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# 3. Limitations and sources of error in DSP systems This question will evaluate different designs for an analogue to digital converter for a digital filter. You are to decide whether

the cheaper ADC can be used to achieve the following specification for the signal-to-quantization-noise ratio. SQNR > 60 dB Minimum Sample frequency fs = 100 kHz%3D Maximum frequency content of input signal = 50 kHz%3D Two ADCS are available: ADC 1: 10-bit, fs = 100 kHz, cost £4.00 ADC 2: 8-bit, fs = 400 kHz, cost £3.00 Using the following formula for SQNR: where B is the number of bits, Ox is the mean-square signal level and R is the ADC range involts. Calculate SQNR for ADC 1, and explain how you made an engineering estimate for the value of °x/p. Does it meet the SQNR specification?[2] Calculate the SQNR for ADC 2. Show that it does not meet the SQNR specification. ADC 2's sample rate is higher than the Nyquist frequency. Explain whether, by adding a digital filter (no need to design it!), it would be possible to meet the SQNR specification at the cheaper price of £3.00. If feasible, suggest a pass band edge frequency for that filter that would meet the SQNR specification.[6] S Q N R=10.79+6.02 B+20 \log _{10}\left(\frac{\sigma_{x}}{R}\right)

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