Guitar Effects Pitch Scaling
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Background Digital Representation of an Electric Guitar Signal In an electric guitar, pickup devices are used to convert the string vibration into an electric current. This transformation is achieved by the creation of a current in a coil because of the varying magnetic flux applied to that coil by the string when vibrating. The typical frequency spectrum of a guitar signal can be seen in Figure 1. The signal comprises of a fundamental frequency (880 Hz) at the note A, with harmonic overtones at 1760, 2640, 3520 Hertz etc. This note is near the highest note that can be played on a guitar with conventional strings and tuning.
Figure 1: Frequency Spectrum of guitar note A When sampling a signal, it is important that a sampling rate is used that ensures all frequencies of interest are present. The sampling theorem states that a rate of at least double the highest frequency component in the signal should be used. In Figure 1, the magnitude of the harmonic overtones becomes very small after around 4kHz. Therefore, by using an anti-aliasing filter to remove frequency components above 4 kHz, and then sampling at 8kHz, a reasonable quality digital representation of a guitar signal can be achieved. However, by using a significantly higher sampling rate, more of the higher order harmonics are kept in the signal. This leads to a very high quality, accurate sound upon playback of the digitised waveform. Because the maximum sampling rate of the DSP development board used in this project is 24kHz, this is the rate used. DSP Specifications Table 1. DSP Device Specifications
This device has enough speed and memory to implement all of the developed algorithms. If greater speed / memory is required in the future when implementing the chaining together of effects and processes, other Texas Instruments C32054xx family chips can be substituted to gain improved performance. The C5000 series are optimised for power efficiency, making it an ideal choice for implementation in a portable guitar effects device running off battery power. The price in purchases of at least 1000 units is reasonable, with the 80MHz C5402 version costing only $7 US per unit. There are many versions of the Analogue Interface Chip that can be substituted for the model used in this project. This chip contains the ADC, DAC, amplification and filters required to interface the DSP with analogue audio band signals. Higher sample rates (up to 48kHz) with stereo inputs are available and might be considered if this project were to be further developed.
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