to 500 Hz. This graph is shown below in figure 4. Figure 4 We increased the oversampling to 24 kHz to eliminate the aliasing. The time domain graph is shown below in figure 5. Figure 5 With sufficient oversampling we can see that the signal appears quite normal. The sample rate was chosen to be 20kHz because it was higher than the required 15kHz required to prevent aliasing due to the 7.5kHz multiple. The frequency domain graph is shown below in figure 6. Figure 6 We can see that the graph appears as it should with the frequency components showing up where they should be, 2.5 kHz for the fundamental tone, 5 kHz for the squared tone, and 2.5 and 7.5 kHz for the cubed tone. Part 2 Overdrive The overdrive characteristic is achieved by pushing the output signal past the level of the input signal. The output signal reaches its maximum value far befor the input signal does. This is shown in figure 7 below. Figure 7 We can see that the rate of signal increase is greatly increased till the input signal reaches half of its maximum, where the output becomes pinned to its maximum over the rest of the input's range. We implemented the code to mimic an overdrive circuit in matlab by following the format shown in the text. This is shown below for reference. When we applied the overdrive to a 1 kHz sine wave we get the following response, shown in Figure 8 below. Figure 8 The overdrive increases the slope of the sine wave, causing it to clip earlier than the unmodified signal would. When we processed a wav clip of a guitar using our overdrive code we get the following response, shown below in figure 9. Figure 9 We can see that the amplitude of the signal is increased, representing the increase of output signal relative to input signal. We can also see that the signal appears undistorted. Distortion The distortion characteristic like is an exponential overdrive characteristic. The rate of increase of output relative to the input is higher, with the signal being driven into clipping earlier. The output to input characteristic is shown below in figure 10. Figure 10 We can see that the signal increases rapidly and then slows as it reaches maximum signal. The following equation was used to model the distortion characteristic in matlab. When we applied our distortion code to a 1 kHz sine wave we get the following output, shown below in figure 11. Figure 11 We can see that the rate of increase of the waveform is higher than the overdriven signal as expected, and that the signal is in clipping longer per period. When we view the frequency spectrum of the sine wav versus the distorted wav, we can see the harmonics that are created by the distortion effect. This is shown below in figure 12. Figure 12 When we applied distortion to a guitar wav file we get the following response, shown in figure 13. Figure 13 We can see that not only is the wave form amplified, but it is also a distorted version of the input. The output wave shapes do not mimic the input wave shapes. Fuzz The fuzz effect was accomplished with the asymmetric soft clipping equation as used in section 5.3 of DAFX. The asymmetrical soft clipping produces enhanced even order harmonics in the signal. The time domain representation of a sinusoid passed through the fuzz effect is shown in Figure 14 Figure 14 The guitar file was passed through the fuzz effect as well. The time domain representation is shown in Figure 15. The resultant sound file sounded rich in extra harmonics and had a bit of a buzzing quality to it. Figure 15 Part 3 The exciter is composed of a high pass filter and a harmonic generator. The block diagram is shown below ...

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