Q1. Sketch a simple diagram of the digital processing system. Assume a scismic signal x(t) =...

  

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Q1. Sketch a simple diagram of the digital processing system. Assume a scismic signal x(t) = 3cos (100nt) + 2sin(250xt) V (where t is in seconds) is applied to the DSP system above for digital processing and storage of the signal. (a) What will be the cut-off frequency that could be used to design the lowpass anti-aliasing filter. (b) Find the discrete time signal x[n] that will be quantized and binarized by the ADC if the sampling period of the ADC is T-5 ms. What is the folding frequency, which is the maximum frequency that can be uniquely represented by the sampled signal. (c) What is the dynamic range of the seismic signal x(1) and x[n]? (d) If the discrete time signal x[n] is quantized with a resolution or quantization step of A = 0.02 (where A = (dynamic range)/[L-1], where L. is quantization level), find the number of bits that was used by the ADC. What is the bit rate of the sampling? (c) Draw a table and show the first 10 samples of the signal x[n] for n = 0:9, the truncated signal values (values from the quantization without rounding) xa[n], the rounded values (values after the rounding operation), Xar[n], the binary representation of each sample xb[n], and the quantization error, eq[n] = xa[n] - x[n], where xa[n] = Q(x[n]) and Q() is the quantizer operation. (f) If the DAC reconstructs the analog signal at zero-order hold, find the frequency at which the signal is reconstructed. (g) What cut-off frequency would be used by the lowpass reconstruction filter to filter the analog signal from the DAC to produce smooth analog signal x(t). Q3. The relationship between the input and output of a certain LTI discrete time system is defined by the expression below. Sketch the system implementation diagram. With the aid of a simple flow diagram, explain how the MAC operation is performed to implement the DSP algorithm. Write a short program using C (or C++ or Python) to implement to loop operation. Assume your own set of values for the coefficients and the input. Assume the case of N-10. y[n] b(k) x[n-k] where 0 ≤k≤N-I Q1. Sketch a simple diagram of the digital processing system. Assume a scismic signal x(t) = 3cos (100nt) + 2sin(250xt) V (where t is in seconds) is applied to the DSP system above for digital processing and storage of the signal. (a) What will be the cut-off frequency that could be used to design the lowpass anti-aliasing filter. (b) Find the discrete time signal x[n] that will be quantized and binarized by the ADC if the sampling period of the ADC is T-5 ms. What is the folding frequency, which is the maximum frequency that can be uniquely represented by the sampled signal. (c) What is the dynamic range of the seismic signal x(1) and x[n]? (d) If the discrete time signal x[n] is quantized with a resolution or quantization step of A = 0.02 (where A = (dynamic range)/[L-1], where L. is quantization level), find the number of bits that was used by the ADC. What is the bit rate of the sampling? (c) Draw a table and show the first 10 samples of the signal x[n] for n = 0:9, the truncated signal values (values from the quantization without rounding) xa[n], the rounded values (values after the rounding operation), Xar[n], the binary representation of each sample xb[n], and the quantization error, eq[n] = xa[n] - x[n], where xa[n] = Q(x[n]) and Q() is the quantizer operation. (f) If the DAC reconstructs the analog signal at zero-order hold, find the frequency at which the signal is reconstructed. (g) What cut-off frequency would be used by the lowpass reconstruction filter to filter the analog signal from the DAC to produce smooth analog signal x(t). Q3. The relationship between the input and output of a certain LTI discrete time system is defined by the expression below. Sketch the system implementation diagram. With the aid of a simple flow diagram, explain how the MAC operation is performed to implement the DSP algorithm. Write a short program using C (or C++ or Python) to implement to loop operation. Assume your own set of values for the coefficients and the input. Assume the case of N-10. y[n] b(k) x[n-k] where 0 ≤k≤N-I