Question

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? 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. S Q N R=10.79+6.02 B+20 \log _{10}\left(\frac{\sigma_{x}}{R}\right)  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13  Fig: 14