17
The full bass response [fig 16] begins at 2.5dB and follows the same low pass slope that we expect from [fig 7]. This response also correctly intersects the full treble response at 1kHz seen in [fig 19]. Taking a closer look at the mid frequency response we can see that indeed we do not obtain a flat frequency response [4]; in [fig 20] we observe a ballpark figure of the specified 7dB loss at the notch (ours is closer to 8dB loss).
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Figure 20. Mid Frequency Response 1kHz Notch
CONCLUSION In conclusion, this project has been successful in achieving results in the digital domain that are extremely close, if not identical to, the original analog tone control and its associated frequency response. However, itβs important to discuss some of the trade-offs that were made to obtain these results. The main trade-off pertains to the potValue values (πΌ). In order to honour the precise values for (πΌ) specified during the analog filter design process, the argument potValue is rounded to the nearest one decimal place and then (somewhat experimentally) scaled to adhere to the desired range and intermediary values. The discrepancy here is that this rounding produces a non-continuous knob. Instead, this produces a dial capable of only representing a limited number of increments. This could be misleading to a user if they wanted to enter a specific value between 0 β 1 that exceeds one decimal place, as the function will allow the input but will immediately round it. For whatever reason, via pre-warping, we didnβt seem to generate cut-off frequencies that were substantially closer to that of our ideal design. What is meant by this, is that if we observe our original analog frequency response [fig 7] we want the junction of the full bass and the full treble response and the notch of the mid frequency to sit at 1kHz.
